Adjusting for time-varying confounding in survival analysis

In this paper we illustrate how directly including endogenous time-varying confounders in the model of the effect of an exposure on a response can lead to bias in discrete time survival analysis. An alternative to this method is Hernán, Brumback, and Robins' (1999) use of sample weights to adjust for endogenous time-varying confounding. We discuss when this method can be used to provide unbiased estimators, and we illustrate the method by addressing a substantive research question using existing survey data. We also critically examine the robustness of the weighting method to violations of the underlying assumptions via a simulation analysis.