Alessio Crippa
Department of Medical Epidemiology and Biostatistics
Karolinska Institutet
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
39 20 6 1 34
ARA DRD TP53 TEfus prev
1 - - - - 0.3238
2 - - - + 0.0667
3 - - + - 0.1714
4 - - + + 0.1143
5 - + - - 0.0667
6 - + - + 0.0476
7 - + + - 0.0190
8 - + + + 0.0095
9 + - - - 0.0476
10 + - - + 0.0381
11 + - + - 0.0095
12 + - + + 0.0381
13 + + - - 0.0286
14 + + - + 0.0095
15 + + + - 0.0095
signatures ---- ---+ --+- --++ -+-- -+-+ -++- -+++ +--- +--+ +-+- +-++ ++-- ++-+ +++- n prev
1 all X X X X X X X X X X X X X X X 105 1.00
2 TP53- & AR- X X X X 53 0.50
3 TP53+ | AR+ X X X X X X X X X X X 52 0.50
4 DRD+ X X X X X X X 20 0.19
5 DRD- X X X X X X X X 85 0.81
6 TEfus+ X X X X X X X 34 0.32
7 TEfus- X X X X X X X X 71 0.68
\( T_{ixk} \sim Weibull(\textrm{shape} = 2, \textrm{scale}_{xk}) \)
\( i = 1, \dots, n_{xk}, \;\; \) \( x = 2, \dots, 6 \; \) \( k = 1, \dots, 15 \)
Mean PFS: 5.3 months for an ineffective treatment (median 5)
Mean PFS: 13.3 months for an effective treatment, HR: 2 (median 12.5)
Waiting for more data
Control Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
---- 223 2 46 51 74 90
---+ 32 23 2 15 27 1
--+- 102 34 11 79 4 14
--++ 57 7 32 2 22 37
-+-- 33 21 4 9 7 21
-+-+ 20 11 3 7 9 5
-++- 13 4 3 2 7 1
-+++ 2 2 2 1 2 0
+--- 25 17 3 13 6 4
+--+ 15 8 6 2 20 13
+-+- 8 4 4 1 3 2
+-++ 16 6 18 3 9 1
++-- 9 8 4 0 5 4
++-+ 6 2 2 3 3 0
+++- 2 4 0 3 1 1
Control Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 563 153 140 191 199 194
TP53- & AR- 308 57 55 82 117 117
TP53+ | AR+ 255 96 85 109 82 77
DRD+ 85 52 18 25 34 32
DRD- 478 101 122 166 165 162
TEfus+ 148 59 65 33 92 57
TEfus- 415 94 75 158 107 137
\[ \begin{cases} \log(T, x) = \beta_{01} + \beta_{11}trt + \sigma W \\ \log(T, x) = \beta_{02} + \beta_{12}trt + \beta_{22}(\text{TP53}_- \text{& AR}_-) + \beta_{32}(trt\cdot \text{TP53}_- \text{& AR}_-) + \sigma W \\ \log(T, x) = \beta_{03} + \beta_{13}trt + \beta_{23}\text{DRD}_+ + \beta_{33}(trt\cdot \text{DRD}_+) + \sigma W \\ \log(T, x) = \beta_{04} + \beta_{14}trt + \beta_{24}\text{TEfus}_+ + \beta_{34}(trt\cdot \text{TEfus}_+) + \sigma W \end{cases} \]
Put a common prior on the \( \beta_{i3} \), \( i = 2, 3, 4 \)
True mean PF times
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
---- 5.3 5.3 5.3 5.3 5.3
---+ 5.3 5.3 5.3 5.3 5.3
--+- 5.3 5.3 5.3 5.3 5.3
