Evaluating the effect of change on change: a different viewpoint

When a causal variable and its presumed effect are measured at two time points in a cohort study, most researchers prefer to fit some type of a change model. Many of them believe that such an analysis is superior to a cross-sectional analysis 'because change models estimate the effect of change on change', which sounds epistemologically stronger than 'estimating a cross-sectional association'.

In this paper I trace two commonly used regression models of change to their cross-sectional origin and describe these models from the perspectives of time-stable confounders, effect modification, and causal diagrams. In addition, I cite three viewpoints from the statistical literature.

The so-called change models do not estimate anything conceptually different from cross-sectional models. A change model is superior to a cross-sectional model mainly because it corresponds to a self-matched design. Statistical viewpoints markedly differ about the appropriate parameterization and interpretation of such data.

Contrary to prevailing thought, a model of changes between two time points does not estimate any special causal idea called 'longitudinal effect'. The main advantage of regressing 'change on change' is complete control of time-stable confounders, a key concern in observational studies. Many analysts fail to realize that that important advantage is usually lost when they fit a random effects model.