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 into different populations: those who respond better to treatment 1 and those who respond better 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 for testing in this kind of trials.
  
  
  OBJECTIVE
  To study whether matrix algebra provides a more appropriate approach for this purpose.
  
  
  CONCLUSIONS
  Using a mathematical model as well as hypothesized examples, it is demonstrated 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 the treatment and carryover effect.
authors.affiliation: Department of Medicine, Merwede Hospital Dordrecht, Sliedrecht, The Netherlands.
authors.forename: T J
authors.initials: TJ
authors.lastname: Cleophas
mesh_terms: D000704:Analysis of Variance; D002986:Clinical Trials as Topic / Q000379:methods*; D018592:Cross-Over Studies; D006801:Humans; D015233:Models, Statistical; D014665:Vasodilator Agents / Q000494:pharmacology
chemical_list: D014665:Vasodilator Agents