Fitting mixture distributions to phenylthiocarbamide (PTC) sensitivity

A technique for fitting mixture distributions to phenylthiocarbamide (PTC) sensitivity is described. Under the assumptions of Hardy-Weinberg equilibrium, a mixture of three normal components is postulated for the observed distribution, with the mixing parameters corresponding to the proportions of the three genotypes associated with two alleles A and a acting at a single locus. The corresponding genotypes AA, Aa, and aa are then considered to have separate means and variances. This paper is concerned with estimating the parameters of the model, and their standard errors, by using an application of the EM algorithm. This technique also caters for the fact that the sensitivity measurements are only known to lie between the endpoints of certain intervals and that the exact measurement of the attribute is not possible.