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Estimating causal effects in an observational study with a survival time endpoint: comparing reformulated versus original antidepressants

*Jaeun Choi, Harvard Medical School 
MaryBeth Landrum, Harvard Medical School 
James O'Malley, Dartmouth College 

Keywords: Comparative effectiveness research, Instrumental variable, Mental health, Observational study, Simultaneous equations model, Survival analysis

Estimation of the effect of a treatment in the presence of unmeasured confounding is a common problem in observational studies. The Two Stage Least Squares Instrumental Variables (IV) procedure is frequently used but cannot be applied to time-to-event data if some observations are censored. We develop a simultaneous equations model to account for unmeasured confounding on the effect of treatment on a survival outcome subject to censoring. The identification of the treatment effect is assisted by IVs that are related to treatment but conditional on treatment does not directly affect the outcome and also the assumed bivariate distribution underlying the data generating process. As the IV and the distributional assumptions cannot be jointly assessed from the observed data, we consider methods for evaluating the sensitivity of the results to these assumptions. We illustrate the methodology by comparing reformulated and original antidepressants on time to discontinuation of the use of medication in a sample of privately or Medicaid insured patients. If time permits, semi-parametric alternatives will be discussed.