btaf430

Author

Tingting Zhan

Published

July 1, 2026

1 btaf430

TipExamples require
library(survival)
library(mgcv)
library(spatstat.geom)

library(groupedHyperframe)
library(hyper.gam)
library(spatstat.mc)
library(Qindex.data)
unique_or_identity = \(x) {
  u <- unique(x)
  if (length(u) == 1L) return(u)
  return(x)
}
Code
Ki67 = Qindex.data::Ki67 |>
  dplyr::rename(
    patientID = PATIENT_ID,
    age = AGE_AT_DX,
    x = inner_x,
    y = inner_y,
    node = NodeSt,
    HR = HRpos,
    Her2 = Her2_path_qIF,
    histology = HistologicalGrade,
    adj_chemo = RadjCHEMO,
    adj_rad = RadjRAD,
    horm = HORM_4cat
  ) |>
  within(expr = {
    logKi67 = log1p(Marker); Marker = NULL
    race = factor(RACE); RACE = NULL
    node[node == -1L] = NA_integer_; node = as.logical(node);
    HR = as.logical(HR)
    Her2 = as.logical(Her2)
    adj_chemo[adj_chemo == 0] = NA_integer_; adj_chemo = (adj_chemo == 1L)
    adj_rad[adj_rad == 0] = NA_integer_; adj_rad = (adj_rad == 1L)
    horm[horm == 0L] = NA_integer_; horm = structure(horm, levels = c('not indicated', 'done', 'recommended, but not done'), class = 'factor'); 
    MSI = NULL
    PFS = survival::Surv(time = RECFREESURV_MO, event = RECURRENCE); RECURRENCE = NULL; RECFREESURV_MO = NULL
  })

