A tutorial on dealing with time-varying eligibility for treatment: Comparing the risk of major bleeding with direct-acting oral anticoagulants vs warfarin.

In this tutorial, we focus on the problem of how to define and estimate treatment effects when some patients develop a contraindication and are thus ineligible to receive a treatment of interest during follow-up. We first describe the concept of positivity, which is the requirement that all subjects in an analysis be eligible for all treatments of interest conditional on their baseline covariates, and the extension of this concept in the longitudinal treatment setting. We demonstrate using simulated datasets and regression analysis that under violations of longitudinal positivity, typical associational estimates between treatment over time and the outcome of interest may be misleading depending on the data-generating structure. Finally, we explain how one may define "treatment strategies," such as "treat with medication unless contraindicated," to overcome the problems linked to time-varying eligibility. Finally, we show how contrasts between the expected potential outcomes under these strategies may be consistently estimated with inverse probability weighting methods. We provide R code for all the analyses described.