Assessing Bias in the Estimation of Causal Hazard Ratio Among Compliers Using Two-Stage Instrumental Variable Approaches

• Activity Number: 270
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 2:45 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Fei Wan* and Dylan Small and Nandita Mitra and Justin Bekelman
• 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 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. Under a principal stratification and potential outcome 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. Our analytic results show that both 2SRI and 2SPS are generally asymptotically biased and such bias increases with the magnitude of unmeasured confounding. However, if the hazard rate function is decreasing, 2SPS generally performs better than 2SRI with respect to bias. We use extensive simulation studies to confirm the analytic results from our closed-form solutions.