The object Ki67q is a hyper data frame with

Listing 1.1: Data: a hyper data frame Ki67q
Ki67q
Hyperframe:
    patientID tissueID age  node Tstage   HR histology  Her2 adj_chemo adj_rad
1     PT00037 (factor)  66  TRUE      2 TRUE         3  TRUE     FALSE   FALSE
2     PT00039 (factor)  42 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
3     PT00040 (factor)  60 FALSE      1 TRUE         3 FALSE        NA   FALSE
4     PT00042 (factor)  53  TRUE      1 TRUE         3 FALSE      TRUE   FALSE
5     PT00054 (factor)  52  TRUE      1 TRUE         3 FALSE      TRUE    TRUE
6     PT00059 (factor)  51  TRUE      4 TRUE         2  TRUE     FALSE    TRUE
7     PT00062 (factor)  50  TRUE      2 TRUE         3 FALSE     FALSE   FALSE
8     PT00068 (factor)  37  TRUE      2 TRUE         2  TRUE     FALSE   FALSE
9     PT00082 (factor)  68 FALSE      2 TRUE         3  TRUE     FALSE   FALSE
10    PT00084 (factor)  55 FALSE      2 TRUE         2  TRUE      TRUE   FALSE
11    PT00085 (factor)  72 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
12    PT00086 (factor)  43  TRUE      2 TRUE         3 FALSE     FALSE   FALSE
13    PT00087 (factor)  36  TRUE      3 TRUE         3 FALSE      TRUE    TRUE
14    PT00088 (factor)  37  TRUE      2 TRUE         1 FALSE      TRUE   FALSE
15    PT00089 (factor)  69 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
16    PT00090 (factor)  63  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
17    PT00093 (factor)  58 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
18    PT00097 (factor)  60  TRUE      2 TRUE         2  TRUE     FALSE   FALSE
19    PT00100 (factor)  50 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
20    PT00186 (factor)  70  TRUE      2 TRUE         1 FALSE     FALSE    TRUE
21    PT00188 (factor)  43 FALSE      2 TRUE         2 FALSE      TRUE    TRUE
22    PT00194 (factor)  48  TRUE      2 TRUE         1 FALSE      TRUE   FALSE
23    PT00202 (factor)  68  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
24    PT00210 (factor)  73  TRUE      4 TRUE         2 FALSE     FALSE    TRUE
25    PT00211 (factor)  51 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
26    PT00212 (factor)  51 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
27    PT00213 (factor)  73 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
28    PT00214 (factor)  80 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
29    PT00215 (factor)  56 FALSE      1 TRUE         1 FALSE      TRUE   FALSE
30    PT00216 (factor)  77  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
31    PT00218 (factor)  36 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
32    PT00220 (factor)  48  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
33    PT00221 (factor)  73 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
34    PT00222 (factor)  56  TRUE      1 TRUE         1 FALSE      TRUE   FALSE
35    PT00226 (factor)  60 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
36    PT00228 (factor)  76 FALSE      4 TRUE         2 FALSE     FALSE   FALSE
37    PT00230 (factor)  72 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
38    PT00232 (factor)  63 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
39    PT00234 (factor)  48  TRUE      1 TRUE         3 FALSE      TRUE    TRUE
40    PT00240 (factor)  59 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
41    PT00241 (factor)  58 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
42    PT00242 (factor)  71 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
43    PT00243 (factor)  68 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
44    PT00244 (factor)  36  TRUE      2 TRUE         3 FALSE     FALSE   FALSE
45    PT00251 (factor)  42 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
46    PT00258 (factor)  80 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
47    PT00260 (factor)  60 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
48    PT00262 (factor)  67  TRUE      2 TRUE         1 FALSE      TRUE    TRUE
49    PT00263 (factor)  53  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
50    PT00270 (factor)  78 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
51    PT00275 (factor)  46  TRUE      1 TRUE         1 FALSE      TRUE    TRUE
52    PT00281 (factor)  85  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
53    PT00283 (factor)  48  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
54    PT00293 (factor)  55 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
55    PT00298 (factor)  45  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
56    PT00302 (factor)  47  TRUE      2 TRUE         1 FALSE      TRUE   FALSE
57    PT00303 (factor)  80 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
58    PT00304 (factor)  49 FALSE      1 TRUE         1 FALSE      TRUE   FALSE
59    PT00308 (factor)  55  TRUE      1 TRUE         2 FALSE      TRUE    TRUE
60    PT00315 (factor)  48  TRUE      2 TRUE         1    NA      TRUE   FALSE
61    PT00317 (factor)  46 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
62    PT00319 (factor)  45  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
63    PT00322 (factor)  63 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
64    PT00323 (factor)  82 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
65    PT00324 (factor)  64  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
66    PT00332 (factor)  51 FALSE      1 TRUE         2  TRUE     FALSE    TRUE
67    PT00333 (factor)  63 FALSE      2 TRUE         1 FALSE      TRUE   FALSE
68    PT00335 (factor)  44 FALSE      2 TRUE         3 FALSE      TRUE   FALSE
69    PT00338 (factor)  39 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
70    PT00344 (factor)  35  TRUE      3 TRUE         2 FALSE      TRUE    TRUE
71    PT00348 (factor)  63 FALSE      1 TRUE         2    NA     FALSE    TRUE
72    PT00349 (factor)  42 FALSE      2 TRUE         2 FALSE      TRUE    TRUE
73    PT00351 (factor)  67 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
74    PT00352 (factor)  66 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
75    PT00355 (factor)  78  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
76    PT00357 (factor)  50  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
77    PT00368 (factor)  64 FALSE      1 TRUE         3  TRUE     FALSE   FALSE
78    PT00380 (factor)  70 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
79    PT00384 (factor)  65  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
80    PT00385 (factor)  51  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
81    PT00386 (factor)  69 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
82    PT00388 (factor)  73 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
83    PT00393 (factor)  58 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
84    PT00395 (factor)  62 FALSE      3 TRUE         3 FALSE      TRUE   FALSE
85    PT00396 (factor)  67  TRUE      2 TRUE         1 FALSE     FALSE    TRUE
86    PT00397 (factor)  32 FALSE      3 TRUE         2 FALSE     FALSE   FALSE
87    PT00401 (factor)  61  TRUE      2 TRUE         2 FALSE        NA      NA
88    PT00413 (factor)  71 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
89    PT00422 (factor)  68 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
90    PT00423 (factor)  70 FALSE      4 TRUE         2    NA      TRUE    TRUE
91    PT00424 (factor)  37 FALSE      1 TRUE         3 FALSE      TRUE   FALSE
92    PT00425 (factor)  79 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
93    PT00426 (factor)  65 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
94    PT00427 (factor)  65 FALSE      1 TRUE         2  TRUE     FALSE   FALSE
95    PT00428 (factor)  45 FALSE      1 TRUE         2 FALSE      TRUE    TRUE
96    PT00433 (factor)  65  TRUE      2 TRUE         1 FALSE     FALSE   FALSE
97    PT00434 (factor)  66  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
98    PT00438 (factor)  55  TRUE      1 TRUE         2 FALSE      TRUE    TRUE
99    PT00439 (factor)  70  TRUE      2 TRUE         1 FALSE     FALSE   FALSE
100   PT00441 (factor)  67 FALSE      1 TRUE         3  TRUE      TRUE   FALSE
101   PT00442 (factor)  50 FALSE      2 TRUE         1 FALSE     FALSE    TRUE
102   PT00443 (factor)  73 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
103   PT00448 (factor)  69  TRUE      1 TRUE         3 FALSE     FALSE   FALSE
104   PT00449 (factor)  70 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
105   PT00450 (factor)  62 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
106   PT00451 (factor)  62 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
107   PT00455 (factor)  58  TRUE      1 TRUE         3 FALSE     FALSE    TRUE
108   PT00456 (factor)  71 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
109   PT00462 (factor)  71 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
110   PT00468 (factor)  61 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
111   PT00469 (factor)  69 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
112   PT00472 (factor)  55    NA      1 TRUE         1 FALSE     FALSE   FALSE
113   PT00478 (factor)  66 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
114   PT00486 (factor)  59  TRUE      1 TRUE         2 FALSE     FALSE    TRUE
115   PT00488 (factor)  40  TRUE      1 TRUE         1    NA      TRUE    TRUE
116   PT00493 (factor)  37 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
117   PT00497 (factor)  59 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
118   PT00500 (factor)  43  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
119   PT00502 (factor)  78 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
120   PT00504 (factor)  78  TRUE      1 TRUE         3 FALSE      TRUE    TRUE
121   PT00505 (factor)  70 FALSE      2 TRUE         3  TRUE     FALSE   FALSE
122   PT00506 (factor)  67 FALSE      2 TRUE         3  TRUE     FALSE   FALSE
123   PT00507 (factor)  70  TRUE      2 TRUE         2 FALSE     FALSE    TRUE
124   PT00511 (factor)  71  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
125   PT00512 (factor)  56 FALSE      2 TRUE         2 FALSE      TRUE    TRUE
126   PT00514 (factor)  72 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
127   PT00515 (factor)  81 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
128   PT00516 (factor)  62 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
129   PT00517 (factor)  85 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
130   PT00518 (factor)  62 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
131   PT00519 (factor)  42 FALSE      1 TRUE         1 FALSE      TRUE    TRUE
132   PT00522 (factor)  60 FALSE      1 TRUE         1 FALSE      TRUE   FALSE
133   PT00525 (factor)  74 FALSE      2 TRUE         1 FALSE     FALSE    TRUE
134   PT00526 (factor)  55 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
135   PT00527 (factor)  56  TRUE      2 TRUE         1 FALSE     FALSE   FALSE
136   PT00529 (factor)  56  TRUE      1 TRUE         1 FALSE      TRUE   FALSE
137   PT00530 (factor)  66 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
138   PT00541 (factor)  45  TRUE      1 TRUE         1    NA      TRUE   FALSE
139   PT00546 (factor)  34  TRUE      1 TRUE         2 FALSE      TRUE    TRUE
140   PT00547 (factor)  59 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
141   PT00550 (factor)  56 FALSE      2 TRUE         3  TRUE     FALSE    TRUE
142   PT00551 (factor)  44  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
143   PT00554 (factor)  53 FALSE      1 TRUE         2 FALSE      TRUE   FALSE
144   PT00555 (factor)  62 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
145   PT00557 (factor)  45 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
146   PT00561 (factor)  35 FALSE      1 TRUE         1    NA     FALSE   FALSE
147   PT00562 (factor)  63  TRUE      1 TRUE         1 FALSE      TRUE   FALSE
148   PT00566 (factor)  68 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
149   PT00567 (factor)  41 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
150   PT00576 (factor)  40  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
151   PT00577 (factor)  79 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
152   PT00585 (factor)  50  TRUE      1 TRUE         3  TRUE      TRUE    TRUE
153   PT00586 (factor)  72 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
154   PT00588 (factor)  70 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
155   PT00589 (factor)  69  TRUE      2 TRUE         1 FALSE     FALSE    TRUE
156   PT00594 (factor)  69 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
157   PT00595 (factor)  64  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
158   PT00596 (factor)  75 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
159   PT00597 (factor)  46 FALSE      2 TRUE         1 FALSE      TRUE   FALSE
160   PT00600 (factor)  60 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
161   PT00601 (factor)  58  TRUE      3 TRUE         2 FALSE      TRUE   FALSE
162   PT00603 (factor)  47  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
163   PT00606 (factor)  47 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
164   PT00608 (factor)  47 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
165   PT00610 (factor)  56 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
166   PT00613 (factor)  45 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
167   PT00614 (factor)  47 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
168   PT00616 (factor)  48  TRUE      2 TRUE         1 FALSE      TRUE   FALSE
169   PT00621 (factor)  79 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
170   PT00626 (factor)  76 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
171   PT00627 (factor)  54  TRUE      1 TRUE         1 FALSE      TRUE    TRUE
172   PT00629 (factor)  52  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
173   PT00633 (factor)  42  TRUE      1 TRUE         3 FALSE      TRUE    TRUE
174   PT00637 (factor)  55 FALSE      1 TRUE         2  TRUE     FALSE   FALSE
175   PT00638 (factor)  49 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
176   PT00639 (factor)  51  TRUE      3 TRUE         1 FALSE      TRUE    TRUE
177   PT00642 (factor)  75 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
178   PT00644 (factor)  49 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
179   PT00646 (factor)  53  TRUE      3 TRUE         3 FALSE      TRUE    TRUE
180   PT00648 (factor)  46 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
181   PT00653 (factor)  67 FALSE      4 TRUE         3 FALSE     FALSE   FALSE
182   PT00654 (factor)  55  TRUE      1 TRUE         1 FALSE      TRUE    TRUE
183   PT00657 (factor)  62  TRUE      2 TRUE         3 FALSE      TRUE   FALSE
184   PT00658 (factor)  64 FALSE      1 TRUE         1  TRUE     FALSE   FALSE
185   PT00659 (factor)  75 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
186   PT00661 (factor)  54 FALSE      1 TRUE         3  TRUE      TRUE    TRUE
187   PT00665 (factor)  58  TRUE      4 TRUE         2 FALSE      TRUE    TRUE
188   PT00666 (factor)  78 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
189   PT00669 (factor)  42  TRUE      2 TRUE         3 FALSE     FALSE    TRUE
190   PT00673 (factor)  56 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
191   PT00675 (factor)  51 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
192   PT00683 (factor)  65  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
193   PT00684 (factor)  52 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
194   PT00690 (factor)  68 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
195   PT00694 (factor)  57 FALSE      1 TRUE         1  TRUE     FALSE    TRUE
196   PT00700 (factor)  39 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
197   PT00703 (factor)  50 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
198   PT00704 (factor)  50  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
199   PT00705 (factor)  65 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
200   PT00706 (factor)  45 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
201   PT00707 (factor)  62  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
202   PT00708 (factor)  82 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
203   PT00710 (factor)  64 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
204   PT00711 (factor)  60 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
205   PT00712 (factor)  65 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
206   PT00714 (factor)  49 FALSE      1 TRUE         3  TRUE     FALSE   FALSE
207   PT00716 (factor)  50  TRUE      3 TRUE         1 FALSE      TRUE   FALSE
208   PT00718 (factor)  57 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
209   PT00719 (factor)  77 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
210   PT00721 (factor)  41 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
211   PT00724 (factor)  51 FALSE      2 TRUE         2 FALSE      TRUE    TRUE
