Mediation Analysis for Count and Zero-Inflated Count Data without Sequential Ignorability and Its Application in Dental Studies

TL;DR

This paper introduces instrumental variable-based causal methods for mediation analysis of count and zero-inflated count data, avoiding the untestable sequential ignorability assumption, with applications in dental and public health studies.

Contribution

It develops new causal inference techniques for count data that do not rely on the assumption of sequential ignorability, using empirical likelihood and sensitivity analysis.

Findings

Method performs well in simulations across various settings

Applied successfully to dental caries prevention trial data

Effect estimates are robust to certain violations of assumptions

Abstract

Mediation analysis seeks to understand the mechanism by which a treatment affects an outcome. Count or zero-inflated count outcome are common in many studies in which mediation analysis is of interest. For example, in dental studies, outcomes such as decayed, missing and filled teeth are typically zero inflated. Existing mediation analysis approaches for count data assume sequential ignorability of the mediator. This is often not plausible because the mediator is not randomized so that there are unmeasured confounders associated with the mediator and the outcome. In this paper, we develop causal methods based on instrumental variable (IV) approaches for mediation analysis for count data possibly with a lot of zeros that do not require the assumption of sequential ignorability. We first define the direct and indirect effect ratios for those data, and then propose estimating equations and use empirical likelihood to estimate the direct and indirect effects consistently. A sensitivity analysis is proposed for violations of the IV exclusion restriction assumption. Simulation studies demonstrate that our method works well for different types of outcomes under different settings. Our method is applied to a randomized dental caries prevention trial and a study of the effect of a massive flood in Bangladesh on children's diarrhea.