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In this work we consider a three-component normal mixture model in which one component is known to have mean zero and the other two contaminating components have a nonnegative and a no positive mean respectively, while all three components share a common unknown variance parameter. One potential application of this model may be in prioritizing statistical scores obtained in biological experiments, including genetics data. Such a mixture model may be useful in describing the distribution of numerous Z test statistics corresponding to different genes or SNPs, such that a “significant” Z test statistic for a particular gene suggests its connection to a medical condition. More specifically, the inferences drawn from such a mixture model may be useful in a filtration algorithm to remove large subsets of genes or SNPs from consideration, thereby reducing the need for stringent and power-depleting multiplicity adjustments for controlling type I error rates on the remaining genes. We show how to test whether there is contamination in at least one direction (i.e., the mixture model truly requires at least two components) and, if so, how to test whether there is contamination in both directions (i.e., the mixture model truly requires all three components). We assess our testing procedures in simulation studies and illustrate them through application to LOD scores in a genome-wide linkage analysis from an autism study.

Hypothesis Testing in Normal Admixture Models to Detect Heterogeneous Genetic Signals