Hypothesis testing for quantitative trait locus effects in both location and scale in genetic backcross studies

TL;DR

This paper develops a statistical framework for hypothesis testing of QTL effects on both location and scale in genetic backcross studies, extending previous models that assumed normality with equal variance.

Contribution

It derives the limiting distribution of the likelihood ratio test for QTL effects in a more general location-scale distribution setting, including explicit representations and asymptotic properties.

Findings

Derived the limiting distribution of the LRT in a general location-scale setting.

Provided explicit representation for the limiting distribution.

Validated results through simulation studies and real-data example.

Abstract

Testing the existence of a quantitative trait locus (QTL) effect is an important task in QTL mapping studies. Most studies concentrate on the case where the phenotype distributions of different QTL groups follow normal distributions with the same unknown variance. In this paper we make a more general assumption that the phenotype distributions come from a location-scale distribution family. We derive the limiting distribution of the LRT for the existence of the QTL effect in both location and scale in genetic backcross studies. We further identify an explicit representation for this limiting distribution. As a complement, we study the limiting distribution of the LRT and its explicit representation for the existence of the QTL effect in the location only. The asymptotic properties of the LRTs under a local alternative are also investigated. Simulation studies are used to evaluate the asymptotic results, and a real-data example is included for illustration.