--++ 5.3 5.3 5.3 5.3 5.3
-+-- 5.3 5.3 5.3 5.3 5.3
-+-+ 5.3 5.3 5.3 5.3 5.3
-++- 5.3 5.3 5.3 5.3 5.3
-+++ 5.3 5.3 5.3 5.3 5.3
+--- 5.3 5.3 5.3 5.3 5.3
+--+ 5.3 5.3 5.3 5.3 5.3
+-+- 5.3 5.3 5.3 5.3 5.3
+-++ 5.3 5.3 5.3 5.3 5.3
++-- 5.3 5.3 5.3 5.3 5.3
++-+ 5.3 5.3 5.3 5.3 5.3
+++- 5.3 5.3 5.3 5.3 5.3
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 193 191 192 192 190
TP53- & AR- 95 98 100 94 97
TP53+ | AR+ 98 93 92 98 93
DRD+ 37 36 36 38 36
DRD- 155 155 155 155 154
TEfus+ 63 62 62 64 60
TEfus- 129 129 129 129 130
Graduation Probabilities
p1 p2
Enzalutamide 0 0.045
Abiraterone 0 0.030
Radium.223 0 0.050
Cabazitaxel 0 0.070
Docetaxel 0 0.040
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 24 24 24
TP53- & AR- 24 24 24 24 24
TP53+ | AR+ 24 24 24 24 24
DRD+ 24 24 24 24 24
DRD- 24 24 24 24 24
TEfus+ 24 24 24 24 24
TEfus- 24 24 24 24 24
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.094 0.087 0.095 0.078 0.053
TP53- & AR- 0.200 0.192 0.207 0.177 0.150
TP53+ | AR+ 0.098 0.094 0.099 0.090 0.069
DRD+ 0.109 0.110 0.111 0.111 0.114
DRD- 0.177 0.180 0.203 0.166 0.116
TEfus+ 0.124 0.137 0.133 0.118 0.111
TEfus- 0.146 0.132 0.147 0.129 0.091
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.000 0.00 0.000 0.000 0.000
TP53- & AR- 0.040 0.02 0.015 0.045 0.025
TP53+ | AR+ 0.000 0.00 0.000 0.000 0.000
DRD+ 0.000 0.00 0.000 0.000 0.000
DRD- 0.000 0.01 0.030 0.025 0.025
TEfus+ 0.000 0.00 0.000 0.000 0.000
TEfus- 0.005 0.00 0.005 0.005 0.000
True mean PF times
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
---- 5.3 13 5.3 5.3 5.3
---+ 5.3 13 5.3 5.3 5.3
--+- 5.3 13 5.3 5.3 5.3
--++ 5.3 13 5.3 5.3 5.3
-+-- 5.3 13 5.3 5.3 5.3
-+-+ 5.3 13 5.3 5.3 5.3
-++- 5.3 13 5.3 5.3 5.3
-+++ 5.3 13 5.3 5.3 5.3
+--- 5.3 13 5.3 5.3 5.3
+--+ 5.3 13 5.3 5.3 5.3
+-+- 5.3 13 5.3 5.3 5.3
+-++ 5.3 13 5.3 5.3 5.3
++-- 5.3 13 5.3 5.3 5.3
++-+ 5.3 13 5.3 5.3 5.3
+++- 5.3 13 5.3 5.3 5.3
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 201 75 201 200 201
TP53- & AR- 102 41 105 100 104
TP53+ | AR+ 99 34 97 99 97
DRD+ 43 14 42 42 42
DRD- 159 60 159 157 160
TEfus+ 66 23 66 67 67
TEfus- 135 52 135 132 134
Graduation Probabilities
p1 p2
Enzalutamide 0.00 0.015
Abiraterone 0.81 0.000
Radium.223 0.00 0.000
Cabazitaxel 0.00 0.005
Docetaxel 0.00 0.000
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 9.3 24 24 24
