Trials, tribulations, and triumphs of the EM algorithm in pedigree analysis

The EM algorithm is an iterative method for finding maximum-likelihood estimates. Its advantages often include numerical stability, simplicity of computer implementation, and natural incorporation of parameter constraints. However, the EM algorithm must be tailored to each specific problem. Smith (1957) and Ott (1977, 1979) have accomplished this for a variety of problems in human pedigree analysis. The present paper clarifies their theory by presenting it from a modern perspective. Five practical numerical examples are also given in an attempt to assess the value of the EM algorithm in realistic genetic modelling. These examples deal with racial admixture, linkage homogeneity, classical segregation analysis, a Mendelian latent trait model for schizophrenia, and a heterozygote detection assay for Ataxia-telangiectasia. Comparison with a quasi-Newton method of optimization reveals that the EM algorithm generally converges more slowly, but also more stably.