ProBio: Assessing Operating Characteristics via Simulations
August 14, 2018
Alessio Crippa
Department of Medical Epidemiology and Biostatistics
Karolinska Institutet
Outline
Update in the simulation design
Check individual simulations
Updated results
Updates in the simulation design
http://rpubs.com/alecri/probio_sim
decision rules (2. graduation):
- \( n_{xl} \ge 50 \)
- \( p_{xl} \ge 0.85 \)
- \( p_{xk} \ge 0.15 \; \forall l = 1, \dots, 9 \textrm{ and } \forall k \in l \)
- \( n_{xl} \ge 50 \)
reassigning patients whose tumor progressed
changing effect sizes in the survival model
Weibull Model
\( T_{ixk} \sim Weibull(\textrm{shape} = 2, \textrm{scale}_{xk}) \)
\( i = 1, \dots, n_{xk}, \;\; \) \( x = 2, \dots, 6 \; \) \( k = 1, \dots, 12 \)
The mean PFS time for an ineffective treatment is 5.32 months (median 5),
while it is 15.95 months for the active ones (median 14.99)
Check individual simulations: http://rpubs.com/alecri/check_sim4_1
Results 1: No treatment effective in any subtype
True mean PF times
$mi_gx
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
$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 163 164 166 164 164
ARA+ 81 81 79 82 80
ARA- 82 83 87 82 84
DRD+ 81 81 79 82 80
DRD- 82 83 87 82 84
TP53+ 62 63 66 62 64
TP53- 101 101 100 102 100
TEfus+ 59 58 60 59 60
TEfus- 105 106 106 105 105
Graduation Probabilities
p1 p2
Enzalutamide 0 0.095
Abiraterone 0 0.075
Radium.223 0 0.085
Cabazitaxel 0 0.085
Docetaxel 0 0.070
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 24 24 24
ARA+ 24 23 23 23 24
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 0.046 0.040 0.042 0.038 0.044
ARA+ 0.124 0.117 0.123 0.124 0.140
ARA- 0.091 0.081 0.083 0.077 0.082
DRD+ 0.118 0.111 0.112 0.113 0.124
DRD- 0.102 0.088 0.089 0.078 0.089
TP53+ 0.165 0.138 0.153 0.139 0.158
TP53- 0.075 0.074 0.073 0.071 0.079
TEfus+ 0.128 0.112 0.114 0.123 0.127
TEfus- 0.088 0.086 0.087 0.076 0.089
Results 2: Radium 223 effective in all subtypes, other treatments ineffective
True mean PF times
$mi_gx
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
-+++ 5.3 5.3 16 5.3 5.3
--++ 5.3 5.3 16 5.3 5.3
++-+ 5.3 5.3 16 5.3 5.3
-+-+ 5.3 5.3 16 5.3 5.3
+--+ 5.3 5.3 16 5.3 5.3
---+ 5.3 5.3 16 5.3 5.3
-++- 5.3 5.3 16 5.3 5.3
--+- 5.3 5.3 16 5.3 5.3
++-- 5.3 5.3 16 5.3 5.3
-+-- 5.3 5.3 16 5.3 5.3
+--- 5.3 5.3 16 5.3 5.3
---- 5.3 5.3 16 5.3 5.3
$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 166 170 89 169 168
ARA+ 77 77 48 78 77
ARA- 89 93 41 91 91
DRD+ 77 77 48 78 77
DRD- 89 93 41 91 91
TP53+ 67 70 33 70 69
TP53- 98 100 56 99 99
TEfus+ 62 66 26 66 63
TEfus- 103 105 63 104 105
Graduation Probabilities
p1 p2
Enzalutamide 0.00 0.040
Abiraterone 0.00 0.030
Radium.223 0.92 0.000
Cabazitaxel 0.00 0.030
Docetaxel 0.00 0.025
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 8.8 24 24
ARA+ 23 23 17.6 23 23
ARA- 24 24 19.0 24 24
DRD+ 24 24 21.7 24 24
DRD- 24 24 18.4 24 24
TP53+ 24 24 21.9 24 24
TP53- 24 24 16.3 24 24
TEfus+ 24 24 23.3 24 24
TEfus- 23 24 13.8 23 23
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.00086 0.0022 1.00 0.0026 0.0013