212   PT00730 (factor)  52 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
213   PT00732 (factor)  61 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
214   PT00733 (factor)  83 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
215   PT00735 (factor)  60 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
216   PT00736 (factor)  71  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
217   PT00747 (factor)  67  TRUE      2 TRUE         1 FALSE      TRUE   FALSE
218   PT00753 (factor)  57 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
219   PT00756 (factor)  45  TRUE      2 TRUE         1  TRUE      TRUE   FALSE
220   PT00760 (factor)  72  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
221   PT00762 (factor)  47  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
222   PT00764 (factor)  58  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
223   PT00768 (factor)  80 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
224   PT00769 (factor)  55  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
225   PT00773 (factor)  53  TRUE      4 TRUE         2  TRUE      TRUE    TRUE
226   PT00776 (factor)  90 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
227   PT00777 (factor)  41 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
228   PT00778 (factor)  89 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
229   PT00783 (factor)  56 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
230   PT00785 (factor)  48  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
231   PT00788 (factor)  46 FALSE      1 TRUE         3 FALSE      TRUE    TRUE
232   PT00789 (factor)  48 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
233   PT00791 (factor)  57 FALSE      1 TRUE         2  TRUE     FALSE    TRUE
234   PT00793 (factor)  72 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
235   PT00795 (factor)  53  TRUE      1 TRUE         1 FALSE      TRUE   FALSE
236   PT00796 (factor)  47 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
237   PT00801 (factor)  69 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
238   PT00804 (factor)  65 FALSE      2 TRUE         3  TRUE     FALSE   FALSE
239   PT00806 (factor)  72 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
240   PT00807 (factor)  49  TRUE      1 TRUE         3 FALSE      TRUE   FALSE
241   PT00810 (factor)  46 FALSE      1 TRUE         1 FALSE      TRUE   FALSE
242   PT00811 (factor)  56  TRUE      1 TRUE         2 FALSE     FALSE    TRUE
243   PT00827 (factor)  75  TRUE      1 TRUE         1  TRUE     FALSE    TRUE
244   PT00838 (factor)  56  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
245   PT00840 (factor)  67  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
246   PT00841 (factor)  29 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
247   PT00843 (factor)  81 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
248   PT00846 (factor)  55 FALSE      1 TRUE         1  TRUE     FALSE    TRUE
249   PT00847 (factor)  78 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
250   PT00852 (factor)  65  TRUE      1 TRUE         3 FALSE     FALSE   FALSE
251   PT00854 (factor)  41  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
252   PT00855 (factor)  54  TRUE      2 TRUE         1 FALSE      TRUE   FALSE
253   PT00859 (factor)  60 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
254   PT00860 (factor)  46 FALSE      1 TRUE         2 FALSE      TRUE   FALSE
255   PT00866 (factor)  67  TRUE      3 TRUE         2 FALSE      TRUE   FALSE
256   PT00867 (factor)  58 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
257   PT00872 (factor)  58 FALSE      3 TRUE         2 FALSE      TRUE   FALSE
258   PT00873 (factor)  53 FALSE      2 TRUE         3 FALSE     FALSE    TRUE
259   PT00878 (factor)  69 FALSE      3 TRUE         2 FALSE     FALSE   FALSE
260   PT00883 (factor)  73  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
261   PT00892 (factor)  65  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
262   PT00896 (factor)  75  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
263   PT00899 (factor)  82  TRUE      2 TRUE         2    NA     FALSE    TRUE
264   PT00901 (factor)  70 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
265   PT00903 (factor)  70  TRUE      4 TRUE         1 FALSE     FALSE   FALSE
266   PT00905 (factor)  35 FALSE      3 TRUE         2  TRUE     FALSE   FALSE
267   PT00906 (factor)  90 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
268   PT00907 (factor)  78  TRUE      2 TRUE         1 FALSE      TRUE   FALSE
269   PT00908 (factor)  32  TRUE      2 TRUE         3 FALSE     FALSE   FALSE
270   PT00910 (factor)  61  TRUE      2 TRUE         1  TRUE      TRUE   FALSE
271   PT00912 (factor)  46  TRUE      2 TRUE         2  TRUE      TRUE   FALSE
272   PT00921 (factor)  72 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
273   PT00922 (factor)  64  TRUE      4 TRUE         2  TRUE      TRUE   FALSE
274   PT00932 (factor)  51 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
275   PT00933 (factor)  69  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
276   PT00934 (factor)  68 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
277   PT00935 (factor)  68 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
278   PT00937 (factor)  50  TRUE      1 TRUE         1 FALSE      TRUE    TRUE
279   PT00939 (factor)  54 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
280   PT00944 (factor)  56 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
281   PT00949 (factor)  48  TRUE      2 TRUE         3  TRUE      TRUE    TRUE
282   PT00950 (factor)  78 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
283   PT00952 (factor)  36  TRUE      2 TRUE         2  TRUE      TRUE    TRUE
284   PT00953 (factor)  37  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
285   PT00956 (factor)  42 FALSE      1 TRUE         2 FALSE      TRUE   FALSE
286   PT00963 (factor)  43 FALSE      1 TRUE         2 FALSE      TRUE    TRUE
287   PT00964 (factor)  77 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
288   PT00965 (factor)  73 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
289   PT00970 (factor)  54 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
290   PT00974 (factor)  69 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
291   PT00975 (factor)  67 FALSE      2 TRUE         2  TRUE     FALSE   FALSE
292   PT00976 (factor)  73  TRUE      2 TRUE         3 FALSE     FALSE    TRUE
293   PT00983 (factor)  67  TRUE      2 TRUE         3 FALSE      TRUE   FALSE
294   PT00990 (factor)  69 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
295   PT00998 (factor)  82 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
296   PT01000 (factor)  43 FALSE      1 TRUE         1  TRUE      TRUE   FALSE
297   PT01002 (factor)  68 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
298   PT01006 (factor)  73 FALSE      1 TRUE        NA  TRUE     FALSE   FALSE
299   PT01015 (factor)  40 FALSE      2 TRUE         3  TRUE      TRUE   FALSE
300   PT01018 (factor)  62 FALSE      3 TRUE         2 FALSE     FALSE    TRUE
301   PT01023 (factor)  72  TRUE      2 TRUE         3  TRUE      TRUE    TRUE
302   PT01031 (factor)  63 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
303   PT01032 (factor)  67 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
304   PT01037 (factor)  48  TRUE      1 TRUE         1 FALSE     FALSE    TRUE
305   PT01038 (factor)  56 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
306   PT01042 (factor)  36  TRUE      2 TRUE         2  TRUE     FALSE    TRUE
307   PT01045 (factor)  64 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
308   PT01046 (factor)  70 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
309   PT01051 (factor)  72  TRUE      1 TRUE         2 FALSE      TRUE    TRUE
310   PT01052 (factor)  63 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
311   PT01062 (factor)  42  TRUE      1 TRUE         2    NA      TRUE   FALSE
312   PT01064 (factor)  32 FALSE      1 TRUE         3 FALSE      TRUE   FALSE
313   PT01067 (factor)  70 FALSE      3 TRUE         3 FALSE      TRUE   FALSE
314   PT01072 (factor)  71  TRUE      2 TRUE         3 FALSE     FALSE   FALSE
315   PT01073 (factor)  86 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
316   PT01074 (factor)  57  TRUE      1 TRUE         3  TRUE     FALSE    TRUE
317   PT01077 (factor)  66 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
318   PT01079 (factor)  51 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
319   PT01081 (factor)  48  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
320   PT01082 (factor)  49  TRUE      4 TRUE         3 FALSE      TRUE   FALSE
321   PT01090 (factor)  85 FALSE      3 TRUE         3 FALSE     FALSE    TRUE
322   PT01095 (factor)  52  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
323   PT01099 (factor)  72 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
324   PT01102 (factor)  48 FALSE      2 TRUE         2  TRUE      TRUE   FALSE
325   PT01104 (factor)  68 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
326   PT01108 (factor)  38 FALSE      1 TRUE         2 FALSE      TRUE    TRUE
327   PT01112 (factor)  41  TRUE      1 TRUE         3 FALSE      TRUE   FALSE
328   PT01122 (factor)  70 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
329   PT01123 (factor)  68 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
330   PT01127 (factor)  58 FALSE      4 TRUE         2 FALSE      TRUE   FALSE
331   PT01128 (factor)  84 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
332   PT01129 (factor)  35  TRUE      1 TRUE         3 FALSE     FALSE    TRUE
333   PT01131 (factor)  54 FALSE      4 TRUE         3 FALSE      TRUE   FALSE
334   PT01134 (factor)  62  TRUE      4 TRUE         3    NA     FALSE   FALSE
335   PT01136 (factor)  64  TRUE      1 TRUE         2 FALSE     FALSE    TRUE
336   PT01138 (factor)  55  TRUE      2 TRUE         2 FALSE     FALSE    TRUE
337   PT01140 (factor)  76  TRUE      3 TRUE         1 FALSE      TRUE   FALSE
338   PT01141 (factor)  55  TRUE      2 TRUE         2    NA     FALSE    TRUE
339   PT01146 (factor)  69 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
340   PT01148 (factor)  45 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
341   PT01150 (factor)  79  TRUE      4 TRUE         1 FALSE     FALSE    TRUE
342   PT01152 (factor)  58 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
343   PT01153 (factor)  59 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
344   PT01157 (factor)  45 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
345   PT01162 (factor)  85  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
346   PT01164 (factor)  35  TRUE      2 TRUE         3 FALSE     FALSE   FALSE
347   PT01165 (factor)  47 FALSE      1 TRUE        NA FALSE     FALSE   FALSE
348   PT01168 (factor)  73 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
349   PT01169 (factor)  51  TRUE      3 TRUE         3  TRUE      TRUE   FALSE
350   PT01175 (factor)  49  TRUE      1 TRUE         2 FALSE     FALSE    TRUE
351   PT01176 (factor)  38 FALSE      3 TRUE         2 FALSE      TRUE   FALSE
352   PT01182 (factor)  62 FALSE      2 TRUE         1 FALSE     FALSE    TRUE
353   PT01183 (factor)  76 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
354   PT01187 (factor)  72 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
355   PT01188 (factor)  61 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
356   PT01189 (factor)  71 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
357   PT01190 (factor)  74 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
358   PT01195 (factor)  83 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
359   PT01198 (factor)  60 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
360   PT01200 (factor)  58  TRUE      4 TRUE         3 FALSE      TRUE    TRUE
361   PT01201 (factor)  42  TRUE      3 TRUE         3 FALSE     FALSE   FALSE
362   PT01203 (factor)  70 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
363   PT01204 (factor)  75 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
364   PT01209 (factor)  46 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
365   PT01213 (factor)  46 FALSE      1 TRUE         2  TRUE      TRUE    TRUE
366   PT01214 (factor)  74 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
367   PT01216 (factor)  55 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
368   PT01218 (factor)  62  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
369   PT01220 (factor)  49 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
370   PT01221 (factor)  74  TRUE      2 TRUE         2 FALSE     FALSE    TRUE
371   PT01225 (factor)  67 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
372   PT01229 (factor)  55 FALSE      2 TRUE         1 FALSE     FALSE    TRUE
373   PT01230 (factor)  39 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
374   PT01233 (factor)  67  TRUE      4 TRUE         3    NA     FALSE   FALSE
375   PT01236 (factor)  41  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
376   PT01237 (factor)  78 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
377   PT01239 (factor)  61  TRUE      2 TRUE         1 FALSE      TRUE   FALSE
378   PT01241 (factor)  84 FALSE      2 TRUE         1    NA     FALSE   FALSE
379   PT01242 (factor)  46  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
380   PT01243 (factor)  65  TRUE      4 TRUE         1    NA     FALSE   FALSE
381   PT01246 (factor)  69 FALSE      1 TRUE        NA FALSE     FALSE    TRUE
382   PT01250 (factor)  59 FALSE      3 TRUE         3  TRUE     FALSE   FALSE
383   PT01252 (factor)  65  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
384   PT01253 (factor)  39  TRUE      2 TRUE         3    NA      TRUE    TRUE
385   PT01254 (factor)  53 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
386   PT01257 (factor)  73 FALSE      1 TRUE         1    NA     FALSE   FALSE
387   PT01258 (factor)  59 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
388   PT01262 (factor)  53  TRUE      3 TRUE         2 FALSE     FALSE   FALSE
389   PT01263 (factor)  61 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
390   PT01264 (factor)  77  TRUE      3 TRUE         3 FALSE     FALSE   FALSE
391   PT01265 (factor)  84 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
392   PT01270 (factor)  59 FALSE      2 TRUE         1 FALSE        NA      NA
393   PT01272 (factor)  67 FALSE      1 TRUE         1 FALSE        NA      NA
394   PT01273 (factor)  82 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
395   PT01277 (factor)  72 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
396   PT01278 (factor)  74 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
397   PT01279 (factor)  45 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
398   PT01280 (factor)  73 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
399   PT01281 (factor)  77 FALSE      1 TRUE         1 FALSE        NA      NA
400   PT01282 (factor)  33 FALSE      1 TRUE         3  TRUE      TRUE    TRUE
401   PT01283 (factor)  72 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
402   PT01284 (factor)  45  TRUE      1 TRUE         2 FALSE      TRUE    TRUE
403   PT01286 (factor)  61  TRUE      1 TRUE         3  TRUE      TRUE    TRUE
404   PT01287 (factor)  67 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
405   PT01288 (factor)  71 FALSE      1 TRUE         1 FALSE        NA      NA
406   PT01289 (factor)  44  TRUE      3 TRUE         2    NA     FALSE   FALSE
407   PT01295 (factor)  75  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
408   PT01296 (factor)  80 FALSE      1 TRUE         1 FALSE        NA      NA
409   PT01297 (factor)  60 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
410   PT01298 (factor)  80 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
411   PT01301 (factor)  66 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
412   PT01302 (factor)  58  TRUE      1 TRUE         1 FALSE      TRUE   FALSE
413   PT01309 (factor)  45 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
414   PT01311 (factor)  69 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
415   PT01315 (factor)  50 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
416   PT01316 (factor)  60 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
417   PT01317 (factor)  65 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
418   PT01321 (factor)  61 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
419   PT01322 (factor)  34  TRUE      2 TRUE         2  TRUE     FALSE    TRUE
420   PT01327 (factor)  64 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
421   PT01328 (factor)  65  TRUE      2 TRUE         2 FALSE     FALSE    TRUE
422   PT01331 (factor)  87  TRUE      2 TRUE         1 FALSE     FALSE   FALSE
423   PT01334 (factor)  53 FALSE      1 TRUE         1    NA     FALSE   FALSE
424   PT01336 (factor)  55 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
