Method and computer program for controlling the family-wise alpha rate in gene association studies involving multiple phenotypes

Multiple significance testing involving multiple phenotypes is not uncommon in the context of gene association studies but has remained largely unaddressed. If no adjustment is made for the multiple tests conducted, the type I error probability will exceed the nominal (per test) alpha level. Nevertheless, many investigators do not implement such adjustments. This may, in part, be because most available methods for adjusting the alpha rate either: 1) do not take the correlation structure among the variables into account and, therefore, tend to be overly stringent; or 2) do not allow statements to be made about specific variables but only about multivariate composites of variables. In this paper we develop a simulation-based method and computer program that holds the actual alpha rate to the nominal alpha rate but takes the correlation structure into account. We show that this method is more powerful than several common alternative approaches and that this power advantage increases as the number of variables and their intercorrelations increase. The method appears robust to marked non-normality and variance heterogeneity even with unequal numbers of subjects in each group. The fact that gene association studies with biallelic loci will have (at most) three groups (i.e., AA, Aa, aa) implies by the closure principle that, after detection of a significant result for a specific variable, pairwise comparisons for that variable can be conducted without further adjustment of the alpha level.