Factorial designs: a graphical aid for choosing study designs accounting for interaction.

The presence of possible treatment interaction when designing a factorial study can be either greeted with dismay (for an antagonistic or negative interaction) or can be welcome (in the case of a synergistic effect). The type of potential interaction may greatly influence the choice of study design. Depending on the magnitude of an expected additive or multiplicative interaction, a three-arm study, instead of a 2 x 2 factorial, may yield greater statistical power. A graphical aid for examining the loss of power due to the presence of such interaction is developed. The technique can also be applied to designing studies where prespecified subgroup analyses are of particular interest. Tests for interaction effects between subgroups are usually underpowered, even if the subgroups have been prespecified in the protocol. The technique can be used to determine the appropriate sample sizes in the subgroups to ensure adequate power to detect potential interaction effects. The method is illustrated with respect to a published 2 x 2 factorial study. In this study, interaction reduced the power of the final analysis to detect significant main effects.