Evaluating the effect of change on change: a different viewpoint

Rationale  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’. Methods  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. Results  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. Conclusion  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.