Two-stage targeted minimum-loss based estimation for non-negative two-part outcomes.

Non-negative two-part outcomes are defined as outcomes with a density function that have a zero point mass but are otherwise positive. Examples, such as healthcare expenditure and hospital length of stay, are common in healthcare utilization research. Despite the practical relevance of non-negative two-part outcomes, few methods exist to leverage knowledge of their semicontinuity to achieve improved performance in estimating causal effects. In this paper, we develop a nonparametric two-stage targeted minimum-loss based estimator (denoted as hTMLE) for non-negative two-part outcomes. We present methods for a general class of interventions, which can accommodate continuous, categorical, and binary exposures. The two-stage TMLE uses a targeted estimate of the intensity component of the outcome to produce a targeted estimate of the binary component of the outcome that may improve finite sample efficiency. We demonstrate the efficiency gains achieved by the two-stage TMLE with simulated examples and then apply it to a cohort of Medicaid beneficiaries to estimate the effect of chronic pain and physical disability on days' supply of opioids.