Nonparametric Efficient Estimation of Dynamic Treatment Regimes with Competing Risks

Abstract

Many observational studies evaluate the risks and benefits of time-varying interventions. In these longitudinal settings, the primary outcome of interest is often a clinical event that is precluded by mortality, which acts as a competing risk. Evaluating dynamic treatment regimes (DTRs) is complicated by time-varying confounding, right-censoring, and progressive sample size reduction over time, for which traditional methods such as the g-formula or inverse probability weighting may be misspecified or highly unstable. In this work, we develop the nonparametric efficiency theory and derive the efficient influence function for the cumulative incidence of an event under a DTR in the presence of a competing risk and right-censoring. Building on this result, we propose a sequentially doubly robust estimator that accommodates flexible machine learning for nuisance estimation while retaining root-n consistency and asymptotic normality. We illustrate the utility of our framework by estimating long-term cumulative incidence of clinical fractures under different bisphosphonate"drug holiday"regimes for osteoporosis.