Score tests for familial correlation in genotyped-proband designs

In the genotyped-proband design, a proband is selected based on an observed phenotype, the genotype of the proband is observed, and then the phenotype s of all first-degree relatives are obtained. The genotypes of these first- degree relatives are not observed. call et al. [(1999) Genet Epidemiol] dis cuss likelihood analysis of this design under the assumption that the pheno types are conditionally independent of one another given the observed and u nobserved genotypes. Li and Thompson [(1997) Biometrics 53:282-293] give an example where this assumption is suspect, thus suggesting that it is impor tant to develop tests for conditional independence. In this paper, we devel op a score test for the conditional independence assumption in models that might include covariates or observation of genotypes for some of the first degree relatives. The problem can be cast more generally as one of score te sting in the presence of missing covariates. A standard analysis would requ ire specifying a distribution for the covariates, which is not convenient a nd could lead to a lack of model-robustness. We show that by considering a natural conditional likelihood, and basing the score test on it, a simple a nalysis results. The methods are applied to a study of the penetrance for b reast cancer of BRCA1 and BRCA2 mutations among Ashkenazi Jews. (C) 2000 Wi ley-Liss, Inc.