Genetic Analysis Workshop 7: Recent progress in statistical methods

There are a number of important new developments in the statistical analysis of pedigrees that potentially offer the opportunity to expand the repertoire of models that are routinely fitted in segregation and linkage analyses. While the feasibility of these methods is not proven, the excitement comes as much from the fact that epidemiologists, biostatisticians, and computer scientists have recognized that recent advances can be applied in genetic epidemiology as from these specific methods. The most interesting of these methods is the Gibbs sampler. Gibbs sampling can be thought of as being analogous to the E-M algorithm except that instead of replacing a parameter by its maximum likelihood estimator as would be performed by the E-M algorithm, the parameter is instead replaced by a sample from the appropriate conditional distribution in Gibbs sampling. The result of the application of Gibbs sampling is not merely the value of the estimator, but instead, the appropriate posterior distribution of that parameter. In the approach adopted by Thomas at this workshop, one other interesting twist to the problem is the acknowledgement that, for instance, for a single major locus model, the genotype of each individual is itself a parameter to be estimated. In one cycle of sampling, each parameter is replaced by a sample from its conditional distribution given the value of all of the other parameters (genotypes and model parameters) and all of the observations on the pedigrees. At this workshop, this method was applied to an analysis of the Utah melanoma and nevus counts, but similar interest in these methods has been shown by Thompson and Wijsman (1990) and Sheehan and Thomas (in press). Developments in computer science were emphasized by Szolovits. While computer scientists have discussed probabilistic networks and geneticists have discussed likelihoods on pedigrees, the two problems have been examined separately (apparently to the detriment of both areas). The approach discussed by Szolovits is to use methods for factoring algebraic formulae. To illustrate the formulation, a prototype program GENINFER-II has been developed for the Macintosh. This program is aimed at genetic counselors and neatly combines the ‘point and click’ friendliness of a Macintosh interface with computational sophistication to allow the counselor to construct pedigrees on the screen and to calculate risks for identified individuals within the pedigree. Pedigree drawing has been a natural focus of attention for computer scientists, but the difficulty of providing a two dimensional representation of a complex pedigree has limited progress. The success of the approach defined by Landre et al. (1972) did not come until Drs. Bennett Dyke, Jean MacCluer, and colleagues adapted the algorithm for the Macintosh (Mamelka et al., 1989). Another approach to pedigree plotting was reported by Round, who has developed an algorithm which is incorporated in his analysis program SCHESIS. This pedigree plotting is based on a two