Two-stage Estimation for Causal Inference Involving a Semi-continuous Exposure

TL;DR

This paper introduces a novel two-stage estimation method for causal inference with semi-continuous exposures, effectively handling exposures with a mass at zero and varying levels.

Contribution

It develops a new causal framework and estimation strategy that disentangles effects of exposure status and dose, with theoretical guarantees and practical evaluation.

Findings

The estimators are consistent and asymptotically normal.

Simulation studies show good finite sample performance and robustness.

Application demonstrates the method's utility in real-world data.

Abstract

Methods for causal inference are well developed for binary and continuous exposures, but in many settings, the exposure has a substantial mass at zero-such exposures are called semi-continuous. We propose a general causal framework for such semi-continuous exposures, together with a novel two-stage estimation strategy. A two-part propensity structure is introduced for the semi-continuous exposure, with one component for exposure status (exposed vs unexposed) and another for the exposure level among those exposed, and incorporates both into a marginal structural model that disentangles the effects of exposure status and dose. The two-stage procedure sequentially targets the causal dose-response among exposed individuals and the causal effect of exposure status at a reference dose, allowing flexibility in the choice of propensity score methods in the second stage. We establish consistency and asymptotic normality for the resulting estimators, and characterise their limiting values under misspecification of the propensity score models. Simulation studies evaluate finite sample performance and robustness, and an application to a study of prenatal alcohol exposure and child cognition demonstrates how the proposed methods can be used to address a range of scientific questions about both exposure status and exposure intensity.