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Biometrika 2004 91(1):219-225; doi:10.1093/biomet/91.1.219
© 2004 by Biometrika Trust
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Miscellanea

Estimating genetic association parameters from family data

Alice S.Whittemore1

1 Department of Health Research and Policy, Stanford University School of Medicine, Stanford, California 94305, U.S.Aalicesw{at}stanford.edu

We consider the problem of estimating a parameter {theta} reflecting association between a disease and genotypes of a genetic polymorphism, using nuclear family data.In many applications, some parental genotypes are missing, and the distribution of these genotypes is unknown. Since misspecification of this distribution can bias estimators for {theta}, we consider estimating functions that are unbiased, regardless of how the distribution is specified. We call the resulting estimators parental-genotype-robust. Rabinowitz (2002) has proposed a constrained optimisation method for obtaining locally optimal unbiased tests of the null hypothesis of no association. We use a similar method to derive estimating functions that yield parental-genotype-robust estimators with minimum variance in the class of all such estimators. We extend the estimating functions to obtain parental-genotype-robust estimators when {theta} is a vector of unknown parameters, and show that the estimating functions enjoy a certain optimality property.

Key Words: Constrained optimisation; Genetic association; Nuclear family; Relative risk estimation

Received June 2002. Revised April 2003


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