The two-treatment crossover experiment for clinical trials

In comparing the efficacy of two drugs in the treatment of a disease, using each patient as his own control by trying both drugs on each patient at different times and comparing the results patient by patient has great appeal. This idea has led to the experimental designs called the crossover or changeover designs. Although crossover designs eliminate between-experimental-unit variation from treatment comparisons, other problems arise in the form of carryover or residual effects. Various aspects of two-treatment crossover and three-period two-treatment crossover designs have been discussed in the literature. Under certain covariance patterns, baseline adjustments using analysis of covariance procedures on the first baseline value may give a more efficient estimate of treatment effect in a two-period two-treatment crossover design. The efficiency of this estimator is compared to other estimators which have been proposed previously. The result of a preliminary test of hypothesis that carryover effects of two treatments are equal is used to define an estimator $\\phi\sb\*$ for the treatment effect. The bias and mean square error of the preliminary test on which the validity of two-period crossover design is based are examined and the regions in the parameter space in which $\ \phi\sb\*$ has smaller mean square error than the between subject estimator are determined. The efficiency of this estimator relative to the between subject estimator is tabulated. These tables can be used to determine a proper choice of significance level of the preliminary test. The use of three periods in the two-treatment unbalanced crossover design for clinical trials is considered here. A design involving two-treatment sequences is found to have the property of orthogonality between treatment effect and carryover effect. It is shown that the analysis using the least squares method with Grizzle's assumptions (on the random components) will lead to an intra-inter block estimate of treatment effects.