Confounding-adjustment methods for the causal difference in medians

TL;DR

This paper evaluates confounding-adjustment methods for estimating causal differences in medians with skewed continuous outcomes, proposing alternatives to traditional mean-based approaches.

Contribution

It compares and assesses several confounding-adjustment methods for median-based causal effects, including less-known g-computation implementations.

Findings

IPW estimator, weighted quantile regression, and g-computation reduce bias when models are correct

G-computation also minimizes variance, outperforming other methods in some scenarios

These methods offer better alternatives to ignore or transform skewed data

Abstract

With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation may no longer be meaningful. In practice the typical approach is to either "ignore or transform" - ignore the skewness altogether or transform the outcome to obtain a more symmetric distribution, although neither approach is entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate this parameter is limited. In this study we described and compared confounding-adjustment methods to address this gap. The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression and two little-known implementations of g-computation for this problem. Motivated by a cohort investigation in the Longitudinal Study of Australian Children, we conducted a simulation study that found the IPW estimator, weighted quantile regression and g-computation implementations minimised bias when the relevant models were correctly specified, with g-computation additionally minimising the variance. These methods provide appealing alternatives to the common "ignore or transform" approach and multivariable quantile regression, enhancing our capability to obtain meaningful causal effect estimates with skewed outcome data.