Crossover Studies with Binary Responses

Abstract

The crossover design is widely used in clinical research especially in the case of a limited number of patients. The main advantage of within-patient over between-patient comparisons is that between-subject variability is not used in the comparisons. However, a prerequisite is that the order of the treatments does not influence the outcome of the treatment. If the effect of the treatment administered in the 1st period carries on into the 2nd period, then it may influence the measured response in the 2nd period. This essentially means that only symptomatic treatments qualify for crossover comparisons and curative treatments do not. However, symptomatic treatments frequently have small curative effects, e.g., wound healing by vasodilators or, more recently, cardiac remodelling by afterload reduction. The treatment group that is treated with the effective compound first and with the less effective compound or placebo second is frequently biased by carryover effect from the 1 st period into the 2nd, whereas the alternative group that is treated in the reverse order is not so.¹ For example, of 73 recently published crossovers only 6 reported the data of the separate periods. In 5 of them (83%) this very type of carryover effect was demonstrable. Such a mechanism may cause a severe underestimation of the treatment results² and this possibility should, therefore, be assessed in the analysis. Most of the reports on the subject of order effects so far have addressed crossover studies with a quantitative rather than binary response.^3–10