425   PT01337 (factor)  65 FALSE      2 TRUE         2 FALSE        NA      NA
426   PT01338 (factor)  50 FALSE      1 TRUE         3  TRUE        NA      NA
427   PT01339 (factor)  67 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
428   PT01344 (factor)  50 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
429   PT01345 (factor)  60 FALSE      1 TRUE         3 FALSE        NA      NA
430   PT01346 (factor)  68  TRUE      1 TRUE         1    NA        NA      NA
431   PT01353 (factor)  65 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
432   PT01355 (factor)  80 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
433   PT01357 (factor)  42  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
434   PT01358 (factor)  44  TRUE      2 TRUE         3 FALSE      TRUE    TRUE
435   PT01363 (factor)  37  TRUE      2 TRUE         3 FALSE      TRUE    TRUE
436   PT01364 (factor)  67 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
437   PT01367 (factor)  61  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
438   PT01369 (factor)  67  TRUE      1 TRUE         3  TRUE     FALSE   FALSE
439   PT01371 (factor)  65 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
440   PT01373 (factor)  70 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
441   PT01384 (factor)  64 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
442   PT01387 (factor)  64 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
443   PT01391 (factor)  72 FALSE      4 TRUE         2 FALSE     FALSE    TRUE
444   PT01398 (factor)  63  TRUE      2 TRUE         3 FALSE        NA      NA
445   PT01400 (factor)  70 FALSE      1 TRUE         2    NA     FALSE    TRUE
446   PT01409 (factor)  75  TRUE      2 TRUE         2 FALSE     FALSE    TRUE
447   PT01413 (factor)  62 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
448   PT01414 (factor)  52 FALSE      1 TRUE         3 FALSE      TRUE    TRUE
449   PT01420 (factor)  56  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
450   PT01421 (factor)  79 FALSE      1 TRUE         1    NA     FALSE    TRUE
451   PT01423 (factor)  52 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
452   PT01425 (factor)  80  TRUE      4 TRUE         3 FALSE      TRUE    TRUE
453   PT01426 (factor)  80 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
454   PT01430 (factor)  71 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
455   PT01431 (factor)  74 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
456   PT01433 (factor)  56 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
457   PT01434 (factor)  71 FALSE      1 TRUE         2    NA     FALSE    TRUE
458   PT01444 (factor)  54 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
459   PT01445 (factor)  60  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
460   PT01447 (factor)  62 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
461   PT01449 (factor)  50  TRUE      1 TRUE         3 FALSE     FALSE   FALSE
462   PT01455 (factor)  59 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
463   PT01456 (factor)  55 FALSE      1 TRUE         1  TRUE     FALSE    TRUE
464   PT01460 (factor)  61 FALSE      1 TRUE         1  TRUE     FALSE   FALSE
465   PT01462 (factor)  54  TRUE      4 TRUE         1 FALSE      TRUE    TRUE
466   PT01463 (factor)  88 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
467   PT01465 (factor)  63 FALSE      2 TRUE         3 FALSE     FALSE    TRUE
468   PT01466 (factor)  44 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
469   PT01468 (factor)  44 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
470   PT01471 (factor)  43  TRUE      2 TRUE         3 FALSE      TRUE    TRUE
471   PT01473 (factor)  72  TRUE      2 TRUE         1    NA        NA      NA
472   PT01474 (factor)  71 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
473   PT01475 (factor)  67  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
474   PT01476 (factor)  80 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
475   PT01477 (factor)  59  TRUE      1 TRUE         3    NA     FALSE   FALSE
476   PT01478 (factor)  64 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
477   PT01481 (factor)  60 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
478   PT01483 (factor)  46 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
479   PT01489 (factor)  51  TRUE      1 TRUE         2 FALSE      TRUE    TRUE
480   PT01490 (factor)  83  TRUE      2 TRUE         3 FALSE     FALSE   FALSE
481   PT01491 (factor)  42 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
482   PT01492 (factor)  49 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
483   PT01494 (factor)  51 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
484   PT01496 (factor)  66  TRUE      1 TRUE         1    NA     FALSE   FALSE
485   PT01498 (factor)  54  TRUE      3 TRUE         2 FALSE      TRUE    TRUE
486   PT01499 (factor)  83 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
487   PT01503 (factor)  61  TRUE      2 TRUE         2 FALSE     FALSE    TRUE
488   PT01505 (factor)  43  TRUE      4 TRUE         1 FALSE      TRUE   FALSE
489   PT01506 (factor)  49 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
490   PT01507 (factor)  38  TRUE      2 TRUE         3 FALSE      TRUE   FALSE
491   PT01513 (factor)  50  TRUE      1 TRUE         3 FALSE      TRUE    TRUE
492   PT01514 (factor)  50 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
493   PT01516 (factor)  75 FALSE      2 TRUE         1  TRUE     FALSE   FALSE
494   PT01517 (factor)  73 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
495   PT01519 (factor)  49 FALSE      1 TRUE         2 FALSE      TRUE   FALSE
496   PT01520 (factor)  80 FALSE      1 TRUE         1  TRUE     FALSE    TRUE
497   PT01521 (factor)  77  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
498   PT01523 (factor)  82  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
499   PT01524 (factor)  59 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
500   PT01525 (factor)  63 FALSE      1 TRUE         2  TRUE        NA      NA
501   PT01529 (factor)  45 FALSE      1 TRUE         3  TRUE     FALSE   FALSE
502   PT01530 (factor)  65 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
503   PT01531 (factor)  85 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
504   PT01532 (factor)  74  TRUE      4 TRUE         3  TRUE     FALSE   FALSE
505   PT01545 (factor)  66 FALSE      2 TRUE         2 FALSE      TRUE   FALSE
506   PT01547 (factor)  74 FALSE      1 TRUE         1    NA     FALSE   FALSE
507   PT01554 (factor)  50 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
508   PT01555 (factor)  43  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
509   PT01559 (factor)  55 FALSE      2 TRUE         2 FALSE      TRUE    TRUE
510   PT01561 (factor)  45 FALSE      2 TRUE         3 FALSE      TRUE    TRUE
511   PT01563 (factor)  68  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
512   PT01569 (factor)  46 FALSE      2 TRUE         2  TRUE     FALSE   FALSE
513   PT01570 (factor)  61  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
514   PT01571 (factor)  80  TRUE      1 TRUE         3 FALSE     FALSE    TRUE
515   PT01572 (factor)  67 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
516   PT01573 (factor)  42  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
517   PT01578 (factor)  59 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
518   PT01582 (factor)  71 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
519   PT01583 (factor)  76 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
520   PT01587 (factor)  71 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
521   PT01590 (factor)  60 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
522   PT01592 (factor)  39  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
523   PT01593 (factor)  80 FALSE      2 TRUE         3 FALSE     FALSE   FALSE
524   PT01595 (factor)  38 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
525   PT01596 (factor)  50 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
526   PT01597 (factor)  48  TRUE      1 TRUE         2 FALSE      TRUE   FALSE
527   PT01598 (factor)  63 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
528   PT01600 (factor)  76 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
529   PT01701 (factor)  67  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
530   PT01702 (factor)  71 FALSE      1 TRUE         1  TRUE     FALSE   FALSE
531   PT01717 (factor)  67  TRUE      2 TRUE         2    NA     FALSE    TRUE
532   PT01719 (factor)  32  TRUE      4 TRUE         2 FALSE      TRUE   FALSE
533   PT01724 (factor)  56  TRUE      2 TRUE         3 FALSE     FALSE   FALSE
534   PT01726 (factor)  72 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
535   PT01727 (factor)  44 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
536   PT01732 (factor)  60 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
537   PT01733 (factor)  60  TRUE      1 TRUE         3 FALSE      TRUE    TRUE
538   PT01734 (factor)  54 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
539   PT01736 (factor)  44 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
540   PT01738 (factor)  57 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
541   PT01740 (factor)  43  TRUE      1 TRUE         1 FALSE     FALSE    TRUE
542   PT01744 (factor)  53 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
543   PT01749 (factor)  74 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
544   PT02323 (factor)  61 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
545   PT02329 (factor)  52  TRUE      3 TRUE         2 FALSE      TRUE   FALSE
546   PT02339 (factor)  63  TRUE      1 TRUE         2 FALSE     FALSE   FALSE
547   PT02340 (factor)  63  TRUE      1 TRUE         3  TRUE     FALSE   FALSE
548   PT02355 (factor)  77 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
549   PT02365 (factor)  73 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
550   PT02380 (factor)  87 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
551   PT02382 (factor)  48 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
552   PT02384 (factor)  73 FALSE      1 TRUE         2    NA     FALSE    TRUE
553   PT02385 (factor)  86 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
554   PT02387 (factor)  35 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
555   PT02400 (factor)  60  TRUE      2 TRUE         2 FALSE     FALSE    TRUE
556   PT02401 (factor)  67 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
557   PT02402 (factor)  73 FALSE      2 TRUE         3  TRUE     FALSE    TRUE
558   PT02403 (factor)  61  TRUE      4 TRUE         3 FALSE     FALSE   FALSE
559   PT02404 (factor)  63 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
560   PT02405 (factor)  61 FALSE      1 TRUE         2  TRUE     FALSE   FALSE
561   PT02408 (factor)  57  TRUE      1 TRUE         3 FALSE      TRUE    TRUE
562   PT02416 (factor)  55  TRUE      3 TRUE         3 FALSE     FALSE   FALSE
563   PT02421 (factor)  68  TRUE      1 TRUE         1 FALSE      TRUE   FALSE
564   PT02422 (factor)  42 FALSE      1 TRUE         2  TRUE     FALSE   FALSE
565   PT02431 (factor)  61 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
566   PT02432 (factor)  58 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
567   PT02435 (factor)  73  TRUE      1 TRUE         1 FALSE     FALSE   FALSE
568   PT02438 (factor)  52  TRUE      2 TRUE         1 FALSE     FALSE   FALSE
569   PT02444 (factor)  52 FALSE      1 TRUE         3 FALSE      TRUE   FALSE
570   PT02445 (factor)  73 FALSE      2 TRUE         3 FALSE     FALSE    TRUE
571   PT02446 (factor)  44 FALSE      1 TRUE         3  TRUE      TRUE    TRUE
572   PT02447 (factor)  50 FALSE      2 TRUE         2 FALSE      TRUE   FALSE
573   PT02450 (factor)  57 FALSE      1 TRUE         2  TRUE     FALSE    TRUE
574   PT02453 (factor)  47 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
575   PT02457 (factor)  51  TRUE      1 TRUE         2 FALSE      TRUE    TRUE
576   PT02461 (factor)  62 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
577   PT02464 (factor)  71  TRUE      1 TRUE         3 FALSE     FALSE   FALSE
578   PT02467 (factor)  49  TRUE      2 TRUE         2 FALSE      TRUE    TRUE
579   PT02475 (factor)  45  TRUE      2 TRUE         2 FALSE     FALSE   FALSE
580   PT02478 (factor)  34 FALSE      1 TRUE         2 FALSE      TRUE    TRUE
581   PT02484 (factor)  71 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
582   PT02489 (factor)  52 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
583   PT02490 (factor)  75 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
584   PT02492 (factor)  45 FALSE      4 TRUE         2 FALSE      TRUE   FALSE
585   PT02494 (factor)  44 FALSE      2 TRUE         1 FALSE      TRUE   FALSE
586   PT02673 (factor)  64 FALSE      1 TRUE         2 FALSE        NA      NA
587   PT02676 (factor)  66  TRUE      1 TRUE         2 FALSE        NA      NA
588   PT02678 (factor)  60  TRUE      1 TRUE         2 FALSE        NA      NA
589   PT02683 (factor)  66 FALSE      1 TRUE         2 FALSE        NA      NA
590   PT02684 (factor)  81 FALSE      1 TRUE         2 FALSE        NA      NA
591   PT02776 (factor)  67  TRUE      2 TRUE         2 FALSE      TRUE   FALSE
592   PT02779 (factor)  53 FALSE      1 TRUE         2 FALSE      TRUE   FALSE
593   PT02781 (factor)  51  TRUE      1 TRUE         2 FALSE      TRUE    TRUE
594   PT02783 (factor)  44 FALSE      1 TRUE         2 FALSE      TRUE    TRUE
595   PT02786 (factor)  61  TRUE      2 TRUE         3 FALSE      TRUE   FALSE
596   PT02788 (factor)  82 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
597   PT02789 (factor)  83 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
598   PT02791 (factor)  76 FALSE      2 TRUE         2 FALSE     FALSE   FALSE
599   PT02792 (factor)  39 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
600   PT02793 (factor)  48 FALSE      1 TRUE         2 FALSE     FALSE    TRUE
601   PT02800 (factor)  86 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
602   PT02801 (factor)  42  TRUE      2 TRUE         1 FALSE      TRUE    TRUE
603   PT02802 (factor)  51 FALSE      1 TRUE         3 FALSE     FALSE    TRUE
604   PT02804 (factor)  39 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
605   PT02805 (factor)  57 FALSE      1 TRUE         3 FALSE     FALSE   FALSE
606   PT02807 (factor)  45 FALSE      1 TRUE         2 FALSE      TRUE   FALSE
607   PT02810 (factor)  50  TRUE      3 TRUE         2 FALSE      TRUE   FALSE
608   PT02812 (factor)  66 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
609   PT02813 (factor)  46 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
610   PT02814 (factor)  56 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
611   PT02816 (factor)  53  TRUE      2 TRUE         1 FALSE     FALSE   FALSE
612   PT02818 (factor)  35  TRUE      2 TRUE         3  TRUE     FALSE   FALSE
613   PT02822 (factor)  44 FALSE      2 TRUE         2 FALSE     FALSE    TRUE
614   PT02823 (factor)  82  TRUE      4 TRUE         1 FALSE     FALSE   FALSE
615   PT02825 (factor)  48 FALSE      1 TRUE         2 FALSE     FALSE   FALSE
616   PT02826 (factor)  55 FALSE      2 TRUE         1 FALSE     FALSE   FALSE
617   PT02828 (factor)  52 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
618   PT02829 (factor)  82 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
619   PT02830 (factor)  62 FALSE      1 TRUE         1 FALSE     FALSE    TRUE
620   PT02849 (factor)  81 FALSE      1 TRUE         1 FALSE     FALSE   FALSE
621   PT02850 (factor)  66  TRUE      2 TRUE         3 FALSE     FALSE    TRUE
622   PT02852 (factor)  51  TRUE      2 TRUE         3 FALSE      TRUE    TRUE
                         horm  PFS                                      race
1                        <NA> 100+                                     White
2               not indicated   22                                     Black
3                        <NA>  99+                                     White
4               not indicated  99+                                     White
5                        done  112                                     White
6               not indicated   12                                     Black
7               not indicated  64+                                     Asian
8               not indicated  56+                                     White
9               not indicated  79+                                     White
10              not indicated   26                                     Black
11              not indicated   73                                     White
12              not indicated  97+                                     White
13              not indicated   19                                     White
14                       done  95+                                     White
15                       <NA>  92+                                     White
