Diseases having two classes of severity: estimation of the proportions of each manifestation by maximum likelihood.

In diseases having variable expressivity, the proportions of the different manifestations of the affection in the population may be different from the observed proportions in a sample when probabilities of ascertainment of these various manifestations are different from each other. This bias can be avoided by taking into account the respective probabilities of ascertainment of these manifestations and by estimating the proportions by maximum likelihood. In this paper, the method of estimation is developed for the particular case of two different phenotypes. Probabilities of observations are calculated, and scores and measures of information are derived. The different factors affecting the respective proportions of affected individuals are: the difference between probabilities of ascertainment of the two forms, the probability of ascertainment of the milder form, the proportion of the more severe form in the population, and the proportion of sibships with a single affected child in the population. The method is applied to published data on retinoblastoma. Validity of the assumptions is discussed and these assumptions are checked using the retinoblastoma data.