title: Bias in estimating the causal hazard ratio when using two-stage instrumental variable methods.
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. 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.
authors: Department of Biostatistics and Epidemiology, University of Pennsylvania, Philadelphia, PA, U.S.A.
authors: Fei
authors: F
authors: Wan
authors: Department of Statistics, University of Pennsylvania, Philadelphia, PA, U.S.A.
authors: Dylan
authors: http://orcid.org/0000-0003-4928-2646
authors: D
authors: Small
authors: Department of Radiation Oncology, Abramson Cancer Center, University of Pennsylvania, Philadelphia, PA, U.S.A.
authors: Justin E
authors: JE
authors: Bekelman
authors: Department of Biostatistics and Epidemiology, University of Pennsylvania, Philadelphia, PA, U.S.A.
authors: Nandita
authors: N
authors: Mitra
mesh_terms: D000368:Aged; D015982:Bias; D015984:Causality; D003198:Computer Simulation; D015986:Confounding Factors, Epidemiologic; D005069:Evaluation Studies as Topic; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008297:Male; D006278:Medicare / Q000706:statistics & numerical data; D010043:Outcome and Process Assessment, Health Care / Q000706:statistics & numerical data*; D011336:Probability; D016016:Proportional Hazards Models; D011471:Prostatic Neoplasms / Q000188:drug therapy / Q000401:mortality* / Q000532:radiotherapy; D016032:Randomized Controlled Trials as Topic / Q000379:methods / Q000706:statistics & numerical data; D012044:Regression Analysis; D018426:SEER Program; D016019:Survival Analysis; D014481:United States / Q000453:epidemiology
keywords: bias; instrumental variable; survival; two-stage predictor substitution; two-stage residual inclusion; unmeasured confounding