Likelihood-based Instrumental Variable Methods for Cox Proportional Hazard Models

In biometrics and related fields, the Cox proportional hazards model are widely used to analyze with covariate adjustment. However, when some covariates are not observed, an unbiased estimator usually cannot be obtained. Even if there are some unmeasured covariates, instrumental variable methods can be applied under some assumptions. In this paper, we propose the new instrumental variable estimator for the Cox proportional hazards model. The estimator is the similar feature as Martinez-Camblor et al., 2019, but not the same exactly; we use an idea of limited-information maximum likelihood. We show that the estimator has good theoretical properties. Also, we confirm properties of our method and previous methods through simulations datasets.