16              not indicated 101+                                     White
17              not indicated   24                                     White
18              not indicated  84+                                     White
19              not indicated  89+                                     White
20  recommended, but not done   10                                     White
21  recommended, but not done   60                                     White
22                       done 201+                                     White
23                       done  39+                                   Unknown
24                       done 196+                                     Asian
25  recommended, but not done  165                                     White
26  recommended, but not done   45                                     Black
27  recommended, but not done 125+                                     White
28  recommended, but not done  16+                                     White
29                       done 208+                                     White
30                       done  70+                                     White
31  recommended, but not done   28                                     White
32                       done   10                                     White
33  recommended, but not done 160+                                     White
34  recommended, but not done   18                                     White
35  recommended, but not done 195+                                     Black
36                       done  47+                                     Black
37                       done 180+                                     White
38  recommended, but not done  61+                                     White
39                       done   48                                     White
40  recommended, but not done  95+                                   Unknown
41  recommended, but not done  105                                     White
42                       done   23                                     Black
43  recommended, but not done 155+                                     White
44  recommended, but not done  37+                                     White
45              not indicated 180+                                     Black
46  recommended, but not done  18+                                     White
47                       done 204+                                     White
48  recommended, but not done   63                                     White
49  recommended, but not done  15+                                     Black
50  recommended, but not done 188+                                     White
51  recommended, but not done 210+                                     White
52  recommended, but not done 105+                                     White
53                       done   37                                     White
54              not indicated 147+                                     White
55  recommended, but not done 205+                                     Black
56                       done 198+                                     Black
57                       done  83+                                     Black
58              not indicated 152+                                     White
59                       done 165+                                     White
60                       done 193+                                     White
61                       <NA> 189+                                     White
62              not indicated 196+                                     White
63              not indicated  71+                                     White
64                       done  48+                                     White
65              not indicated 138+                                     White
66              not indicated   10                                     White
67              not indicated 135+                                     White
68  recommended, but not done 157+                                     White
69              not indicated 193+                                     White
70              not indicated 149+                                     White
71              not indicated 141+                                     White
72              not indicated   55                                     White
73              not indicated 177+                                     White
74              not indicated 189+                                     White
75                       done  55+                                     White
76  recommended, but not done 165+                                     White
77                       done 203+                                     White
78  recommended, but not done  80+                                     White
79  recommended, but not done 189+                                     White
80                       done 144+                                     White
81                       done 135+                                     White
82  recommended, but not done  90+                                     White
83                       done  94+                                     White
84                       done 146+                                     White
85                       done  163                                     White
86  recommended, but not done   49                                     White
87                       <NA>  97+                                     White
88              not indicated  90+                                     White
89                       done  25+                                     White
90                       done  67+                                     White
91  recommended, but not done   63                                     White
92              not indicated  23+                                     White
93              not indicated 128+                                     White
94              not indicated  52+                                     White
95                       <NA>   15                                     White
96              not indicated   79                                     White
97                       done  75+                                     White
98                       done 185+                                     White
99                       done 145+                                     White
100                      done 185+                                     White
101                      <NA>  175                                     White
102                      done 107+                                     White
103                      done 161+                                     Black
104                      done 183+                                     White
105             not indicated 127+                                     White
106             not indicated 127+                                     White
107             not indicated 174+                                     Asian
108                      done  108                                     White
109             not indicated   44                                     White
110 recommended, but not done  85+                                     White
111 recommended, but not done 115+                                     White
112             not indicated 122+                                     White
113             not indicated  85+                                     White
114                      done 163+                                     White
115 recommended, but not done   71                                     White
116             not indicated  93+                                     Asian
117                      done 115+                                     Asian
118             not indicated   17                                     White
119             not indicated 165+                                     Black
120 recommended, but not done 132+                                     White
121                      done 184+                                     Black
122 recommended, but not done   41                                     White
123                      done   29                                     White
124             not indicated   24                                     White
125                      done 108+                                     White
126             not indicated  55+                                     White
127                      done 154+                                     White
128 recommended, but not done 170+                                     White
129 recommended, but not done  78+                                     White
130             not indicated 101+                                     White
131                      done 178+                                     White
132                      done 145+                                     White
133             not indicated 182+                                     White
134 recommended, but not done   81                                   Unknown
135             not indicated 197+                                     White
136             not indicated 182+                                     White
137 recommended, but not done 136+                                     White
138             not indicated  88+                                     White
139             not indicated  68+                                     White
140             not indicated    7                                     Black
141                      <NA> 118+                                     White
142                      done 140+                                     White
143             not indicated  58+                                     Asian
144             not indicated  94+                                     White
145             not indicated 169+                                     White
146                      done  84+                                     White
147             not indicated 125+                                     White
148             not indicated 167+                                     White
149                      done  73+                                     White
150             not indicated  97+                                     White
151             not indicated 164+                                     White
152                      done 117+                                     White
153             not indicated 116+                                     White
154             not indicated  71+                                     White
155             not indicated 129+                                     White
156                      done 150+                                     White
157             not indicated  43+                                     White
158                      done 130+                                     White
159             not indicated 150+                                     White
160             not indicated 152+                                     White
161             not indicated 140+                                     Black
162                      done  142                                     Asian
163             not indicated 152+                                     White
164             not indicated 136+                                     White
165             not indicated 154+                                     White
166             not indicated   25                                     White
167             not indicated 150+                                     White
168                      done 139+                                     White
169                      done  95+                                     White
170             not indicated  30+                                     White
171                      done 152+                                     White
172                      <NA> 148+                                     White
173                      <NA> 147+                                     White
174                      <NA> 135+                                     White
175                      done 152+                                     Black
176                      <NA>  136                                     White
177             not indicated 132+                                     White
178             not indicated 143+                                     White
179                      done 171+                                     White
180             not indicated 159+                                     White
181             not indicated   30                                     White
182                      done   42                                     White
183             not indicated   36                                     White
184             not indicated 106+                                     White
185                      done 149+                                     White
186                      done 161+                                     White
187                      done  38+                                     White
188             not indicated 166+                                     White
189             not indicated  70+                                     White
190             not indicated 101+                                     White
191                      done 151+                                     White
192             not indicated 133+                                     White
193             not indicated 135+                                     White
194             not indicated 102+                                     White
195                      done 118+                                     White
196                      <NA> 146+                                     White
197             not indicated 152+                                     White
198                      done  93+                                     White
199             not indicated 129+                                     White
200             not indicated 152+                                     White
201                      done  98+                                     White
202             not indicated  44+                                     White
203             not indicated  96+                                     White
204                      done 116+                                     White
205             not indicated 147+                                     White
206             not indicated  71+                                     White
207             not indicated  23+                                     White
208             not indicated 154+                                     White
209                      done  86+                                     White
210             not indicated   18                                     White
211                      done  141                                     White
212             not indicated 158+                                     White
213             not indicated 149+                                     White
214                      done  65+                                   Unknown
215 recommended, but not done  92+                                     White
216             not indicated 117+                                     Black
217                      done  18+                                     White
218 recommended, but not done   71                                     Black
219                      <NA> 150+                                     White
220             not indicated  47+                                     White
221             not indicated 139+                                     White
222                      done  39+                                     White
223             not indicated  33+                                   Unknown
224             not indicated 150+                                     Asian
225             not indicated  72+                                     White
226             not indicated 103+                                     Black
227             not indicated 130+                                     Asian
228             not indicated  27+                                     White
229             not indicated 121+                                     White
230                      <NA> 148+                                   Unknown
231             not indicated 141+                                     White
232             not indicated 128+                                     White
233             not indicated   88                                     White
234             not indicated 101+                                     White
235             not indicated 130+                                     White
236             not indicated 108+                                     White
237                      done 145+                                     White
