Analyses of 'change scores' do not estimate causal effects in observational data

TL;DR

This paper demonstrates that using change scores in observational data often leads to misleading causal inferences, and recommends alternative analytical strategies based on DAGs.

Contribution

It provides a clear explanation, supported by simulations, of why change scores do not reliably estimate causal effects in observational studies.

Findings

Change scores are only valid when baseline outcome measures are a competing exposure.

Analyses of change scores diverge from DAG-informed causal estimates when baseline measures are confounders or mediators.

Future studies should avoid change score analysis and use DAG-based methods for causal inference.

Abstract

Background: In longitudinal data, it is common to create 'change scores' by subtracting measurements taken at baseline from those taken at follow-up, and then to analyse the resulting 'change' as the outcome variable. In observational data, this approach can produce misleading causal effect estimates. The present article uses directed acyclic graphs (DAGs) and simple simulations to provide an accessible explanation of why change scores do not estimate causal effects in observational data. Methods: Data were simulated to match three general scenarios where the variable representing measurements of the outcome at baseline was a 1) competing exposure, 2) confounder, or 3) mediator for the total causal effect of the exposure on the variable representing measurements of the outcome at follow-up. Regression coefficients were compared between change-score analyses and DAG-informed analyses. Results: Change-score analyses do not provide meaningful causal effect estimates unless the variable representing measurements of the outcome at baseline is a competing exposure, as in a randomised experiment. Where such variables (i.e. baseline measurements of the outcome) are confounders or mediators, the conclusions drawn from analyses of change scores diverge (potentially substantially) from those of DAG-informed analyses. Conclusions: Future observational studies that seek causal effect estimates should avoid analysing change scores and adopt alternative analytical strategies.