Crossover Designs in Nutrition: New Methodology Accounting for Individually Varying Responses

SUMMARY Crossover designs are a mainstay in human nutrition research. Traditionally, analyses use ANOVA, with subjects and diets as main effects and the subject–diet interaction serving as the error term (since subjects do not replicate diets). If subjects do not respond to diets in the same way, then the subject–diet interaction term is large, the ANOVA model is misspecified, and the test on the diet main effect becomes too liberal. Nonetheless, in the more than 40,000 nutritional studies using crossover designs done since 2000, none estimated the potentially important subject–diet interaction. A multiplicative (singular value or principal components) decomposition of the “residual” is proposed, which separates the subject–diet interaction from error. The method is demonstrated using a recent crossover study and then compared with a second study where subjects repeated some diets to allow for an independent estimate of error. In other data sets available to us, over half of the dependent variables had significant subject–diet interactions.