Comparison of crossover and parallel‐group designs for the identification of a binary predictive biomarker of the treatment effect

Pros and cons of crossover design are well known for estimating the treatment effect compared to parallel‐group design, but remain unclear for identifying and estimating an interaction between a potential biomarker and the treatment effect. Such ‘predictive’ biomarkers, or ‘effect modifiers’, help to predict the response to specific treatments. The purpose of this report was to better characterize the advantages and disadvantages of crossover versus parallel‐group design to identify predictive biomarkers. The treatment effect, the effect of a binary biomarker and their interaction were modelled using a linear model. The intra‐subject correlation in the crossover design was taken into account through an intra‐class correlation coefficient. The variance‐covariance matrix of the parameters was derived and compared. For both trial designs, the variance of the parameter estimating an interaction between the treatment effect and a potential predictive biomarker corresponds to the variance of the parameter estimating the treatment effect, multiplied by the inverse of the frequency of the candidate biomarker. The ratio of the variance of the interaction parameter in the crossover to the variance estimated in the parallel‐group design depends on the complement of the intra‐class correlation coefficient. When planning a clinical trial including a search for candidate biomarker, the frequency of the candidate biomarker helps design the sample size, and the intra‐subject correlation of the outcome should be taken into account for choosing between parallel‐group and crossover designs.