Estimating genetic association parameters from family data

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.