Crossover Studies with Continuous Variables

Abstract

Crossover studies with continuous variables are routinely used in clinical drug research: for example, no less than 22% of the double-blind placebo-controlled hypertension trials in 1993 were accordingly designed (Niemeyer et al. 1998). A major advantage of the crossover design is that it eliminates between-subject variability of symptoms. However, problems include the occurrence of carryover effect, sometimes wrongly called treatment-by-period interaction (see also Chap. 17): if the effect of the first period carries on into the next one, then it may influence the response to the latter period. Second, the possibility of time effects due to external factors such as the change of the seasons has to be taken into account in lengthy crossover studies. Third, negative correlations between drug responses, although recently recognized in clinical pharmacology, is an important possibility not considered in the design and analysis of clinical trials so far. Many crossover studies may have a positive correlation-between-drug-response, not only because treatments in a given comparison are frequently from the same class of drugs, but also because one subject is used for comparisons of two treatments. Still, in treatment comparisons of completely different treatments patients may fall into different populations, those who respond better to the test-treatment and those who do so to the reference-treatment. This phenomenon has already lead to treatment protocols based on individualized rather than stepped care (Scheffé 1959). Power analyses for crossover studies with continuous variables so far only accounted for the possibility of approximately zero levels of correlations (Cleophas 1993; Willan and Pater 1986; Freeman 1989; Fleiss 1989; Senn 1994; Grieve 1994). While considering different levels of correlation, we recently demonstrated (Cleophas and Van Lier 1996) that the crossover design with binary variables is a powerful means of determining the efficacy of new drugs in spite of such factors as carryover effects. Crossover trials with continuous variables, however, have not yet been similarly studied.