title: Evaluating the effect of change on change: a different viewpoint.
abstract: BACKGROUND
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Division of Epidemiology and Biostatistics, Mel and Enid Zuckerman College of Public Health, University of Arizona, Tucson, AZ 85724, USA. shahar@email.arizona.edu
authors.forename: Eyal
authors.initials: E
authors.lastname: Shahar
mesh_terms: D000465:Algorithms; D015984:Causality; D015331:Cohort Studies; D003430:Cross-Sectional Studies; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D012044:Regression Analysis