Less is more, except when less is less: Studying joint effects.

Most diseases are complex in that they are caused by the joint action of multiple factors, both genetic and environmental. Over the past few decades, the mathematical convenience of logistic regression has served to enshrine the multiplicative model, to the point where many epidemiologists believe that departure from additivity on a log scale implies that two factors interact in causing disease. Other terminology in epidemiology, where students are told that inequality of relative risks across levels of a second factor should be seen as "effect modification," reinforces an uncritical acceptance of multiplicative joint effect as the biologically meaningful no-interaction null. Our first task, when studying joint effects, is to understand the limitations of our definitions for "interaction," and recognize that what statisticians mean and what biologists might want to mean by interaction may not coincide. Joint effects are notoriously hard to identify and characterize, even when asking a simple and unsatisfying question, like whether two effects are log-additive. The rule of thumb for such efforts is that a factor-of-four sample size is needed, compared with that needed to demonstrate main effects of either genes or exposures. So strategies have been devised that focus on the most informative individuals, either through risk-based sampling for a cohort, or case-control sampling, extreme phenotype sampling, pooling, two-stage sampling, exposed-only, or case-only designs. These designs gain efficiency, but at a cost of flexibility in models for joint effects. A relatively new approach avoids population controls by genotyping case-parent triads. Because it requires parents, the method works best for diseases with onset early in life. With this design, the role of autosomal genetic variants is assessed by in effect treating the nontransmitted parental alleles as controls for affected offspring. Despite advantages for looking at genetic effects, the triad design faces limitations when examining joint effects of genetic and environmental factors. Because population-based controls are not included, main effects for exposures cannot be estimated, and consequently one only has access to inference related to a multiplicative null. We have proposed a hybrid approach that offers the best features of both case-parent and case-control designs. Through genotyping of parents of population-based controls and assuming Mendelian transmission, power is markedly enhanced. One can also estimate main effects for exposures and now flexibly assess models for joint effects.