Interaction, subgroup analysis and sample size

The term "interaction" has both statistical and scientific connotations that do not always coincide. Multistage models are used as a bridge between these two viewpoints and as a way of illustrating the different types of qualitative interaction. The most important type of interaction for metabolic polymorphisms is between a genetic trait and an environmental or lifestyle exposure. In some cases these factors act multiplicatively on the risk ratios and so do not interact in the statistical sense. Nevertheless, the risk can be much higher when both are present. Interactions present severe problems of interpretation, as naive comparisons in subgroups can be very misleading and can produce false positive results because of the large number of comparisons. Methods for combating this are discussed. The main requirement, however, is for a substantially larger sample size than would be required for estimating the main effects.