238                      <NA> 139+                                     White
239             not indicated 153+                                     White
240             not indicated  27+                                     Black
241             not indicated 139+                                     White
242             not indicated 135+                                   Unknown
243             not indicated  36+                                     White
244 recommended, but not done   19                                     White
245 recommended, but not done  33+                                     Black
246 recommended, but not done   22                                     White
247 recommended, but not done  86+                                     White
248 recommended, but not done  172                                     White
249 recommended, but not done 129+                                     White
250                      done  121                                     White
251 recommended, but not done  31+                                   Unknown
252 recommended, but not done  37+                                     White
253 recommended, but not done  12+                                     White
254 recommended, but not done 228+                                     White
255 recommended, but not done   13                                   Unknown
256 recommended, but not done 122+                                     White
257 recommended, but not done   24                                   Unknown
258 recommended, but not done 172+                                     Black
259             not indicated  104                                     White
260 recommended, but not done  86+                                   Unknown
261 recommended, but not done 117+                                     White
262                      done  47+                                     Black
263                      done 100+                                     White
264 recommended, but not done   36                                     Black
265                      done  33+                                     White
266 recommended, but not done   30                                     White
267 recommended, but not done   43                                     White
268 recommended, but not done  23+                                     White
269 recommended, but not done   83                                     White
270 recommended, but not done   15                                   Unknown
271 recommended, but not done  32+                                     Black
272 recommended, but not done 114+                                     White
273 recommended, but not done   49                                     White
274 recommended, but not done   13                                     White
275                      done 129+                                     White
276             not indicated 144+                                     White
277 recommended, but not done  80+                                     White
278                      <NA> 179+                                     White
279             not indicated 183+                                     White
280             not indicated 171+                                     White
281                      done   21                                     White
282             not indicated 132+                                     White
283                      done 109+                                     White
284                      done   11                                     White
285             not indicated 172+                                     White
286 recommended, but not done 172+                                     White
287             not indicated 110+                                     White
288             not indicated  93+                                     Black
289                      done   33                                     White
290             not indicated 124+                                     White
291             not indicated 124+                                     White
292                      done  22+                                     White
293             not indicated  68+                                     White
294             not indicated 175+                                     White
295                      done  82+                                     White
296 recommended, but not done 132+                                     White
297 recommended, but not done 160+                                     White
298 recommended, but not done 206+                                     White
299 recommended, but not done   18                                     White
300                      done   11                                     Black
301                      done   10                                     White
302 recommended, but not done 145+                                     White
303             not indicated  97+                                     White
304             not indicated  71+                                     White
305             not indicated 146+                                     White
306                      <NA> 122+                                     White
307             not indicated  55+                                     White
308             not indicated  56+                                     White
309                      done 118+                                     White
310                      done 158+                                     White
311                      done   56                                     White
312                      done 101+                                     White
313                      done  21+                                     White
314                      done    5                                     White
315 recommended, but not done  98+                                     White
316                      done 189+                                     White
317 recommended, but not done 175+                                     White
318                      done 122+                                     White
319 recommended, but not done  136                                     White
320 recommended, but not done  23+                                     White
321 recommended, but not done 195+                                     White
322 recommended, but not done  95+                                     White
323                      done   39                                     White
324                      done 238+                                     Black
325 recommended, but not done 177+                                     White
326 recommended, but not done  96+                                     White
327 recommended, but not done    9                                     White
328 recommended, but not done   83                                     White
329 recommended, but not done  82+                                   Unknown
330                      done   45                                     White
331 recommended, but not done  29+                                     White
332 recommended, but not done 148+                                     White
333 recommended, but not done   34                                     White
334 recommended, but not done   44                                     White
335                      done 137+                                     White
336                      done   12                                     Black
337 recommended, but not done 151+                                     White
338 recommended, but not done  34+                                     White
339 recommended, but not done 206+                                     White
340 recommended, but not done   36                                     White
341 recommended, but not done 105+                                     White
342 recommended, but not done  71+                                     White
343 recommended, but not done  49+                                     White
344 recommended, but not done 205+                                     White
345 recommended, but not done  55+                                     White
346 recommended, but not done    7                                     Black
347 recommended, but not done  38+                                     White
348 recommended, but not done 235+                                     White
349 recommended, but not done  12+                                     White
350 recommended, but not done 191+                                     White
351 recommended, but not done 187+                                     White
352 recommended, but not done  38+                                     Black
353 recommended, but not done   47                                     White
354 recommended, but not done 194+                                     White
355                      done   3+                                     White
356 recommended, but not done 145+                                     White
357 recommended, but not done  95+                                     White
358 recommended, but not done  29+                                     White
359 recommended, but not done 154+                                     White
360 recommended, but not done    4                                     Black
361 recommended, but not done  25+                                     White
362 recommended, but not done   37                                     White
363 recommended, but not done 198+                                     White
364 recommended, but not done  45+                                     White
365 recommended, but not done 214+                                     White
366 recommended, but not done 179+                                     White
367 recommended, but not done 118+                                     White
368 recommended, but not done   18                                     White
369 recommended, but not done 165+                                     White
370                      done  131                                     White
371                      done 133+                                     White
372 recommended, but not done 158+                                     White
373 recommended, but not done   13                                     White
374 recommended, but not done   11                                     White
375 recommended, but not done 157+                                     White
376 recommended, but not done 120+                                     White
377 recommended, but not done 135+                                     Black
378 recommended, but not done 108+                                     White
379 recommended, but not done  83+                                     Black
380                      done  67+                                     Black
381 recommended, but not done 110+                                     White
382 recommended, but not done  75+                                     White
383 recommended, but not done 145+                                     White
384             not indicated   35                                     White
385                      done 236+                                     White
386                      done 146+                                   Unknown
387 recommended, but not done 111+                                     White
388 recommended, but not done   34                                     White
389 recommended, but not done 135+                                     White
390                      done  70+                                     White
391 recommended, but not done 115+                                     White
392                      <NA>  59+                                     Black
393                      <NA> 225+                                     White
394 recommended, but not done  60+                                     White
395 recommended, but not done  12+                                     White
396             not indicated  95+                                     White
397 recommended, but not done 114+                                     White
398 recommended, but not done   29                                     White
399                      <NA> 129+                                     White
400 recommended, but not done  51+                                     White
401 recommended, but not done 153+                                     White
402 recommended, but not done 174+                                     White
403                      done  58+                                     White
404                      done  97+                                     White
405                      <NA> 231+                                     White
406 recommended, but not done   45                                     White
407 recommended, but not done  15+                                     White
408                      <NA> 130+                                     White
409 recommended, but not done   73                                     White
410                      done 189+                                     White
411 recommended, but not done  57+                                     White
412 recommended, but not done 231+                                     White
413 recommended, but not done 221+                                     White
414                      done  30+                                     White
415 recommended, but not done 230+                                     White
416 recommended, but not done  86+                                     White
417                      done 105+                                     White
418 recommended, but not done 171+                                     White
419 recommended, but not done   15                                     Black
420 recommended, but not done 230+                                     White
421                      done 230+                                     White
422 recommended, but not done  56+                                     White
423                      done 205+                                     White
424 recommended, but not done 160+                                     White
425                      <NA>   83                                     White
426                      <NA> 233+                                     White
427 recommended, but not done 203+                                     White
428 recommended, but not done  28+                                     White
429                      <NA> 231+                                     White
430                      <NA> 181+                                     White
431 recommended, but not done   67                                     White
432                      done  72+                                     White
433 recommended, but not done  13+                                     White
434                      done   22 Native Hawaiian or Other Pacific Islander
435 recommended, but not done  54+                                     White
436 recommended, but not done 148+                                     White
437                      done  94+                                     White
438                      done  131                                     White
439 recommended, but not done 233+                                     White
440 recommended, but not done 137+                                     White
441                      done  224                                     White
442 recommended, but not done  74+                                     White
443                      done  73+                                     White
444                      <NA>  23+                                     White
445 recommended, but not done 202+                                     White
446                      done   35                                     White
447 recommended, but not done 211+                                     White
448 recommended, but not done 131+                                     White
449                      done 103+                                     White
450 recommended, but not done  53+                                     White
451                      done  145                                     White
452 recommended, but not done  32+                                     Black
453                      done  58+                                     Black
454                      done 141+                                     White
455 recommended, but not done  94+                                     White
456                      done 228+                                     White
457                      done 140+                                     Asian
458                      done  95+                                     White
