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The consistency of the posterior probability of linkage
Journal article   Open access   Peer reviewed

The consistency of the posterior probability of linkage

K Wang, J Huang and V J Vieland
Annals of human genetics, Vol.64(Pt 6), pp.533-553
11/2000
DOI: 10.1046/j.1469-1809.2000.6460533.x
PMID: 11281217
url
https://doi.org/10.1046/j.1469-1809.2000.6460533.xView
Published (Version of record) Open Access

Abstract

When searching for trait loci along the genome, properly incorporating prior genomic information into the analysis will almost certainly increase the chance of success. Recently, we devised a method that utilizes such prior information in the mapping of trait genes for complex disorders (Vieland, 1998; Wang el al. 1999; Vieland et al. 2000). This method uses the posterior probability of linkage (PPL) based on the admixture model as a measure of linkage information. In this paper, we study the consistency of the PPL. It is shown that, as the number of pedigrees increases, the PPL converges in probability to 1 when there is linkage between the marker and a trait locus, and converges to 0 otherwise. This conclusion is shown to be true for general pedigrees and trait models, even, when the likelihood functions are based on misspecified trait models. As part of the effort to prove this conclusion, it is shown that when there is no linkage, the maximum likelihood estimator of the recombination fraction in the admixture model is asymptotically 0.5, even when the admixture model misrepresents the true model.
 Likelihood Functions Quantitative Trait, Heritable Pedigree Computer Simulation Humans Models, Genetic Multifactorial Inheritance Genetic Linkage

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