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
## [1,] 1 0.6 0.6122858 0.3541147 0.8809254 0.6127045
## [2,] 2 0.6 0.6330012 0.3567026 0.9287781 0.6332369
## [3,] 3 0.6 0.6253671 0.3778519 0.9327721 0.6255042
## [4,] 4 0.6 0.6353167 0.3693025 1.0257595 0.6356602
## [5,] 5 0.6 0.6403124 0.3756853 1.0513067 0.6404287
## [6,] 6 0.6 0.6383754 0.3599452 1.0510177 0.6388835
## [7,] 7 0.6 0.6436431 0.3387878 1.1428774 0.6438613
## [8,] 8 0.6 0.6475877 0.3237641 1.1580211 0.6478710
## Est_HR_borrow
## [1,] 0.6189078
## [2,] 0.6178243
## [3,] 0.6116496
## [4,] 0.6434465
## [5,] 0.6439359
## [6,] 0.6293283
## [7,] 0.7116872
## [8,] 0.7109846Bias
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
## [1,] 1 0.6 0.6128024 0.4209642 0.8543661 0.6128577
## [2,] 2 0.6 0.6170422 0.3916010 0.8941404 0.6170642
## [3,] 3 0.6 0.6229371 0.4021110 0.9388623 0.6230421
## [4,] 4 0.6 0.6239814 0.3762303 0.9773094 0.6241219
## [5,] 5 0.6 0.6276665 0.3563083 0.9790538 0.6279829
## [6,] 6 0.6 0.6282223 0.3671664 1.0192130 0.6284702
## [7,] 7 0.6 0.6380099 0.3633080 1.0061365 0.6378667
## [8,] 8 0.6 0.6453266 0.3629871 1.1717160 0.6454285
## Est_HR_borrow
## [1,] 0.6511256
## [2,] 0.6566096
## [3,] 0.6620958
## [4,] 0.6785797
## [5,] 0.6884598
## [6,] 0.6798808
## [7,] 0.7111417
## [8,] 0.7355108Bias
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
## [1,] 1 0.6 0.6147608 0.3603036 0.9216107 0.6148990
## [2,] 2 0.6 0.6336919 0.3831456 0.9104772 0.6338210
## [3,] 3 0.6 0.6284179 0.3492131 1.0340624 0.6286859
## [4,] 4 0.6 0.6398435 0.3501594 0.9872208 0.6401729
## [5,] 5 0.6 0.6428885 0.3355981 1.1519909 0.6431702
## [6,] 6 0.6 0.6419535 0.3506648 1.1493039 0.6422353
## [7,] 7 0.6 0.6581935 0.3206350 1.1340437 0.6580438
## [8,] 8 0.6 0.6480507 0.3407553 1.1948866 0.6482052
## Est_HR_borrow
## [1,] 0.6018469
## [2,] 0.6217875
## [3,] 0.6221501
## [4,] 0.6304157
## [5,] 0.6367195
## [6,] 0.6344810
## [7,] 0.7068768
## [8,] 0.6898418Bias
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
## [1,] 1 0.6 0.6152606 0.3743334 0.8940532 0.6155454
## [2,] 2 0.6 0.6287820 0.3632231 0.9121388 0.6289674
## [3,] 3 0.4 0.4163445 0.2398441 0.6802538 0.4166212
## [4,] 4 0.4 0.4243497 0.2176350 0.6902141 0.4246338
## [5,] 5 0.4 0.4215612 0.2128665 0.6568887 0.4220004
## [6,] 6 0.4 0.4272264 0.2294055 0.7260239 0.4275338
## [7,] 7 0.4 0.4348827 0.2158463 0.7481923 0.4354480
## [8,] 8 0.4 0.4380947 0.2207228 0.7858465 0.4386471
## Est_HR_borrow
## [1,] 0.6305303
## [2,] 0.6174154
## [3,] 0.4092434
## [4,] 0.4359593
## [5,] 0.4310747
## [6,] 0.4242292
## [7,] 0.4839298
## [8,] 0.4855076Bias
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
## [1,] 1 0.6 0.6126200 0.4204122 0.8491343 0.6128577
## [2,] 2 0.6 0.6170115 0.3912004 0.8929255 0.6170642
## [3,] 3 0.4 0.4134157 0.2632658 0.6596468 0.4136359
## [4,] 4 0.4 0.4173980 0.2337005 0.6497578 0.4177946
## [5,] 5 0.4 0.4170428 0.2411115 0.6544047 0.4174430
## [6,] 6 0.4 0.4222395 0.2444053 0.7293989 0.4225395
## [7,] 7 0.4 0.4225540 0.2410636 0.6624895 0.4231071
## [8,] 8 0.4 0.4279771 0.2153521 0.7513211 0.4283949
## Est_HR_borrow
## [1,] 0.6512946
## [2,] 0.6565342
## [3,] 0.4394342
## [4,] 0.4536053
## [5,] 0.4575089
## [6,] 0.4568959
## [7,] 0.4718041
## [8,] 0.4876867Bias
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
## [1,] 1 0.6 0.6145611 0.3632412 0.9215783 0.6148990
## [2,] 2 0.6 0.6336000 0.3841654 0.9076384 0.6338210
## [3,] 3 0.4 0.4177965 0.2219271 0.7030201 0.4182304
## [4,] 4 0.4 0.4279517 0.2093290 0.7416046 0.4281818
## [5,] 5 0.4 0.4337324 0.2152692 0.7356100 0.4340914
## [6,] 6 0.4 0.4205821 0.1945044 0.7830199 0.4206936
## [7,] 7 0.4 0.4397731 0.2175672 0.7890023 0.4400914
## [8,] 8 0.4 0.4382504 0.2154793 0.8205759 0.4386800
## Est_HR_borrow
## [1,] 0.6020445
## [2,] 0.6218248
## [3,] 0.4138462
## [4,] 0.4216697
## [5,] 0.4294380
## [6,] 0.4156622
## [7,] 0.4730854
## [8,] 0.4667589Bias
HR estimation
