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Within\u2010patient comparison of different treatments is a promising approach for improving study efficiency across multiple populations by eliminating between\u2010patient variability in treatment evaluation. This study provides a framework for evaluating treatment efficacy in multiple populations for  crossover trials and evaluates the efficacy gain in comparison with the standard parallel\u2010group analysis. Simulation experiments confirm that the crossover analysis consistently outperforms the parallel\u2010group analysis in statistical power, especially when carryover effects are small. An application to a clinical trial in Type 2 diabetes demonstrates the efficiency advantages of the crossover analysis. 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