We first analyze the four class genotype data that have been previously analyzed by a number of authors (Louis and Dempster, 1987; Guo and Thompson, 1992). The data are given by (A1A1,A2A1,A2A2,A3A1,A3A2,A3A3,A4A1,A4A2,A4A3,A4A4)=(0,3,1,5,18,1,3,7,5,2). The exact p-value for these data is 0.01744, which under conventional levels would be deemed as showing mild evidence of departure from HWE. These data are described in Thomson et al. (1986) and concern the antigen class of 45 French type 1 diabetes patients, with the classes being DR1, DR3, DR4, and Y, a fourth class corresponding to all other antigens. In our notation these classes correspond to (A1, A2, A3, A4). The interest here is in the mode of inheritance of type 1 diabetes, with a hypothesized recessive model being equivalent to the HWE model (Thomson, 1983). The translation into the HWE framework is as follows. Assume a hypothetical two-locus model with k = 4 alleles at one (antigen) locus along with a second disease locus. Under a recessive model of inheritance we require two disease alleles, D, and among cases we may consider the probabilities of
