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Best Linear Unbiased Allele‐Frequency Estimation in Complex Pedigrees
Author(s) -
Sara McPeek Mary,
Wu Xiaodong,
Ober Carole
Publication year - 2004
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2004.00180.x
Subject(s) - estimator , pedigree chart , statistics , allele frequency , mathematics , sample size determination , best linear unbiased prediction , mean squared error , allele , computer science , biology , genetics , artificial intelligence , selection (genetic algorithm) , gene
Summary . Many types of genetic analyses depend on estimates of allele frequencies. We consider the problem of allele‐frequency estimation based on data from related individuals. The motivation for this work is data collected on the Hutterites, an isolated founder population, so we focus particularly on the case in which the relationships among the sampled individuals are specified by a large, complex pedigree for which maximum likelihood estimation is impractical. For this case, we propose to use the best linear unbiased estimator (BLUE) of allele frequency. We derive this estimator, which is equivalent to the quasi‐likelihood estimator for this problem, and we describe an efficient algorithm for computing the estimate and its variance. We show that our estimator has certain desirable small‐sample properties in common with the maximum likelihood estimator (MLE) for this problem. We treat both the case when parental origin of each allele is known and when it is unknown. The results are extended to prediction of allele frequency in some set of individuals S based on genotype data collected on a set of individuals R . We compare the mean‐squared error of the BLUE, the commonly used naive estimator (sample frequency) and the MLE when the latter is feasible to calculate. The results indicate that although the MLE performs the best of the three, the BLUE is close in performance to the MLE and is substantially easier to calculate, making it particularly useful for large complex pedigrees in which MLE calculation is impractical or infeasible. We apply our method to allele‐frequency estimation in a Hutterite data set.