Estimating the treatment effect on the treated under time-dependent confounding in an application to the Swiss HIV Cohort Study

When comparing time varying treatments in a non-randomized setting, one must often correct for time-dependent confounders that influence treatment choice over time and that are themselves influenced by treatment. We present a new two-step procedure, based on additive hazard regression and linear increments models, for handling such confounding when estimating average treatment effects on the treated. The approach can also be used for mediation analysis. The method is applied to data from the Swiss HIV Cohort Study, estimating the effect of antiretroviral treatment on time to acquired immune deficiency syndrome or death. Compared with other methods for estimating the average treatment effects on the treated the method proposed is easy to implement by using available software packages in R.