ProBio: Assessing Operating Characteristics via Simulations

September 19, 2018

Alessio Crippa
Department of Medical Epidemiology and Biostatistics
Karolinska Institutet

Outline


  • Changes in the parameters of the simulation design

  • Updated results

Prevalences of diseases subtypes and signatures

   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

Assumed progression free survival times

\( T_{ixk} \sim Weibull(\textrm{shape} = 2, \textrm{scale}_{xk}) \)
\( i = 1, \dots, n_{xk}, \;\; \) \( x = 2, \dots, 6 \; \) \( k = 1, \dots, 15 \)

Mean PFS: 3.5 months for an ineffective treatment (median 3.3)

Mean PFS: 7.1 months for an effective treatment, HR: 2 (median 6.7)

Waiting for more data

Results 1: No treatment effective in any subtype


True mean PF times

     Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
----          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       3.5

Average Number of Participants by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                  144         144        146         144       145
TP53- & AR-           75          75         74          74        74
TP53+ | AR+           69          69         72          70        71
DRD+                  36          37         37          36        37
DRD-                 108         107        109         108       108
TEfus+                46          46         49          47        47
TEfus-                98          98         97          98        98

Graduation Probabilities

             p1    p2
Enzalutamide  0 0.040
Abiraterone   0 0.020
Radium.223    0 0.020
Cabazitaxel   0 0.020
Docetaxel     0 0.045

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                0.060       0.061      0.059       0.061     0.060
TP53- & AR-        0.157       0.169      0.156       0.163     0.160
TP53+ | AR+        0.098       0.098      0.097       0.098     0.095
DRD+               0.156       0.160      0.164       0.164     0.159
DRD-               0.097       0.100      0.092       0.096     0.093
TEfus+             0.136       0.140      0.135       0.138     0.133
TEfus-             0.119       0.122      0.117       0.122     0.119

Results 1: No treatment effective in any subtype

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                 0.00       0.000      0.000       0.000     0.000
TP53- & AR-         0.04       0.020      0.010       0.015     0.030
TP53+ | AR+         0.00       0.000      0.000       0.000     0.000
DRD+                0.00       0.000      0.000       0.000     0.000
DRD-                0.00       0.005      0.015       0.000     0.015
TEfus+              0.00       0.000      0.000       0.000     0.000
TEfus-              0.00       0.000      0.005       0.005     0.005

Results 2: Abiraterone effective in all subtypes, other treatments ineffective


True mean PF times

     Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
----          3.5         7.1        3.5         3.5       3.5
---+          3.5         7.1        3.5         3.5       3.5
--+-          3.5         7.1        3.5         3.5       3.5
--++          3.5         7.1        3.5         3.5       3.5
-+--          3.5         7.1        3.5         3.5       3.5
-+-+          3.5         7.1        3.5         3.5       3.5
-++-          3.5         7.1        3.5         3.5       3.5
-+++          3.5         7.1        3.5         3.5       3.5
+---          3.5         7.1        3.5         3.5       3.5
+--+          3.5         7.1        3.5         3.5       3.5
+-+-          3.5         7.1        3.5         3.5       3.5
+-++          3.5         7.1        3.5         3.5       3.5
++--          3.5         7.1        3.5         3.5       3.5
++-+          3.5         7.1        3.5         3.5       3.5
+++-          3.5         7.1        3.5         3.5       3.5

Average Number of Participants by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                  149          78        150         150       151
TP53- & AR-           78          43         76          77        76
TP53+ | AR+           71          35         75          74        75
DRD+                  40          17         41          40        41
DRD-                 109          62        109         110       109
TEfus+                49          23         51          50        51
TEfus-               100          55         99         100        99

Graduation Probabilities

               p1    p2
Enzalutamide 0.00 0.000
Abiraterone  0.69 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        11.3         24          24        24
TP53- & AR-           24        19.7         24          24        24
TP53+ | AR+           24        23.6         24          24        24
DRD+                  24        23.9         24          24        24
DRD-                  24         7.9         24          24        24
TEfus+                24        23.7         24          24        24
TEfus-                24        14.2         24          24        24

Probability of superiority by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                0.017        0.84      0.015       0.015     0.015
TP53- & AR-        0.065        0.90      0.059       0.052     0.057
TP53+ | AR+        0.047        0.66      0.043       0.044     0.044
DRD+               0.116        0.51      0.104       0.103     0.106
DRD-               0.026        0.92      0.025       0.024     0.026
TEfus+             0.077        0.69      0.066       0.071     0.071
TEfus-             0.049        0.81      0.048       0.044     0.045

Results 2: Abiraterone effective in all subtypes, other treatments ineffective

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                    0       0.695          0       0.000         0
TP53- & AR-            0       0.300          0       0.005         0
TP53+ | AR+            0       0.025          0       0.000         0
DRD+                   0       0.030          0       0.000         0
DRD-                   0       0.880          0       0.000         0
TEfus+                 0       0.030          0       0.000         0
TEfus-                 0       0.545          0       0.000         0

Results 3: Abiraterone effective for TP53- & AR (prev = 0.50), other treatments ineffective