ARA+ 0.01062 0.0178 1.00 0.0176 0.0120
ARA- 0.01157 0.0167 0.95 0.0159 0.0144
DRD+ 0.05287 0.0562 0.72 0.0532 0.0503
DRD- 0.00167 0.0068 1.00 0.0048 0.0040
TP53+ 0.03188 0.0414 0.95 0.0395 0.0356
TP53- 0.00521 0.0090 0.99 0.0097 0.0065
TEfus+ 0.02857 0.0418 0.89 0.0342 0.0358
TEfus- 0.00492 0.0053 1.00 0.0084 0.0050
Results 3: Radium 223 effective for ARA+ (prev = 0.51), other treatments ineffective
True mean PF times
$mi_gx
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 16.0 5.3 5.3
-+-+ 5.3 5.3 5.3 5.3 5.3
+--+ 5.3 5.3 16.0 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 16.0 5.3 5.3
-+-- 5.3 5.3 5.3 5.3 5.3
+--- 5.3 5.3 16.0 5.3 5.3
---- 5.3 5.3 5.3 5.3 5.3
$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 169 168 120 165 167
ARA+ 81 80 58 79 79
ARA- 87 88 62 86 88
DRD+ 81 80 58 79 79
DRD- 87 88 62 86 88
TP53+ 66 66 51 64 66
TP53- 103 102 69 101 100
TEfus+ 63 62 38 61 62
TEfus- 106 106 81 104 105
Graduation Probabilities
p1 p2
Enzalutamide 0.00 0.045
Abiraterone 0.00 0.050
Radium.223 0.74 0.190
Cabazitaxel 0.00 0.055
Docetaxel 0.00 0.030
Graduation Times by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 24 24 21 24 24
ARA+ 23 23 11 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 14 24 24
TEfus+ 24 24 24 24 24
TEfus- 24 24 17 24 24
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.0071 0.0081 0.91 0.0077 0.011
ARA+ 0.0085 0.0144 1.00 0.0083 0.012
ARA- 0.0736 0.0731 0.12 0.0746 0.086
DRD+ 0.0663 0.0723 0.54 0.0691 0.073
DRD- 0.0163 0.0206 0.96 0.0172 0.024
TP53+ 0.1388 0.1364 0.20 0.1335 0.157
TP53- 0.0097 0.0123 0.97 0.0101 0.013
TEfus+ 0.0627 0.0719 0.56 0.0572 0.084
TEfus- 0.0194 0.0155 0.96 0.0218 0.017
Results 4: Enzalutamide effective for ARA+ (prev = 0.51), other treatments ineffective
True mean PF times
$mi_gx
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
++-+ 16.0 5.3 5.3 5.3 5.3
-+-+ 5.3 5.3 5.3 5.3 5.3
+--+ 16.0 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
++-- 16.0 5.3 5.3 5.3 5.3
-+-- 5.3 5.3 5.3 5.3 5.3
+--- 16.0 5.3 5.3 5.3 5.3
---- 5.3 5.3 5.3 5.3 5.3
$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 150 151 152 154 150
ARA+ 70 71 71 74 70
ARA- 80 80 81 80 80
DRD+ 70 71 71 74 70
DRD- 80 80 81 80 80
TP53+ 64 59 61 58 58
TP53- 86 91 92 95 92
TEfus+ 56 52 54 53 50
TEfus- 94 99 98 101 99
Graduation Probabilities
p1 p2
Enzalutamide 0.72 0.105
Abiraterone 0.00 0.005
Radium.223 0.00 0.005
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+ 12 18 19 19 18
ARA- 24 24 24 24 24
DRD+ 23 24 24 24 24
DRD- 24 22 22 22 21
TP53+ 24 24 24 24 24
TP53- 19 24 24 24 24
TEfus+ 24 24 24 24 24
TEfus- 21 23 24 24 23
Probability of superiority by Signature
Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all 0.96 0.0056 0.0060 0.0056 0.0072
ARA+ 1.00 0.0047 0.0056 0.0058 0.0067
ARA- 0.15 0.0864 0.0831 0.0799 0.0824
DRD+ 0.64 0.0658 0.0637 0.0666 0.0705
DRD- 0.98 0.0143 0.0190 0.0158 0.0164
TP53+ 0.23 0.1423 0.1481 0.1415 0.1394
TP53- 0.99 0.0076 0.0081 0.0070 0.0083
TEfus+ 0.75 0.0494 0.0624 0.0521 0.0548
TEfus- 0.98 0.0172 0.0141 0.0208 0.0203