Alessio Crippa
Department of Medical Epidemiology and Biostatistics
Karolinska Institutet
Describe the design of the study and illustrate the simulation settings
Present the preliminary results (N = 200)
Explicit the hypothesis
Next steps
Determine if treatment assignment based on a biomarker signature can improve Progression Free Survival (PFS) compared to standard of care
ARA DRD TP53 TEfus prev (%)
1 - + + + 0.5
2 - - + + 15.0
3 + + - + 5.0
4 - + - + 0.5
5 + - - + 7.0
6 - - - + 4.0
7 - + + - 3.0
8 - - + - 18.0
9 + + - - 7.0
10 - + - - 3.0
11 + - - - 32.0
12 - - - - 5.0
signatures -+++ --++ ++-+ -+-+ +--+ ---+ -++- --+- ++-- -+-- +--- ---- prev
1 all X X X X X X X X X X X X 1.00
2 ARA+ X X X X 0.51
3 ARA- X X X X X X X X 0.49
4 DRD+ X X X X X X 0.19
5 DRD- X X X X X X 0.81
6 TP53+ X X X X 0.36
7 TP53- X X X X X X X X 0.64
8 TEfus+ X X X X X X 0.32
9 TEfus- X X X X X X 0.68
Enter participants in a simulated trial:
Simulate partipants' subtypes (based on observed prevalences)
Assign treatment within each subtype, according to probability of superiority (initially equal randomization)
The control group had probabilities 33%, 33%, 11%, 11%, 11% of receiving treatment Enzalutamide, Abiraterone, Radium 223, Cabazitaxel, Docetaxel respectively
Simulate outcome: PFS according to selected scenarios
Update probability of superiority within subtypes
Update probability of superiority within signatures (deciding for early stopping)
Update randomization probabilities based on the quantities calculated in 4
Repeat 1-6 until stopping rules are met, or after reaching maximum number of patients (100) within each signature
Maximum trial duration (24 months)
\( T_{ixk} \sim Exp(\lambda_{xk}) \)
\( i = 1, \dots, n_{xk}, \;\; \) \( x = 2, \dots, 6 \; \) \( k = 1, \dots, 12 \)
Distributional assumption: \( \mu_{xk} = \frac{1}{\lambda_{xk}} \sim IG(\alpha_{xk}, \beta_{xk}) \)
Observed data: censored survival times \( t_{ixk} \) and event indicators \( \delta_{ixk} \)
Update parameters of prior distribution: \( \alpha_{xk}' = \alpha_{xk} + \sum_i \delta_{ixk} \) and \( \beta_{xk}' = \beta_{xk} + \sum_i t_{ixk} \)
Compare the mean PFS times \( \mu_{xk} \) within each subtype by computing (update randomization probabilities)
\( p_{xk} = Pr(\mu_{xk} - \mu_{1k} \ge d | data) \)
\( x = 2, \dots, 6 \), \( k = 1, \dots, 12 \)
Compare the mean PFS times \( \mu_{xl} \) within each signature by computing (deciding for early stopping)
\( p_{xl} = Pr(\mu_{xl} - \mu_{1l} \ge d | data) \)
\( x = 2, \dots, 6 \), \( l = 1, \dots, 9 \)
Futility:
Graduation:
Stop randomization:
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.002 0.000 0.164 0.090 0.000
ARA+ 0.007 0.082 0.981 0.299 0.005
ARA- 0.003 0.000 0.003 0.092 0.008
DRD+ 0.022 0.128 0.244 0.413 0.059
DRD- 0.001 0.000 0.229 0.043 0.004
TP53+ 0.012 0.010 0.008 0.195 0.011
TP53- 0.004 0.007 0.623 0.144 0.007
TEfus+ 0.046 0.045 0.210 0.475 0.019
TEfus- 0.000 0.000 0.269 0.029 0.004
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
-+++ 0.299 0.419 0.321 0.408 0.346
--++ 0.076 0.003 0.007 0.166 0.000
++-+ 0.276 0.789 0.404 0.942 0.447
-+-+ 0.165 0.106 0.175 0.135 0.165
+--+ 0.603 0.591 0.959 0.727 0.288
---+ 0.091 0.150 0.388 0.711 0.195
-++- 0.280 0.274 0.323 0.691 0.213
--+- 0.009 0.033 0.002 0.049 0.186
++-- 0.017 0.299 0.824 0.172 0.036
-+-- 0.227 0.152 0.156 0.376 0.382
+--- 0.000 0.000 0.929 0.008 0.000
---- 0.204 0.089 0.123 0.146 0.195
No treatment effective in any subtype
Radium 223 effective in all subtypes, other treatments ineffective
Radium 223 effective for ARA+ (prev = 0.51), other treatments ineffective