True mean PF times

     Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
----          3.5         7.1        3.5         3.5       3.5
---+          3.5         7.1        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         7.1        3.5         3.5       3.5
-+-+          3.5         7.1        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

Average Number of Participants by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                  150         114        148         147       148
TP53- & AR-           78          55         75          75        76
TP53+ | AR+           72          59         74          72        72
DRD+                  39          22         40          39        39
DRD-                 110          92        109         109       109
TEfus+                50          39         49          48        48
TEfus-                99          75         99          99       100

Graduation Probabilities

              p1    p2
Enzalutamide 0.0 0.015
Abiraterone  0.9 0.085
Radium.223   0.0 0.010
Cabazitaxel  0.0 0.010
Docetaxel    0.0 0.015

Graduation Times by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                   24        22.2         24          24        24
TP53- & AR-           24         9.6         24          24        24
TP53+ | AR+           24        24.0         24          24        24
DRD+                  24        24.0         24          24        24
DRD-                  24        18.8         24          24        24
TEfus+                24        24.0         24          24        24
TEfus-                24        17.3         24          24        24

Probability of superiority by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                0.032        0.40      0.033       0.030     0.033
TP53- & AR-        0.058        0.92      0.058       0.052     0.057
TP53+ | AR+        0.089        0.13      0.095       0.089     0.094
DRD+               0.124        0.34      0.136       0.119     0.138
DRD-               0.056        0.52      0.053       0.055     0.051
TEfus+             0.117        0.34      0.110       0.100     0.104
TEfus-             0.064        0.51      0.076       0.072     0.077

Results 3: Abiraterone effective for TP53- & AR (prev = 0.50), other treatments ineffective

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                0.000        0.10      0.000        0.00     0.000
TP53- & AR-        0.010        0.90      0.005        0.01     0.010
TP53+ | AR+        0.000        0.00      0.000        0.00     0.000
DRD+               0.000        0.00      0.000        0.00     0.000
DRD-               0.000        0.29      0.005        0.00     0.000
TEfus+             0.000        0.00      0.000        0.00     0.000
TEfus-             0.005        0.39      0.000        0.00     0.005

Results 4: Mixed of effective treatments


True mean PF times

     Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
----          7.1         7.1        3.5         3.5       3.5
---+          7.1         7.1        3.5         3.5       7.1
--+-          3.5         3.5        3.5         3.5       3.5
--++          3.5         3.5        3.5         3.5       7.1
-+--          7.1         7.1        3.5         3.5       3.5
-+-+          7.1         7.1        3.5         3.5       7.1
-++-          3.5         3.5        3.5         3.5       3.5
-+++          3.5         3.5        3.5         3.5       7.1
+---          3.5         3.5        3.5         3.5       3.5
+--+          3.5         3.5        3.5         3.5       7.1
+-+-          3.5         3.5        3.5         3.5       3.5
+-++          3.5         3.5        3.5         3.5       7.1
++--          3.5         3.5        3.5         3.5       3.5
++-+          3.5         3.5        3.5         3.5       7.1
+++-          3.5         3.5        3.5         3.5       3.5

Average Number of Participants by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                  129         130        152         150       152
TP53- & AR-           64          64         75          72        69
TP53+ | AR+           65          65         77          78        82
DRD+                  26          25         42          41        45
DRD-                 104         105        110         109       107
TEfus+                37          38         54          55        59
TEfus-                92          92         98          95        93

Graduation Probabilities

               p1    p2
Enzalutamide 0.92 0.005
Abiraterone  0.90 0.020
Radium.223   0.00 0.000
Cabazitaxel  0.00 0.000
Docetaxel    0.78 0.020

Graduation Times by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                 24.0        23.9         24          24        24
TP53- & AR-          9.2         9.7         24          23        23
TP53+ | AR+         24.0        24.0         24          24        24
DRD+                24.0        24.0         24          24        24
DRD-                23.4        23.8         24          24        24
TEfus+              24.0        24.0         24          24        14
TEfus-              22.6        22.1         24          24        24

Probability of superiority by Signature

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                0.175       0.168     0.0060      0.0052     0.429
TP53- & AR-        0.682       0.692     0.0103      0.0064     0.337
TP53+ | AR+        0.068       0.059     0.0503      0.0513     0.504
DRD+               0.252       0.252     0.0809      0.0688     0.335
DRD-               0.238       0.218     0.0096      0.0114     0.566
TEfus+             0.145       0.131     0.0275      0.0253     0.873
TEfus-             0.388       0.388     0.0396      0.0369     0.061

Results 4: Mixed of effective treatments

            Enzalutamide Abiraterone Radium 223 Cabazitaxel Docetaxel
all                0.000       0.005          0           0     0.000
TP53- & AR-        0.925       0.895          0           0     0.055
TP53+ | AR+        0.000       0.000          0           0     0.010
DRD+               0.000       0.000          0           0     0.000
DRD-               0.035       0.015          0           0     0.015
TEfus+             0.000       0.000          0           0     0.780
TEfus-             0.080       0.110          0           0     0.000