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 after load 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 1st period into the 2nd, whereas the alternative group that is treated in the reverse order is not so (Cleophas 1995). For example, of 73 recently published crossovers only six reported the data of the separate periods. In five of them (83%) this very type of carryover effect was demonstrable. Such a mechanism may cause a severe underestimation of the treatment results (Cleophas 1990) 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 (Brown 1980; Barker et al. 1982; Louis et al. 1984; Willan and Pater 1986; Packer 1989; Fleiss 1989; Freeman 1989; Senn 1993). Although Hills and Armitage ( and 1979) in an overview of methods in crossover clinical trials mentioned the tests of Gart (1969) and Prescott (1981) for crossover trials with a binary response and Fidler (1984) presented a model, little attention has been paid to this kind of trials. A binary response is different from a quantitative in that it generally does not answer what exactly can be expected in an individual. Rather it addresses whether or not a particular result has a predictive value, which one of two treatments is better, or whether there is a treatment effect in the data. One might contend, therefore, that some undervaluation of a difference in binary data is not that important as long as it does not cause a type II error of finding no difference were there is one. The main issue of the present chapter is the question whether in a crossover trial with a binary response a significant carryover effect does leave enough power in the data to demonstrate a treatment effect.