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Mathematical Medicine and Biology 1991 8(3):149-169; doi:10.1093/imammb/8.3.149
© 1991 by Institute of Mathematics and its Applications
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Evaluation of Likelihood Ratios for Complex Genetic Models

E. A. THOMPSON and SUN WEI GUO

University of Washington, Seattle Washington 98195, USA

Although methods for computing likelihoods for simple genetic models on large and complex pedigrees have been known for some time, and although methods for evaluating likelihoods for complex genetic models on small pedigrees have likewise been well known, likelihood evaluation for complex models given data on extended pedigrees has remained an intractable problem. The Gibbs sampler provides a method of Monte Carlo evaluation of likelihood ratios for complex models on extended and/or complex pedigrees. With increasing computer speeds, this approach provides a tractable and efficient approach to many such likelihood evaluation problems in linkage and segregation analysis. In this paper, however, the authors restrict attention to two basic building-blocks of the overall process. The first is the sequential computation of Gaussian likelihoods for multiple random-effects models on extended pedigrees. The second is the use of this in the Monte Carlo evaluation of likelihoods for the classical mixed model of segregation analysis. The implementation of the Gibbs sampler on pedigrees that permits this Monte Carlo evaluation is detailed. An example is then presented, and finally, in the context of this same example, it is also shown how linkage analysis for a quantitative trait falls within this same framework.

Keywords: Monte Carlo integration; Gibbs sampler; extended pedigrees; complex genetic models; likelihood evaluation


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