TP53- & AR- 23 20.7 23 23 24
TP53+ | AR+ 24 22.5 24 24 24
DRD+ 24 24.0 24 24 24
DRD- 24 7.3 24 24 24
TEfus+ 24 24.0 24 24 24
TEfus- 24 13.0 24 24 24
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.018 0.86 0.016 0.016 0.021
TP53- & AR- 0.078 0.92 0.061 0.062 0.079
TP53+ | AR+ 0.037 0.65 0.037 0.037 0.035
DRD+ 0.068 0.47 0.082 0.080 0.070
DRD- 0.051 0.94 0.046 0.036 0.056
TEfus+ 0.065 0.68 0.056 0.053 0.062
TEfus- 0.040 0.85 0.040 0.041 0.044
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.000 0.810 0 0.000 0
TP53- & AR- 0.015 0.230 0 0.005 0
TP53+ | AR+ 0.000 0.095 0 0.000 0
DRD+ 0.000 0.005 0 0.000 0
DRD- 0.000 0.900 0 0.000 0
TEfus+ 0.000 0.010 0 0.000 0
TEfus- 0.000 0.610 0 0.000 0
True mean PF times
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
---- 5.3 13.3 5.3 5.3 5.3
---+ 5.3 13.3 5.3 5.3 5.3
--+- 5.3 5.3 5.3 5.3 5.3
--++ 5.3 5.3 5.3 5.3 5.3
-+-- 5.3 13.3 5.3 5.3 5.3
-+-+ 5.3 13.3 5.3 5.3 5.3
-++- 5.3 5.3 5.3 5.3 5.3
-+++ 5.3 5.3 5.3 5.3 5.3
+--- 5.3 5.3 5.3 5.3 5.3
+--+ 5.3 5.3 5.3 5.3 5.3
+-+- 5.3 5.3 5.3 5.3 5.3
+-++ 5.3 5.3 5.3 5.3 5.3
++-- 5.3 5.3 5.3 5.3 5.3
++-+ 5.3 5.3 5.3 5.3 5.3
+++- 5.3 5.3 5.3 5.3 5.3
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 199 120 200 199 199
TP53- & AR- 98 54 104 102 101
TP53+ | AR+ 101 66 96 97 98
DRD+ 41 18 42 40 40
DRD- 158 102 159 158 158
TEfus+ 65 43 64 64 65
TEfus- 134 77 136 134 134
Graduation Probabilities
p1 p2
Enzalutamide 0.00 0.025
Abiraterone 0.94 0.055
Radium.223 0.00 0.010
Cabazitaxel 0.00 0.000
Docetaxel 0.00 0.005
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 20.7 24 24 24
TP53- & AR- 24 8.5 24 24 24
TP53+ | AR+ 24 24.0 24 24 24
DRD+ 24 24.0 24 24 24
DRD- 24 17.4 24 24 24
TEfus+ 24 23.9 24 24 24
TEfus- 24 14.7 24 24 24
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.038 0.48 0.035 0.034 0.033
TP53- & AR- 0.073 0.95 0.077 0.077 0.057
TP53+ | AR+ 0.075 0.11 0.068 0.069 0.080
DRD+ 0.087 0.29 0.099 0.088 0.089
DRD- 0.092 0.65 0.072 0.079 0.081
TEfus+ 0.080 0.42 0.071 0.079 0.076
TEfus- 0.077 0.53 0.079 0.073 0.073
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.000 0.185 0.00 0 0.000
TP53- & AR- 0.025 0.935 0.01 0 0.005
TP53+ | AR+ 0.000 0.000 0.00 0 0.000
DRD+ 0.000 0.000 0.00 0 0.000
DRD- 0.000 0.370 0.00 0 0.000
TEfus+ 0.000 0.015 0.00 0 0.000
TEfus- 0.000 0.530 0.00 0 0.000
True mean PF times
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
---- 10.6 10.6 5.3 5.3 5.3
---+ 10.6 10.6 5.3 5.3 13.3
--+- 5.3 5.3 5.3 5.3 5.3
--++ 5.3 5.3 5.3 5.3 13.3
-+-- 10.6 10.6 5.3 5.3 5.3
-+-+ 10.6 10.6 5.3 5.3 13.3
-++- 5.3 5.3 5.3 5.3 5.3
-+++ 5.3 5.3 5.3 5.3 13.3
+--- 5.3 5.3 5.3 5.3 5.3
+--+ 5.3 5.3 5.3 5.3 13.3
+-+- 5.3 5.3 5.3 5.3 5.3
+-++ 5.3 5.3 5.3 5.3 13.3
++-- 5.3 5.3 5.3 5.3 5.3
++-+ 5.3 5.3 5.3 5.3 13.3
+++- 5.3 5.3 5.3 5.3 5.3
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 165 168 184 186 162
TP53- & AR- 74 72 88 89 69
TP53+ | AR+ 91 96 96 97 93
DRD+ 28 29 46 45 35
DRD- 137 139 138 141 127
TEfus+ 52 54 73 73 56
TEfus- 113 113 111 113 106
Graduation Probabilities
p1 p2
Enzalutamide 0.95 0.005
Abiraterone 0.95 0.000
Radium.223 0.00 0.000
Cabazitaxel 0.00 0.000
Docetaxel 0.97 0.000
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24.0 24 24 24
TP53- & AR- 10 9.9 24 24 23
TP53+ | AR+ 24 24.0 24 24 23
DRD+ 24 23.9 24 24 24
DRD- 24 23.8 24 24 24
TEfus+ 24 24.0 24 24 12
TEfus- 23 23.6 24 24 24
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.098 0.108 0.014 0.011 0.58
TP53- & AR- 0.469 0.469 0.051 0.050 0.47
TP53+ | AR+ 0.048 0.048 0.040 0.033 0.61
DRD+ 0.160 0.182 0.073 0.056 0.30
DRD- 0.168 0.167 0.035 0.036 0.74
TEfus+ 0.080 0.083 0.029 0.019 0.95
TEfus- 0.284 0.301 0.073 0.062 0.08
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.000 0.000 0 0 0.005
TP53- & AR- 0.955 0.955 0 0 0.095
TP53+ | AR+ 0.000 0.000 0 0 0.040
DRD+ 0.000 0.005 0 0 0.000
DRD- 0.000 0.010 0 0 0.040
TEfus+ 0.000 0.000 0 0 0.975
TEfus- 0.045 0.025 0 0 0.000
Based on one simulated dataset from scenario 4
\[ h(t, x) = h_0(t) exp(trt + sign2 + trt\cdot sign2) \]
exp(Est.) 2.5% 97.5%
trtEnzalutamide 1.82 1.37 2.43
trtAbiraterone 1.31 0.95 1.80
trtRadium 223 1.37 1.08 1.74
trtCabazitaxel 1.65 1.26 2.17
trtDocetaxel 0.53 0.40 0.71
`TP53- & AR-` 0.86 0.70 1.06
trtEnzalutamide:`TP53- & AR-` 0.33 0.22 0.51
trtAbiraterone:`TP53- & AR-` 0.41 0.26 0.65
trtRadium 223:`TP53- & AR-` 1.24 0.86 1.79
trtCabazitaxel:`TP53- & AR-` 1.28 0.89 1.84
trtDocetaxel:`TP53- & AR-` 3.57 2.46 5.18
Simultaneous Tests for General Linear Hypotheses
Fit: coxph(formula = Surv(time_m, delta) ~ trt * `TP53- & AR-`, data = s_dta)
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
Enz - ctr (0) == 0 0.6003 0.1458 4.12 0.0010 **
Abi - ctr (0) == 0 0.2675 0.1645 1.63 0.8173
Rad - ctr (0) == 0 0.3144 0.1233 2.55 0.2007
Cab - ctr (0) == 0 0.5029 0.1393 3.61 0.0080 **
Doc - ctr (0) == 0 -0.6277 0.1449 -4.33 <0.001 ***
Abi - Enz (0) == 0 -0.3328 0.1915 -1.74 0.7477
Rad - Enz (0) == 0 -0.2859 0.1587 -1.80 0.7035
Cab - Enz (0) == 0 -0.0974 0.1707 -0.57 0.9999
Doc - Enz (0) == 0 -1.2281 0.1799 -6.83 <0.001 ***
Rad - Abi (0) == 0 0.0469 0.1761 0.27 1.0000
Cab - Abi (0) == 0 0.2354 0.1871 1.26 0.9607
Doc - Abi (0) == 0 -0.8953 0.1952 -4.59 <0.001 ***
Cab - Rad (0) == 0 0.1885 0.1528 1.23 0.9658
Doc - Rad (0) == 0 -0.9422 0.1612 -5.85 <0.001 ***
Doc - Cab (0) == 0 -1.1307 0.1743 -6.49 <0.001 ***
Enz - ctr (1) == 0 -0.5012 0.1627 -3.08 0.0479 *
Abi - ctr (1) == 0 -0.6166 0.1586 -3.89 0.0027 **
Rad - ctr (1) == 0 0.5311 0.1418 3.74 0.0049 **
Cab - ctr (1) == 0 0.7512 0.1251 6.01 <0.001 ***
Doc - ctr (1) == 0 0.6443 0.1216 5.30 <0.001 ***
Abi - Enz (1) == 0 -0.1153 0.1980 -0.58 0.9999
Rad - Enz (1) == 0 1.0323 0.1890 5.46 <0.001 ***
Cab - Enz (1) == 0 1.2525 0.1771 7.07 <0.001 ***
Doc - Enz (1) == 0 1.1456 0.1736 6.60 <0.001 ***
Rad - Abi (1) == 0 1.1477 0.1861 6.17 <0.001 ***
Cab - Abi (1) == 0 1.3678 0.1740 7.86 <0.001 ***
Doc - Abi (1) == 0 1.2609 0.1701 7.41 <0.001 ***
Cab - Rad (1) == 0 0.2201 0.1540 1.43 0.9110
Doc - Rad (1) == 0 0.1132 0.1519 0.75 0.9994
Doc - Cab (1) == 0 -0.1069 0.1364 -0.78 0.9990
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Adjusted p values reported -- single-step method)
exp(Est.) 2.5% 97.5%
Enz - ctr (0) 1.82 1.37 2.43
Abi - ctr (0) 1.31 0.95 1.80
Rad - ctr (0) 1.37 1.08 1.74
Cab - ctr (0) 1.65 1.26 2.17
Doc - ctr (0) 0.53 0.40 0.71
Abi - Enz (0) 0.72 0.49 1.04
Rad - Enz (0) 0.75 0.55 1.03
Cab - Enz (0) 0.91 0.65 1.27
Doc - Enz (0) 0.29 0.21 0.42
Rad - Abi (0) 1.05 0.74 1.48
Cab - Abi (0) 1.27 0.88 1.83
Doc - Abi (0) 0.41 0.28 0.60
Cab - Rad (0) 1.21 0.89 1.63
Doc - Rad (0) 0.39 0.28 0.53
Doc - Cab (0) 0.32 0.23 0.45
Enz - ctr (1) 0.61 0.44 0.83
Abi - ctr (1) 0.54 0.40 0.74
Rad - ctr (1) 1.70 1.29 2.25
Cab - ctr (1) 2.12 1.66 2.71
Doc - ctr (1) 1.90 1.50 2.42
Abi - Enz (1) 0.89 0.60 1.31
Rad - Enz (1) 2.81 1.94 4.07
Cab - Enz (1) 3.50 2.47 4.95
Doc - Enz (1) 3.14 2.24 4.42
Rad - Abi (1) 3.15 2.19 4.54
Cab - Abi (1) 3.93 2.79 5.52
Doc - Abi (1) 3.53 2.53 4.92
Cab - Rad (1) 1.25 0.92 1.69
Doc - Rad (1) 1.12 0.83 1.51
Doc - Cab (1) 0.90 0.69 1.17