Premium
Bias in estimating the causal hazard ratio when using two‐stage instrumental variable methods
Author(s) -
Wan Fei,
Small Dylan,
Bekelman Justin E.,
Mitra Nandita
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6470
Subject(s) - instrumental variable , censoring (clinical trials) , statistics , confounding , hazard ratio , econometrics , proportional hazards model , causal inference , mathematics , computer science , confidence interval
Two‐stage instrumental variable methods are commonly used to estimate the causal effects of treatments on survival in the presence of measured and unmeasured confounding. Two‐stage residual inclusion (2SRI) has been the method of choice over two‐stage predictor substitution (2SPS) in clinical studies. We directly compare the bias in the causal hazard ratio estimated by these two methods. Under a principal stratification framework, we derive a closed‐form solution for asymptotic bias of the causal hazard ratio among compliers for both the 2SPS and 2SRI methods when survival time follows the Weibull distribution with random censoring. When there is no unmeasured confounding and no always takers, our analytic results show that 2SRI is generally asymptotically unbiased, but 2SPS is not. However, when there is substantial unmeasured confounding, 2SPS performs better than 2SRI with respect to bias under certain scenarios. We use extensive simulation studies to confirm the analytic results from our closed‐form solutions. We apply these two methods to prostate cancer treatment data from Surveillance, Epidemiology and End Results‐Medicare and compare these 2SRI and 2SPS estimates with results from two published randomized trials. Copyright © 2015 John Wiley & Sons, Ltd.