Enzalutamide effective for ARA+, other treatments ineffective
As in 4., but with Enzalutamide representing 75% of the control group
Assumed PFS times (and definition of control group)
Average number of enrolled participants
Graduation times for each treatments
Power (percentage of times we graduated a treatment for the true biomarker signature)
False-positive rate (percentage of times that a treatment graduated only for a signature that didn't benefit)
Graduation times for each signature
Probability of superiority for each signature
True PFS times
$mi_gx
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
-+++ 6 6 6 6 6
--++ 6 6 6 6 6
++-+ 6 6 6 6 6
-+-+ 6 6 6 6 6
+--+ 6 6 6 6 6
---+ 6 6 6 6 6
-++- 6 6 6 6 6
--+- 6 6 6 6 6
++-- 6 6 6 6 6
-+-- 6 6 6 6 6
+--- 6 6 6 6 6
---- 6 6 6 6 6
$p_ctr
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
0.33 0.33 0.11 0.11 0.11
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 161 164 162 164 164
ARA+ 80 79 79 81 78
ARA- 81 84 83 82 86
DRD+ 80 79 79 81 78
DRD- 81 84 83 82 86
TP53+ 61 64 63 63 65
TP53- 101 99 98 100 99
TEfus+ 57 59 57 59 59
TEfus- 104 104 105 104 105
Graduation Probabilities
p1 p2
Enzalutamide 0 0.075
Abiraterone 0 0.075
Radium.223 0 0.040
Cabazitaxel 0 0.040
Docetaxel 0 0.055
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 24 24 24
ARA+ 23 23 22 23 23
ARA- 24 24 24 24 24
DRD+ 24 24 24 24 24
DRD- 24 24 24 24 24
TP53+ 24 24 24 24 24
TP53- 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 0.08 0.072 0.063 0.072 0.083
ARA+ 0.19 0.182 0.160 0.156 0.182
ARA- 0.12 0.113 0.106 0.122 0.126
DRD+ 0.15 0.144 0.139 0.146 0.172
DRD- 0.15 0.150 0.111 0.137 0.134
TP53+ 0.17 0.169 0.179 0.200 0.194
TP53- 0.13 0.119 0.095 0.104 0.118
TEfus+ 0.15 0.149 0.142 0.154 0.166
TEfus- 0.14 0.130 0.114 0.129 0.138
True PFS times
$mi_gx
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
-+++ 6 6 12 6 6
--++ 6 6 12 6 6
++-+ 6 6 12 6 6
-+-+ 6 6 12 6 6
+--+ 6 6 12 6 6
---+ 6 6 12 6 6
-++- 6 6 12 6 6
--+- 6 6 12 6 6
++-- 6 6 12 6 6
-+-- 6 6 12 6 6
+--- 6 6 12 6 6
---- 6 6 12 6 6
$p_ctr
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
0.33 0.33 0.11 0.11 0.11
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 161 163 143 162 161
ARA+ 75 76 72 77 75
ARA- 86 86 71 85 87
DRD+ 75 76 72 77 75
DRD- 86 86 71 85 87
TP53+ 64 65 57 64 65
TP53- 97 98 86 98 96
TEfus+ 58 59 51 60 60
TEfus- 103 103 92 102 102
Graduation Probabilities
p1 p2
Enzalutamide 0.00 0.040
Abiraterone 0.00 0.025
Radium.223 0.88 0.000
Cabazitaxel 0.00 0.055
Docetaxel 0.00 0.040
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 22 24 24
ARA+ 22 22 17 23 22
ARA- 24 24 21 24 24
DRD+ 24 24 23 24 24
DRD- 24 24 17 24 23
TP53+ 24 24 20 24 24
TP53- 24 24 22 24 24
TEfus+ 24 24 22 24 24
TEfus- 24 24 19 24 23
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.017 0.011 0.97 0.017 0.0084
ARA+ 0.051 0.063 0.95 0.066 0.0500
ARA- 0.048 0.033 0.87 0.048 0.0330
DRD+ 0.086 0.083 0.63 0.093 0.0919
DRD- 0.030 0.018 0.99 0.034 0.0186
TP53+ 0.083 0.069 0.89 0.098 0.0638
TP53- 0.034 0.032 0.91 0.032 0.0294
TEfus+ 0.063 0.056 0.84 0.081 0.0589
TEfus- 0.043 0.047 0.94 0.043 0.0318
True PFS times
$mi_gx
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
-+++ 6 6 6 6 6
--++ 6 6 6 6 6
++-+ 6 6 12 6 6
-+-+ 6 6 6 6 6
+--+ 6 6 12 6 6
---+ 6 6 6 6 6
-++- 6 6 6 6 6
--+- 6 6 6 6 6
++-- 6 6 12 6 6
-+-- 6 6 6 6 6
+--- 6 6 12 6 6
---- 6 6 6 6 6
$p_ctr
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
0.33 0.33 0.11 0.11 0.11
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 163 162 153 162 163
ARA+ 76 76 78 77 77
ARA- 88 86 75 86 86
DRD+ 76 76 78 77 77
DRD- 88 86 75 86 86
TP53+ 67 64 58 64 65
TP53- 97 98 94 98 98
