title: An alternative analysis for crossover studies that accounts for between-group disparities in drug response.
abstract: BACKGROUND
  In crossover clinical trials comparing completely different treatments patients tend to fall apart into different populations: those who respond better to treatment 1 and those who do so to treatment 2. The correlation between treatment response in such trials is negative. The current ANCOVA analysis for crossover studies does not allow for correlations being negative, and is, therefore, not adequate to test this kind of trial.
  
  
  OBJECTIVE
  To study whether matrix algebra provides a more appropriate approach for this purpose.
  
  
  CONCLUSIONS
  Using a mathematical model as well as hypothesized examples I demonstrate that matrix algebra of 2 pairs of cells of the same order not only allows for negative correlations in a crossover design but also provides enough power to test both treatment and carryover effect.
authors.affiliation: Department of Medicine, Merwede Hospital, Dordrecht, Netherlands.
authors.forename: T J
authors.initials: TJ
authors.lastname: Cleophas
mesh_terms: D000465:Algorithms; D000704:Analysis of Variance; D018592:Cross-Over Studies; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D010600:Pharmacology / Q000706:statistics & numerical data*