Sanofi presentation
Durbadal Ghosh
2023-06-20
Simulation Results
Setup
Number of time interval is 8
MCMC iterations = 5000, Number of Chains = 2
Proportional hazard models
Equal Event Rates for Historical Data
Setup
Event Rate for historical data = 0.3
Event Rate for current data = 0.3
HR for historical data =0.6
HR for current data =0.6
Sample size for historical data =800
Sample size for current data =900
Tables
## Time_Int True HR Est_HR 5%_est_HR 95%_est_HR cox_HR Est_HR_borrow
## [1,] 1 0.6 0.6262723 0.4224158 0.9421768 0.6269876 0.6351524
## [2,] 2 0.6 0.6582519 0.4095119 1.0309835 0.6584178 0.6678336
## [3,] 3 0.6 0.6017352 0.3660200 0.9545976 0.6021226 0.6127302
## [4,] 4 0.6 0.6413781 0.3521869 1.0015094 0.6419785 0.6537163
## [5,] 5 0.6 0.6415007 0.3322103 1.0511746 0.6410855 0.6505167
## [6,] 6 0.6 0.6543227 0.3157534 1.0355099 0.6538766 0.6666931
## [7,] 7 0.6 0.6492380 0.3523447 1.0517613 0.6507111 0.6600200
## [8,] 8 0.6 0.6793119 0.3423537 1.2115969 0.6782697 0.6882511
## 5%_y_est_HR 95%_y_est_HR
## [1,] 0.4324312 0.9172447
## [2,] 0.4198885 1.0078552
## [3,] 0.3817849 0.9635884
## [4,] 0.3817810 0.9991035
## [5,] 0.3489675 1.0664518
## [6,] 0.3300194 0.9978377
## [7,] 0.3887578 1.0057411
## [8,] 0.3687186 1.1416212Bias
HR estimation
Event rates for current data is greater than the event rates for true/usual (historical) data.
Setup
Event Rate for historical data = 0.3
Event Rate for current data = 0.4
HR for historical data =0.6
HR for current data =0.6
Sample size for historical data =800
Sample size for current data =900
Tables
## Time_Int True HR Est_HR 5%_est_HR 95%_est_HR cox_HR Est_HR_borrow
## [1,] 1 0.6 0.6233981 0.4511261 0.8363525 0.6231557 0.6692790
## [2,] 2 0.6 0.6220302 0.4160930 0.9291435 0.6219083 0.6653315
## [3,] 3 0.6 0.6206975 0.3870406 0.9029128 0.6214206 0.6687640
## [4,] 4 0.6 0.6157674 0.4011699 0.9323714 0.6158206 0.6668540
## [5,] 5 0.6 0.6194539 0.3563194 0.8983480 0.6191717 0.6693557
## [6,] 6 0.6 0.6334969 0.3915588 1.1217408 0.6332312 0.6922785
## [7,] 7 0.6 0.6349140 0.3776134 0.9674411 0.6349776 0.7021818
## [8,] 8 0.6 0.6780703 0.3597402 1.0870007 0.6786205 0.7423400
## 5%_y_est_HR 95%_y_est_HR
## [1,] 0.4726092 0.8885987
## [2,] 0.4326146 0.9594580
## [3,] 0.4121570 1.0158464
## [4,] 0.4256111 0.9653060
## [5,] 0.3707004 0.9916584
## [6,] 0.4239015 1.1542953
## [7,] 0.4270339 1.0696849
## [8,] 0.3896620 1.2267948Bias
HR estimation
Event rates for current data is lower than the event rates for true/usual (historical) data.
Setup
Event Rate for historical data = 0.3
Event Rate for current data = 0.25
HR for historical data =0.6
HR for current data =0.6
Sample size for historical data =900
Sample size for current data =900
Tables
## Time_Int True HR Est_HR 5%_est_HR 95%_est_HR cox_HR Est_HR_borrow
## [1,] 1 0.6 0.6077887 0.3947382 0.8627060 0.6079796 0.5793919
## [2,] 2 0.6 0.6565594 0.4326266 0.9163769 0.6566531 0.6323982
## [3,] 3 0.6 0.6437558 0.3516121 1.0108220 0.6440839 0.6220166
## [4,] 4 0.6 0.6262344 0.3753594 0.9118636 0.6263961 0.6203086
## [5,] 5 0.6 0.6170303 0.3307877 1.0840495 0.6169368 0.6123612
## [6,] 6 0.6 0.6546694 0.3743803 1.0872543 0.6546788 0.6621578
## [7,] 7 0.6 0.6793174 0.3229004 1.2464561 0.6788342 0.6948763
## [8,] 8 0.6 0.6528191 0.3142469 1.1808945 0.6533926 0.6757409
## 5%_y_est_HR 95%_y_est_HR
## [1,] 0.3688648 0.8450003
## [2,] 0.4159021 0.8832484
## [3,] 0.3497376 0.9844081
## [4,] 0.3803740 0.8954898
## [5,] 0.3511892 1.0435563
## [6,] 0.3919356 1.1954479
## [7,] 0.3550455 1.3106007
## [8,] 0.3470871 1.2538429Bias
HR estimation