TEfus+ 61 58 52 59 61
TEfus- 102 104 101 103 102
Graduation Probabilities
p1 p2
Enzalutamide 0.0 0.040
Abiraterone 0.0 0.040
Radium.223 0.6 0.030
Cabazitaxel 0.0 0.035
Docetaxel 0.0 0.050
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 24 24 24
ARA+ 22 23 15 23 23
ARA- 24 24 24 24 24
DRD+ 24 24 23 24 24
DRD- 24 24 23 24 24
TP53+ 24 24 24 24 24
TP53- 24 24 23 24 24
TEfus+ 24 24 24 24 24
TEfus- 24 24 23 24 24
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.032 0.038 0.58 0.042 0.026
ARA+ 0.069 0.056 0.95 0.071 0.054
ARA- 0.108 0.117 0.12 0.127 0.104
DRD+ 0.117 0.113 0.40 0.147 0.105
DRD- 0.071 0.072 0.68 0.072 0.058
TP53+ 0.181 0.178 0.20 0.199 0.168
TP53- 0.047 0.050 0.77 0.056 0.044
TEfus+ 0.116 0.121 0.40 0.141 0.092
TEfus- 0.070 0.068 0.69 0.076 0.074
True PFS times
$mi_gx
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
-+++ 6 6 6 6 6
--++ 6 6 6 6 6
++-+ 12 6 6 6 6
-+-+ 6 6 6 6 6
+--+ 12 6 6 6 6
---+ 6 6 6 6 6
-++- 6 6 6 6 6
--+- 6 6 6 6 6
++-- 12 6 6 6 6
-+-- 6 6 6 6 6
+--- 12 6 6 6 6
---- 6 6 6 6 6
$p_ctr
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
0.33 0.33 0.11 0.11 0.11
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 160 156 154 154 156
ARA+ 83 73 73 72 73
ARA- 78 83 81 82 82
DRD+ 83 73 73 72 73
DRD- 78 83 81 82 82
TP53+ 62 62 60 62 61
TP53- 98 95 94 92 95
TEfus+ 57 56 56 53 55
TEfus- 103 101 99 101 100
Graduation Probabilities
p1 p2
Enzalutamide 0.41 0.055
Abiraterone 0.00 0.005
Radium.223 0.00 0.010
Cabazitaxel 0.00 0.030
Docetaxel 0.00 0.015
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 24 24 24
ARA+ 18 21 21 21 21
ARA- 24 24 24 24 24
DRD+ 24 24 24 24 24
DRD- 24 22 22 22 22
TP53+ 24 24 24 23 24
TP53- 23 24 24 24 24
TEfus+ 24 24 24 24 24
TEfus- 23 24 23 24 23
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.65 0.034 0.032 0.032 0.033
ARA+ 0.97 0.049 0.065 0.054 0.055
ARA- 0.13 0.121 0.100 0.117 0.120
DRD+ 0.41 0.130 0.123 0.115 0.124
DRD- 0.78 0.069 0.066 0.076 0.066
TP53+ 0.22 0.173 0.163 0.190 0.168
TP53- 0.81 0.045 0.049 0.042 0.043
TEfus+ 0.51 0.111 0.104 0.108 0.099
TEfus- 0.69 0.072 0.071 0.075 0.077
True PFS times
$mi_gx
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
-+++ 6 6 6 6 6
--++ 6 6 6 6 6
++-+ 12 6 6 6 6
-+-+ 6 6 6 6 6
+--+ 12 6 6 6 6
---+ 6 6 6 6 6
-++- 6 6 6 6 6
--+- 6 6 6 6 6
++-- 12 6 6 6 6
-+-- 6 6 6 6 6
+--- 12 6 6 6 6
---- 6 6 6 6 6
$p_ctr
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
0.750 0.083 0.056 0.056 0.056
Average Number of Participants by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 158 146 142 147 144
ARA+ 89 58 55 60 58
ARA- 69 88 87 87 86
DRD+ 89 58 55 60 58
DRD- 69 88 87 87 86
TP53+ 56 63 63 64 64
TP53- 102 83 79 83 80
TEfus+ 56 54 54 56 54
TEfus- 102 91 88 90 90
Graduation Probabilities
p1 p2
Enzalutamide 0.23 0.005
Abiraterone 0.00 0.000
Radium.223 0.00 0.000
Cabazitaxel 0.00 0.000
Docetaxel 0.00 0.000
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 24 24 24
ARA+ 20 17 16 16 16
ARA- 24 24 24 24 24
DRD+ 24 24 24 24 24
DRD- 24 23 22 23 23
TP53+ 24 24 24 24 24
TP53- 24 24 24 24 24
TEfus+ 24 24 24 24 24
TEfus- 24 23 22 22 22
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.65 0.037 0.033 0.038 0.028
ARA+ 0.97 0.052 0.038 0.058 0.042
ARA- 0.12 0.131 0.128 0.137 0.119
DRD+ 0.45 0.125 0.109 0.109 0.101
DRD- 0.73 0.067 0.071 0.089 0.066
TP53+ 0.22 0.182 0.181 0.195 0.176
TP53- 0.81 0.048 0.038 0.046 0.036
TEfus+ 0.53 0.099 0.109 0.120 0.097
TEfus- 0.67 0.091 0.065 0.075 0.074
PFS scenarios:
General settings:
Decision rules:
Number of simulations: N = 200
Extend simulation to investigate
SMART design:
Effectiveness (current practice) vs efficacy: