The use of baseline covariates in crossover studies

• Published in: Biostatistics (Oxford, England) Vol. 11; no. 1; pp. 1 - 17
• Main Authors: Kenward, Michael G., Roger, James H.
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 01.01.2010; Oxford Publishing Limited (England)
• Subjects: Algorithms; Analysis of Variance; Antihypertensive Agents - therapeutic use; Aza Compounds - therapeutic use; Bias; Biostatistics; Blood Pressure - drug effects; Bronchial Hyperreactivity - drug therapy; Bronchial Hyperreactivity - metabolism; Bronchial Hyperreactivity - physiopathology; Controlled Clinical Trials as Topic - methods; Cross-Over Studies; Efficiency; Electrocardiography - drug effects; Epidemiologic Research Design; Fluoroquinolones; Forced Expiratory Volume - drug effects; Forced Expiratory Volume - physiology; Heart Diseases - drug therapy; Humans; Hypertension - drug therapy; Likelihood Functions; Models, Statistical; Nitric Oxide - metabolism; Pain - drug therapy; Quinolines - therapeutic use; Random variables; Statistical Distributions; Variance analysis; Restricted maximum likelihood; Cross-level bias; REML; Analysis of covariance; Experimental design; Covariance structure; Causal pathway
• ISSN: 1465-4644; 1468-4357; 1468-4357
• DOI: 10.1093/biostatistics/kxp046

It is our experience that in many settings, crossover trials that have within-period baseline measurements are analyzed wrongly. A "conventional" analysis of covariance in this setting uses each baseline as a covariate for the following outcome variable in the same period but not for any other outcome. If used with random subject effects such an analysis leads to biased treatment comparisons; this is an example of cross-level bias. Using a postulated covariance structure that reflects the symmetry of the crossover setting, we quantify such bias and, at the same time, investigate potential gains and losses in efficiency through the use of the baselines. We then describe alternative methods of analysis that avoid the cross-level bias. The development is illustrated throughout with 2 example trials, one balanced and orthogonal and one highly unbalanced and nonorthogonal.