Bias in Estimating the Causal Hazard Ratio Using Two-Stage Instrumental Variable Methods

• Activity Number: 609
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Health Policy Statistics Section
• Author(s): Fei Wan*+ and Dylan Small and Justin E. Bekelman and Nandita Mitra
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
• Keywords: instrumental variable ; two stage residual inclusion ; two stage predictor substitution ; unmeasured confounding ; survival ; bias

Abstract

Two stage instrumental variable methods are commonly used to determine the causal eects of treat- ments 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 stratication 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 conrm the analytic results from our closed-form solutions. We apply these two methods to prostate cancer treatment data from SEER-Medicare and compare these results to randomized trial data.