459 recommended, but not done  129                                     White
460 recommended, but not done 210+                                     White
461 recommended, but not done 147+                                     White
462 recommended, but not done 205+                                     White
463                      done 211+                                     White
464 recommended, but not done  70+                                     White
465 recommended, but not done  73+                                     White
466 recommended, but not done 122+                                     White
467 recommended, but not done 194+                                     White
468 recommended, but not done 227+                                     White
469 recommended, but not done 226+                                     White
470 recommended, but not done  145                                     White
471                      <NA> 144+                                     White
472 recommended, but not done 109+                                     White
473 recommended, but not done 141+                                     White
474                      done 213+                                     White
475 recommended, but not done  68+                                     White
476 recommended, but not done 154+                                     White
477 recommended, but not done 184+                                     White
478 recommended, but not done 218+                                     White
479                      done 226+                                     Black
480 recommended, but not done 121+                                   Unknown
481 recommended, but not done 139+                                     White
482 recommended, but not done 140+                                     White
483                      done 147+                                     White
484 recommended, but not done 215+                                     White
485 recommended, but not done   27                                     White
486 recommended, but not done 118+                                     White
487                      done  25+                                     White
488 recommended, but not done   27                                     Black
489 recommended, but not done 213+                                     White
490 recommended, but not done 226+                                     Black
491                      done  116                                     White
492 recommended, but not done 137+                                     White
493 recommended, but not done  62+                                     White
494                      done   30                                     White
495 recommended, but not done   27          American Indian or Alaska Native
496                      done  39+                                     White
497                      done    8                                     White
498 recommended, but not done  67+                                     White
499 recommended, but not done 163+                                     White
500                      <NA> 187+                                     White
501                      done 115+                                     White
502 recommended, but not done  160                                     Black
503 recommended, but not done 109+                                     White
504                      done 102+                                     Black
505 recommended, but not done 126+                                     White
506 recommended, but not done 131+                                   Unknown
507 recommended, but not done 227+                                     White
508                      done  70+                                     Black
509 recommended, but not done 217+                                     White
510 recommended, but not done   12                                     Black
511 recommended, but not done  98+                                     White
512 recommended, but not done 142+                                     White
513                      done 163+                                     White
514                      done 155+                                     White
515 recommended, but not done 106+                                     White
516 recommended, but not done 168+                                     White
517             not indicated 167+                                     White
518             not indicated 167+                                     White
519             not indicated 123+                                     White
520                      done  97+                                     White
521                      done 168+                                     Black
522             not indicated 129+                                     White
523             not indicated  20+                                     White
524             not indicated  35+                                   Unknown
525                      done 168+                                     White
526             not indicated 172+                                     White
527             not indicated 133+                                     White
528                      done  98+                                     White
529                      done 142+                                     White
530 recommended, but not done   2+                                     White
531                      done 212+                                     White
532                      done   32                                     White
533 recommended, but not done  23+                                     White
534                      done  22+                                     White
535 recommended, but not done 155+                                     White
536 recommended, but not done  87+                                     White
537                      done   19                                     White
538 recommended, but not done   56                                     White
539 recommended, but not done 155+                                     White
540 recommended, but not done 149+                                     White
541 recommended, but not done   15                                     White
542 recommended, but not done  94+                                     White
543 recommended, but not done 133+                                     White
544 recommended, but not done  75+                                     White
545 recommended, but not done  40+                                     White
546 recommended, but not done 172+                                     White
547 recommended, but not done 172+                                     White
548 recommended, but not done   48                                   Unknown
549                      done 221+                                     White
550                      done   10                                     White
551 recommended, but not done 134+                                     White
552                      done 135+                                     White
553             not indicated  26+                                     White
554                      done   63                                     White
555                      done   98                                     White
556             not indicated 192+                                     White
557             not indicated 123+                                     White
558 recommended, but not done  27+                                     Black
559             not indicated 125+                                     White
560             not indicated   26                                     White
561             not indicated  17+                                     Black
562             not indicated  25+                                     White
563             not indicated 129+                                   Unknown
564             not indicated  90+                                     White
565                      done 129+                                     White
566 recommended, but not done 173+                                     White
567             not indicated  36+                                     White
568             not indicated 179+                                     White
569                      done 116+                                     White
570             not indicated  18+                                     White
571             not indicated 187+                                     White
572                      done 174+                                     White
573             not indicated  58+                                     White
574             not indicated 195+                                     White
575                      done 180+                                     White
576             not indicated 157+                                     White
577                      done 175+                                     White
578             not indicated 170+                                     White
579 recommended, but not done 129+                                     Black
580 recommended, but not done 127+                                     White
581 recommended, but not done  87+                                     White
582                      done 165+                                     White
583                      done  92+                                     Black
584                      done 102+                                     White
585 recommended, but not done 109+                                     White
586                      <NA> 189+                                     White
587                      <NA> 101+                                     White
588                      <NA> 197+                                     White
589                      <NA>  59+                                     White
590                      <NA>  15+                                     White
591 recommended, but not done   39                                     White
592                      done 163+                                     Black
593             not indicated 170+                                     White
594                      done 117+                                     White
595             not indicated 137+                                     White
596             not indicated 112+                                     White
597                      done  42+                                     White
598             not indicated 181+                                     White
599             not indicated 143+                                     White
600             not indicated 154+                                     White
601             not indicated  22+                                     White
602                      done 163+                                     Black
603                      done 142+                                     White
604             not indicated 152+                                     White
605             not indicated 156+                                     White
606                      done 161+                                     White
607                      done  75+                                     White
608             not indicated 104+                                     White
609             not indicated 121+                                     White
610             not indicated 163+                                     White
611             not indicated  46+                                     White
612             not indicated  86+                                     White
613             not indicated 106+                                     White
614                      done 109+                                     White
615             not indicated 161+                                     White
616             not indicated 157+                                     White
617             not indicated 159+                                     White
618                      done  67+                                     White
619             not indicated 140+                                     White
620             not indicated  64+                                     White
621                      done  59+                                     White
622             not indicated  40+                                     White
      logKi67  logKi67q
1   (anylist) (numeric)
2   (anylist) (numeric)
3   (anylist) (numeric)
4   (anylist) (numeric)
5   (anylist) (numeric)
6   (anylist) (numeric)
7   (anylist) (numeric)
8   (anylist) (numeric)
9   (anylist) (numeric)
10  (anylist) (numeric)
11  (anylist) (numeric)
12  (anylist) (numeric)
13  (anylist) (numeric)
14  (anylist) (numeric)
15  (anylist) (numeric)
16  (anylist) (numeric)
17  (anylist) (numeric)
18  (anylist) (numeric)
19  (anylist) (numeric)
20  (anylist) (numeric)
21  (anylist) (numeric)
22  (anylist) (numeric)
23  (anylist) (numeric)
24  (anylist) (numeric)
25  (anylist) (numeric)
26  (anylist) (numeric)
27  (anylist) (numeric)
28  (anylist) (numeric)
29  (anylist) (numeric)
30  (anylist) (numeric)
31  (anylist) (numeric)
32  (anylist) (numeric)
33  (anylist) (numeric)
34  (anylist) (numeric)
35  (anylist) (numeric)
36  (anylist) (numeric)
37  (anylist) (numeric)
38  (anylist) (numeric)
39  (anylist) (numeric)
40  (anylist) (numeric)
41  (anylist) (numeric)
42  (anylist) (numeric)
43  (anylist) (numeric)
44  (anylist) (numeric)
45  (anylist) (numeric)
46  (anylist) (numeric)
47  (anylist) (numeric)
48  (anylist) (numeric)
49  (anylist) (numeric)
50  (anylist) (numeric)
51  (anylist) (numeric)
52  (anylist) (numeric)
53  (anylist) (numeric)
54  (anylist) (numeric)
55  (anylist) (numeric)
56  (anylist) (numeric)
57  (anylist) (numeric)
58  (anylist) (numeric)
59  (anylist) (numeric)
60  (anylist) (numeric)
61  (anylist) (numeric)
62  (anylist) (numeric)
63  (anylist) (numeric)
64  (anylist) (numeric)
65  (anylist) (numeric)
66  (anylist) (numeric)
67  (anylist) (numeric)
68  (anylist) (numeric)
69  (anylist) (numeric)
70  (anylist) (numeric)
71  (anylist) (numeric)
72  (anylist) (numeric)
73  (anylist) (numeric)
74  (anylist) (numeric)
75  (anylist) (numeric)
76  (anylist) (numeric)
77  (anylist) (numeric)
78  (anylist) (numeric)
79  (anylist) (numeric)
80  (anylist) (numeric)
81  (anylist) (numeric)
82  (anylist) (numeric)
83  (anylist) (numeric)
84  (anylist) (numeric)
85  (anylist) (numeric)
86  (anylist) (numeric)
87  (anylist) (numeric)
88  (anylist) (numeric)
89  (anylist) (numeric)
90  (anylist) (numeric)
91  (anylist) (numeric)
92  (anylist) (numeric)
93  (anylist) (numeric)
94  (anylist) (numeric)
95  (anylist) (numeric)
96  (anylist) (numeric)
97  (anylist) (numeric)
98  (anylist) (numeric)
99  (anylist) (numeric)
100 (anylist) (numeric)
101 (anylist) (numeric)
102 (anylist) (numeric)
103 (anylist) (numeric)
104 (anylist) (numeric)
105 (anylist) (numeric)
106 (anylist) (numeric)
107 (anylist) (numeric)
108 (anylist) (numeric)
109 (anylist) (numeric)
110 (anylist) (numeric)
111 (anylist) (numeric)
112 (anylist) (numeric)
113 (anylist) (numeric)
114 (anylist) (numeric)
115 (anylist) (numeric)
116 (anylist) (numeric)
117 (anylist) (numeric)
118 (anylist) (numeric)
119 (anylist) (numeric)
120 (anylist) (numeric)
121 (anylist) (numeric)
122 (anylist) (numeric)
123 (anylist) (numeric)
124 (anylist) (numeric)
125 (anylist) (numeric)
126 (anylist) (numeric)
127 (anylist) (numeric)
128 (anylist) (numeric)
129 (anylist) (numeric)
130 (anylist) (numeric)
131 (anylist) (numeric)
132 (anylist) (numeric)
133 (anylist) (numeric)
134 (anylist) (numeric)
135 (anylist) (numeric)
136 (anylist) (numeric)
137 (anylist) (numeric)
138 (anylist) (numeric)
139 (anylist) (numeric)
140 (anylist) (numeric)
141 (anylist) (numeric)
142 (anylist) (numeric)
143 (anylist) (numeric)
144 (anylist) (numeric)
145 (anylist) (numeric)
146 (anylist) (numeric)
147 (anylist) (numeric)
148 (anylist) (numeric)
149 (anylist) (numeric)
150 (anylist) (numeric)
151 (anylist) (numeric)
152 (anylist) (numeric)
153 (anylist) (numeric)
154 (anylist) (numeric)
155 (anylist) (numeric)
156 (anylist) (numeric)
157 (anylist) (numeric)
158 (anylist) (numeric)
159 (anylist) (numeric)
160 (anylist) (numeric)
161 (anylist) (numeric)
162 (anylist) (numeric)
163 (anylist) (numeric)
164 (anylist) (numeric)
165 (anylist) (numeric)
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  • a numeric-hypercolumn of the aggregated sample quantiles logKi67q per patientID. These quantiles are calculated at a pre-specified grid of probabilities \(\{p_k, k=1,\cdots,K \} \in [0,1]\). Note that the aggregation must be performed at the level of biologically independent clusters, e.g., ~patientID, to produce independent quantile predictors.
  • Metadata, including the outcome of interest, e.g., progression free survival PFS, Her2, HR, etc.

