An alternative foundation for the planning and evaluation of linkage analysis. II. Implications for multiple test adjustments.

The 'multiple testing problem' currently bedevils the field of genetic epidemiology. Briefly stated, this problem arises with the performance of more than one statistical test and results in an increased probability of committing at least one Type I error. The accepted/conventional way of dealing with this problem is based on the classical Neyman-Pearson statistical paradigm and involves adjusting one's error probabilities. This adjustment is, however, problematic because in the process of doing that, one is also adjusting one's measure of evidence. Investigators have actually become wary of looking at their data, for fear of having to adjust the strength of the evidence they observed at a given locus on the genome every time they conduct an additional test. In a companion paper in this issue (Strug & Hodge I), we presented an alternative statistical paradigm, the 'evidential paradigm', to be used when planning and evaluating linkage studies. The evidential paradigm uses the lod score as the measure of evidence (as opposed to a p value), and provides new, alternatively defined error probabilities (alternative to Type I and Type II error rates). We showed how this paradigm separates or decouples the two concepts of error probabilities and strength of the evidence. In the current paper we apply the evidential paradigm to the multiple testing problem - specifically, multiple testing in the context of linkage analysis. We advocate using the lod score as the sole measure of the strength of evidence; we then derive the corresponding probabilities of being misled by the data under different multiple testing scenarios. We distinguish two situations: performing multiple tests of a single hypothesis, vs. performing a single test of multiple hypotheses. For the first situation the probability of being misled remains small regardless of the number of times one tests the single hypothesis, as we show. For the second situation, we provide a rigorous argument outlining how replication samples themselves (analyzed in conjunction with the original sample) constitute appropriate adjustments for conducting multiple hypothesis tests on a data set.