The cumulative effect of genetic markers on classification performance: Insights from simple models

The cumulative effect of markers on classification accuracy, with even slight between-population allele frequency differences, has been a mainstay of empirical genetic research. The simple theoretical model of Edwards (2003) has enabled a clear elucidation of the effect of additional markers on average classification error. The present paper describes a mathematical generalization necessary to alleviate an oversimplification, but at the same time revealing an inherent drawback of the simple model. An alternative model for explaining the effect of additional loci on classification is proposed based on an optimal classifier. In particular, cases in which the expected performance does not profit from information at additional loci are characterized in simple terms. Further insight into the capacity of classifiers to exploit the potential afforded by each additional locus comes from an information-theoretic perspective. Multilocus correlation and multivariate mutual information measures are shown to tightly correspond with the dynamics of misclassification rates, under the cumulative effect of loci.