Causal Analysis of Individual Change Using the Difference Score

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Causal analysis of change in time-related characteristics such as health or disease is an increasingly important area of epidemiology. Change is often analyzed using data from 2 waves of a longitudinal study, using the difference score—the difference between the scores at the 2 waves—as the outcome in a regression model. In this article, I show how and when causal analysis of change can be performed using simple linear regression models of continuous difference scores. Not only do causal analyses require making adjustments for confounding bias, but also for the shape of individual “growth curves”—the way in which each individual's score changes over time. In practice, the type of growth curve is critical to determining whether age or start score or neither is included in the regression model. For valid analyses, both sets of adjustments require assumptions based on prior theory that cannot be tested using the study data; choosing to make adjustments using variables based solely on observed associations with the difference score can give misleading results. However, analysts can state their assumptions clearly using this framework and put them up for rigorous scientific scrutiny. The approach is illustrated by an application to data from the Whitehall II study of British civil servants.

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