The equivalence of two tests and models for HLA data with no observed double blanks.
Gart and Nam (1984, Biometrics 40, 887-894) consider the analysis of an ABO-like model based on the Hardy-Weinberg law in the commonly occurring case of human leukocyte antigen (HLA) data where there are no double blanks, that is, no recessive homozygotes. They derive a score test, based on the truncated likelihood, of the hypothesis that the true recessive gene (or allele) frequency is zero. Yasuda (1968, Biometrics 24, 915-935) considers a similar codominant system wherein the true recessive gene frequency is assumed zero, but the Hardy-Weinberg law does not hold. In particular, he considers the possibility of a nonzero inbreeding coefficient. We show that the two models are equivalent; each likelihood can be shown to be a reparameterization of the other. Furthermore, the score test of the zero gene frequency in Gart and Nam is identical to the score test for a zero inbreeding coefficient given by Yasuda. The results are applied to an example wherein it appears that the Hardy-Weinberg model is appropriate. Thus, it is not possible in this population to identify homozygous individuals without error from phenotypic data alone.
Gart
J J
JJ
Biostatistics Branch, National Cancer Institute, Bethesda, Maryland 20892.
Nam
J M
JM
D003241:Consanguinity; D005787:Gene Frequency; D005799:Genes, Dominant; D006680:HLA Antigens / Q000235:genetics*; D006579:Heterozygote; D006720:Homozygote; D006801:Humans; D008957:Models, Genetic
D006680:HLA Antigens