Studying “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 “a cross-sectional association”. In this article I trace two regression models of change to their cross-sectional origin and explain that these models do not test anything conceptually different from cross-sectional models. A change model is superior to a cross-sectional model because it corresponds to a self-matched design. Therefore, the main advantage of regressing “change on change” is complete control of time-stable confounders.