Using mixture models to characterize disease-related traits

We consider 12 event-related potentials and one electroencephalogram measure as disease-related traits to compare alcohol-dependent individuals (cases) to unaffected individuals (controls). We use two approaches: 1) two-way analysis of variance (with sex and alcohol dependency as the factors), and 2) likelihood ratio tests comparing sex adjusted values of cases to controls assuming that within each group the trait has a 2 (or 3) component normal mixture distribution. In the second approach, we test the null hypothesis that the parameters of the mixtures are equal for the cases and controls. Based on the two-way analysis of variance, we find 1) males have significantly (p < 0.05) lower mean response values than females for 7 of these traits. 2) Alcohol-dependent cases have significantly lower mean response than controls for 3 traits. The mixture analysis of sex-adjusted values of I of these traits, the event-related potential obtained at the parietal midline channel (ttth4), found the appearance of a 3-component normal mixture in cases and controls. The mixtures differed in that the cases had significantly lower mean values than controls and significantly different mixing proportions in 2 of the 3 components. Implications of this study are: 1) Sex needs to be taken into account when studying risk factors for alcohol dependency to prevent finding a spurious association between alcohol dependency and the risk factor. 2) Mixture analysis indicates that for the event-related potential "ttth4", the difference observed reflects strong evidence of heterogeneity of response in both the cases and controls.