A causal proportional hazards estimator under homogeneous or heterogeneous selection in an IV setting.

In this paper we present a framework to do estimation in a structural Cox model when there may be unobserved confounding. The model is phrased in terms of a selection bias function and a baseline model that describes how covariates affect the survival time in a scenario without exposure. In this way model congeniality is ensured. The method uses an instrumental variable. Interestingly, the formulated model turns out to have similarities to the so-called Cox-Aalen survival model for the observed data. We exploit this to enhance estimation of the unknown parameters. This also allows us to derive large sample properties of the proposed estimator.