Causal Mediation and Sensitivity Analysis for Mixed-Scale Data

TL;DR

This paper develops a flexible causal mediation analysis framework for mixed-scale data, including ordinal and boundary-censored responses, and demonstrates its application with sensitivity analysis on real data.

Contribution

It introduces a novel parametric modeling approach for mixed-scale outcomes and mediators, extending causal mediation analysis beyond normal/Bernoulli models.

Findings

Supports non-normal models for mediation effects

Enables estimation of average and quantile mediation effects

Provides a method for sensitivity analysis with unidentified parameters

Abstract

The goal of causal mediation analysis, often described within the potential outcomes framework, is to decompose the effect of an exposure on an outcome of interest along different causal pathways. Using the assumption of sequential ignorability to attain non-parametric identification, Imai et al. (2010) proposed a flexible approach to measuring mediation effects, focusing on parametric and semiparametric normal/Bernoulli models for the outcome and mediator. Less attention has been paid to the case where the outcome and/or mediator model are mixed-scale, ordinal, or otherwise fall outside the normal/Bernoulli setting. We develop a simple, but flexible, parametric modeling framework to accommodate the common situation where the responses are mixed continuous and binary, and apply it to a zero-one inflated beta model for the outcome and mediator. Applying our proposed methods to a publicly-available JOBS II dataset, we (i) argue for the need for non-normal models, (ii) show how to estimate both average and quantile mediation effects for boundary-censored data, and (iii) show how to conduct a meaningful sensitivity analysis by introducing unidentified, scientifically meaningful, sensitivity parameters.