Crossover Studies with Continuous Variables: Power Analysis

Crossover studies with continuous variables are routinely used in clinical drug re-search: for example, no less than 22% of the double-blind placebo-controlled hypertension trials in 1993 were accordingly designed.1 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 chapter 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 response, 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.2 Power analyses for crossover studies with continuous variables so far only accounted for the possibility of approximately zero levels of correlations.3–8 While considering different levels of correlation, we recently demonstrated9 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.