The null distribution of likelihood-ratio statistics in the conditional-logistic linkage model

Olson's conditional-logistic model retains the nice property of the LOD score formulation and has advantages over other methods that make it an appropriate choice for complex trait linkage mapping. However, the asymptotic distribution of the conditional-logistic likelihood-ratio (CL-LR) statistic with genetic constraints on the model parameters is unknown for some analysis models, even in the case of samples comprising only independent sib pairs. We derive approximations to the asymptotic null distributions of the CL-LR statistics and compare them with the empirical null distributions by simulation using independent affected sib pairs. Generally, the empirical null distributions of the CL-LR statistics match well the known or approximated asymptotic distributions for all analysis models considered except for the covariate model with a minimum-adjusted binary covariate. This work will provide useful guidelines for linkage analysis of real data sets for the genetic analysis of complex traits, thereby contributing to the identification of genes for disease traits.