Non-Proportional hazard models
Equal Event Rates for Historical Data
Setup
Event Rate for historical data = 0.3
Event Rate for current data = 0.3
HR for historical data =0.6, 0.4
HR for current data =0.6, 0.4
Sample size for historical data = 800
Sample size for current data = 900
Tables
## Time_Int True HR Est_HR 5%_est_HR 95%_est_HR cox_HR Est_HR_borrow
## [1,] 1 0.9 0.9392929 0.6403865 1.3771834 0.9402050 0.9569987
## [2,] 2 0.9 0.9412777 0.7060575 1.4050062 0.9414951 0.9652451
## [3,] 3 0.6 0.6342978 0.3866306 0.9736019 0.6338602 0.6405491
## [4,] 4 0.6 0.6207246 0.3625493 0.9528250 0.6208712 0.6283158
## [5,] 5 0.6 0.6319010 0.3258246 0.9366568 0.6323435 0.6504819
## [6,] 6 0.6 0.6390416 0.3659963 1.1109447 0.6395110 0.6497869
## [7,] 7 0.6 0.6532937 0.3549605 1.1219127 0.6532828 0.6733605
## [8,] 8 0.6 0.6485214 0.3583650 1.0963829 0.6493011 0.6701435
## 5%_y_est_HR 95%_y_est_HR
## [1,] 0.6784414 1.3760126
## [2,] 0.7072333 1.3832263
## [3,] 0.3993213 1.0087298
## [4,] 0.3937601 0.9417595
## [5,] 0.3282611 1.0741855
## [6,] 0.3854399 1.0711034
## [7,] 0.3748896 1.1786802
## [8,] 0.3801997 1.1185199Bias
HR estimation
Event rates for current data is greater than the event rates for true/usual (historical) data
Setup
Event Rate for historical data = 0.3
Event Rate for current data = 0.4
HR for historical data =0.6, 0.4
HR for current data =0.6, 0.4
Sample size for historical data = 800
Sample size for current data = 900
Tables
## Time_Int True HR Est_HR 5%_est_HR 95%_est_HR cox_HR Est_HR_borrow
## [1,] 1 0.9 0.9313349 0.6641617 1.2293114 0.9316268 1.0003032
## [2,] 2 0.9 0.9282126 0.6109323 1.3748837 0.9280659 0.9944413
## [3,] 3 0.6 0.6248056 0.3954876 0.8957159 0.6243848 0.6718724
## [4,] 4 0.6 0.6186859 0.3952936 0.9560129 0.6185068 0.6688152
## [5,] 5 0.6 0.6160705 0.3534927 0.8806196 0.6163151 0.6658858
## [6,] 6 0.6 0.6343815 0.3724007 1.1334172 0.6346638 0.6936094
## [7,] 7 0.6 0.6320211 0.3776346 1.0005613 0.6310615 0.6980989
## [8,] 8 0.6 0.6772826 0.3482383 1.0986099 0.6788463 0.7424516
## 5%_y_est_HR 95%_y_est_HR
## [1,] 0.6975733 1.3431221
## [2,] 0.6476169 1.4791851
## [3,] 0.4158897 0.9949328
## [4,] 0.4318449 1.0103563
## [5,] 0.3679884 0.9791280
## [6,] 0.4074217 1.1324861
## [7,] 0.4239607 1.0918633
## [8,] 0.3829745 1.1992181Bias
HR estimation
Event rates for current data is lower than the event rates for true/usual (historical) data
Setup
Event Rate for historical data = 0.3
Event Rate for current data = 0.25
HR for historical data =0.6, 0.4
HR for current data =0.6, 0.4
Sample size for historical data = 800
Sample size for current data = 900
Tables
## Time_Int True HR Est_HR 5%_est_HR 95%_est_HR cox_HR Est_HR_borrow
## [1,] 1 0.9 0.9409496 0.5937264 1.3552388 0.9408852 0.8972136
## [2,] 2 0.9 0.9556685 0.6487346 1.4342293 0.9550902 0.9180057
## [3,] 3 0.6 0.6460053 0.3598721 1.0175902 0.6456314 0.6241308
## [4,] 4 0.6 0.6290101 0.3709885 0.9609838 0.6289864 0.6227141
## [5,] 5 0.6 0.6179912 0.3354584 1.1047419 0.6167216 0.6128929
## [6,] 6 0.6 0.6520069 0.3720471 1.1219569 0.6519702 0.6593842
## [7,] 7 0.6 0.6843680 0.3239721 1.2957890 0.6850730 0.7005224
## [8,] 8 0.6 0.6536861 0.3268332 1.1953146 0.6539861 0.6779432
## 5%_y_est_HR 95%_y_est_HR
## [1,] 0.5908943 1.3401549
## [2,] 0.6362803 1.3280308
## [3,] 0.3617479 0.9482513
## [4,] 0.3727634 0.9406897
## [5,] 0.3534999 1.0394797
## [6,] 0.3827467 1.0847017
## [7,] 0.3443625 1.3860134
## [8,] 0.3503105 1.3131275Bias
HR estimation
