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, very 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-step targeted minimum-loss based estimator (denoted as hTMLE) for non-negative two-part outcomes. We present methods for a general class of interventions referred to as modified treatment policies, which can accommodate continuous, categorical, and binary exposures. The two-step 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-step 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.

翻译：非负二部结果定义为具有零质量点但其他取值为正的密度函数的结果。例如医疗支出和住院时长等案例在医疗利用研究中十分常见。尽管非负二部结果具有实际相关性，但利用其半连续性特性来提升因果效应估计性能的方法仍极为有限。本文针对非负二部结果开发了一种非参数两步靶向最小损失估计量（记为hTMLE）。我们提出了适用于修正治疗策略这一通用干预类别的方法，可兼容连续型、分类型和二元暴露变量。该两步靶向最小损失估计量通过靶向估计结果变量的强度分量，产生结果变量二元分量的靶向估计，从而可能提升有限样本效率。我们通过模拟案例证明了两步靶向最小损失估计量的效率增益，并将其应用于医疗补助受益人群组，以估计慢性疼痛与身体残疾对阿片类药物供应天数的影响。