Abstract

Several methods are available for estimating the causal effect of time-varying treatment strategies on survival outcomes in observational studies. These include singly robust methods such as inverse probability weighting (IPW) that requires a sequence of correctly specified models of the observed treatment distribution (the propensity score), and iterative conditional expectation (ICE) that require a sequence of correctly specified models of the nested conditional outcome means. Alternatively, doubly robust estimators that combine IPW and ICE require that only one of the sequences of models be correctly specified, and thus offer more than one opportunity for valid estimation. In recent years, these methods have been generalized to accommodate effects of stochastic strategies such that treatment assignment at each time is non-deterministic within levels of the measured past. Many authors have considered stochastic strategies that depend on the propensity score which would suggest that doubly robust estimators are not possible to construct. However, this is not the case. In this talk, I will give an intuition into why some strategies that depend on the propensity score can still be estimated by doubly robust estimators, and describe a class of stochastic treatment interventions that will always have doubly robust estimators in point treatment processes and multiply robust estimators in longitudinal observational studies. I also propose a new stochastic treatment intervention dependent on the propensity score motivated by an application to Pre-Exposure Prophylaxis (PrEP) initiation studies that allows doubly and multiply robust estimators.