The heterogeneity problem. I: Separating genetic from environmental forms of the same disease.

The purposes of this work were 1) to reparameterize the likelihood used in segregation analysis in a way particularly suited to detecting heterogeneity (the result of the analysis is a parameter giving the proportion of families with the genetic form of the disease in the dataset) and 2) to test how well this reparameterization works using simulation. We assume that a dataset contains nuclear family data, with some of the families having a form of the disease that is environmentally caused and the others with a genetic form of the disease. In this study, we considered the case where the genetic form is a simple recessive and the environmental form a random model. The underlying parameters were the gene frequency, q, and the frequency of sporadics, R. We reparameterized the likelihood in terms of alpha, the percentage of genetic families in the dataset, which we attempt to estimate. We contrast the estimates of alpha with the population heterogeneity as reflected in the estimates of q and R. For the simulation, nuclear families are generated. Genetic families were simulated with a mendelian recessive pattern and environmental families according to a simple random model. Over a wide range of generating parameters, estimates of alpha were good, differing from the "true" values by only a few percent. Estimates of q and R, on the other hand, ranged from fair to poor. Our results indicate that the amount of heterogeneity in a dataset can be accurately estimated using segregation analysis, even when estimates of the gene frequency and penetrance among sporadics are unreliable.