Statistics and Its Interface

Volume 2 (2009)

Number 2

Missing data methods for linkage analysis of IBS and incomplete IBD from affected sib-pairs

Pages: 133 – 144

DOI: http://dx.doi.org/10.4310/SII.2009.v2.n2.a3

Authors

Dennis W. Buckman (Information Management Services, Inc., Silver Spring, Maryland, U.S.A.)

Zhaohai Li (Department of Statistics, George Washington University, Washington, D.C.)

Abstract

We derive linkage statistics for situations where the number of marker alleles shared identical-by-descent (IBD) is incomplete, and the number of marker alleles shared identicalby- state (IBS) is known. The linkage statistics are based on the assumption that the parental genotypes are missing at random (MAR). We first assume the marker IBD is unambiguous for a sib-pair if the parental genotypes are available. Then we relax this assumption to assess the impact of marker ambiguity. The derivation of each statistic involves a Taylor series expansion of a log likelihood that is a function of the recombination fraction and nuisance parameters and incorporates the missing data situation. The first derivative of the log likelihood is zero under the null hypothesis of no recombination, so the Taylor series expansion of the log likelihood reveals a linkage statistic that is proportional to the second derivative of the log likelihood evaluated at the null hypothesis value of the recombination fraction. We prove that the standardized linkage statistics have asymptotic normal distributions, and we provide required sample sizes and simulation results and consider the impact of parent availability and marker ambiguity.

Keywords

incomplete data, missing at random, identity-by-descent, identity-by-state, complex traits, required sample size, power, Type I error

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