Readers are encouraged to learn more about the hyper data frame (hyperframe) from package spatstat.geom (Baddeley et al. 2015; Baddeley and Turner 2005).

Linear quantile index (QI) (Equation 1.1) is a predictor in a functional generalized linear model (James 2002) for outcomes from the exponential family of distributions, or a linear functional Cox model (Gellar et al. 2015) for survival outcomes,

\[ \text{QI}_{i}=\int_{0}^{1} \beta(p)Q_i(p)dp \tag{1.1}\]

where \(Q_i(p)\) is the (aggregated) sample quantiles logKi67q for the \(i\)-th subject, and \(\beta(p)\) is the unknown coefficient function to be estimated. Listing 1.2 fits a generalized additive model (gam(), Wood 2017, v1.9.4, GPL (>= 2)) with integrated linear spline-based smoothness estimation (s(), Wood 2003, v1.9.4, GPL (>= 2)). This is a scalar-on-function model (Reiss et al. 2017) that predicts a scalar outcome (e.g., progression free survival time PFS[,1L]) using the aggregated quantiles as a functional predictor.

Listing 1.2: Linear functional Cox model for survival outcome (Gellar et al. 2015) (Listing 1.1)
m0

Family: Cox PH 
Link function: identity 

Formula:
PFS[, 1L] ~ s(logKi67q.x, by = logKi67q.L * logKi67q.y, bs = "cr")

Estimated degrees of freedom:
2  total = 2 

REML score: 714.9095     

Nonlinear quantile index (nlQI) (Equation 1.2) is a predictor in the functional generalized additive model (McLean et al. 2014) for outcomes from the exponential family of distributions, or an additive functional Cox model (Cui et al. 2021) for survival outcomes.

\[ \text{nlQI}_{i}= \int_{0}^{1} F\big(p, Q_i(p)\big)dp \tag{1.2}\]

where \(F(\cdot,\cdot)\) is an unknown bivariate twice differentiable function. Listing 1.3 fits a generalized additive model (gam(), Wood 2017, v1.9.4, GPL (>= 2)) with tensor product interaction estimation (ti(), Wood 2006, v1.9.4, GPL (>= 2)).

Listing 1.3: Additive functional Cox model for survival outcome (Cui et al. 2021) (Listing 1.1)
m1

Family: Cox PH 
Link function: identity 

Formula:
PFS[, 1L] ~ ti(logKi67q.x, logKi67q.y, by = logKi67q.L, bs = "cr", 
    mc = c(FALSE, TRUE))

Estimated degrees of freedom:
5.32  total = 5.32 

REML score: 708.0423     

The function widget_gam() creates an interactive htmlwidget (Vaidyanathan et al. 2023, v1.6.4, MIT + file) visualization of the estimated integrand surfaces for the linear (Equation 1.1) or nonlinear quantile index (Equation 1.2) using package plotly (Sievert 2020, v4.12.0, MIT + file). The integrand surfaces, defined on \(p\in[0,1]\) and \(q\in\text{range}\big\{Q_i(p), i=1,\cdots,n\big\}\), are

\[ \hat{S}(p,q) = \begin{cases} \hat{\beta}(p)\cdot q\\ \hat{F}(p,q) \end{cases} \tag{1.3}\]

Also in this interactive visualization are

  • the contour lines on the integrand surfaces (Equation 1.3), as well as their projections along the \(s\)-axis, i.e., onto the \((p,q)\)-plane (a.k.a., the “floor”);
  • the estimated linear integrand paths \(\hat{\beta}(p)Q_i(p)\) or the nonlinear integrand paths \(\hat{F}(p, Q_i(p))\) on the integrand surfaces (Equation 1.3);
  • the sample quantiles \(Q_i(p)\), i.e., the projections of the estimated linear or nonlinear integrand path along the \(s\)-axis, i.e., onto the \((p,q)\)-plane (a.k.a., the “floor”);
  • the projections of the estimated linear or nonlinear integrand path along the \(q\)-axis, i.e., onto the \((p,s)\)-plane (a.k.a., the “backwall”), so that the area under each projected path is equal to the estimated linear (Equation 1.1) or nonlinear quantile index (Equation 1.2).

Figure 1.1 is a collage (via package htmltools, Cheng et al. 2025, v0.5.9, GPL (>= 2)) of the interactive htmlwidget visualizations of the linear and nonlinear integrand surfaces, contours, integrand paths and their projections to the “floor” and “backwall”. Listing 1.4 uses n=21L to reduce the htmlwidget objects size.

Listing 1.4: Figure: visualize linear and nonlinear quantile index (Listing 1.2, Listing 1.3)
Code
proj = list(
  # x = list(show = TRUE, opacity = .5), # no meaning
  y = list(show = TRUE, opacity = .5),
  z = list(show = TRUE, opacity = .5)
)
scene = list(
  xaxis = list(title = 'Probability (p)', tickformat = '.0%', color = 'dodgerblue'), 
  yaxis = list(title = 'Quantile (q)', color = 'deeppink'),
  zaxis = list(title = 'Integrand (s)', color = 'darkolivegreen')
)
colorscale = list(c(0, 1), c('white', 'lightgreen'))
m0_surface = m0 |> 
  widget_gam(n.grid = 21L, colorscale = colorscale)
m0_trace = m0 |> 
  trace_gam(
    formula = ~ logKi67q,
    projection = proj, 
    marker = list(size = 1.5)
  )
m1_surface = m1 |> 
  widget_gam(colorscale = colorscale)
m1_trace = m1 |> 
  trace_gam(
    formula = ~ logKi67q, 
    projection = proj, 
    marker = list(size = 1.5)
  )
htmltools::tagList(
  plotly::subplot(m0_surface, m0_trace) |> 
    plotly::layout(scene = scene), 
  plotly::subplot(m1_surface, m1_trace) |> 
    plotly::layout(scene = scene)
) |> 
  htmltools::browsable()
Figure 1.1: Linear (top) and nonlinear (bottom) integrand surfaces, contours, integrand paths and their projections to the “floor” and “backwall”