Factorial designs in clinical trials: the effects of non-compliance and subadditivity

Factorial designs in clinical trials allow for the study of several medical treatments simultaneously. This paper distinguishes among different types of settings in which factorial designs are useful. For the experiment that involves investigation of several new or untested therapies, we introduce a model that incorporates rates of non-compliance to therapy as well as various degrees of subadditivity of treatment effects. We compare the operating characteristics of the factorial under this model with those of competing designs and show that a modest negative interaction can considerably diminish the power to detect treatment effects in the factorial even in cases that have little power to detect this interaction. We urge, therefore, that designers of clinical trials with factorial layouts posit realistic estimates of interactions among treatments in order to assure adequate power to detect beneficial effects of treatment.