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Instrumental variable based estimation under the semiparametric accelerated failure time model

Randomized controlled trials are the gold standard for estimating causal effects of treatments or interventions, but in many cases are too costly, too difficult, or even unethical to conduct. Hence, many pressing medical questions can only be investigated using observational studies. However, direct statistical modeling of observational data can result in biased estimates of treatment effects due to unmeasured confounding. In certain cases, instrumental variable based techniques can be used to remove such biases. These techniques are indeed widely studied and used in econometrics under parametric outcome models, however limited works have focused on the utilization of instrumental variables in survival analysis, where semiparametric models are often necessary. The additional challenge in analyzing survival data is the presence of censoring. In this paper, we introduce an instrumental variable method that relaxes the strong assumptions of previous works and provides consistent estimation of the causal effect of a treatment on a survival outcome. We demonstrate the efficacy of our method in various simulated settings and an analysis of Medicare enrollment data comparing two prevalent surgical procedures for abdominal aortic aneurysm from an observational study.