Rapid computation of large numbers of LOD scores in linkage analysis through polynomial expression of genetic likelihoods

This paper introduces a new method for computing large numbers of LOD scores in linkage analysis. The LOD score method is commonly used in genetic linkage analysis to associate functionality of genes to their locations on chromosomes. A LOD score is a log 10 likelihood ratio of linkage to no linkage. Instead of calculating values of likelihoods of linkage and no linkage under given values of genetic parameters directly from pedigree data, we construct expressions for likelihoods of linkage and no linkage as polynomials of genetic parameters. These likelihood polynomials of pedigrees don´t change for different parameter values. After the likelihood polynomials are constructed, the values of likelihoods of linkage and no linkage can be computed by evaluating the likelihood polynomials with specific parameter values. The likelihood polynomials are optimized during construction so that repeated terms within the expressions are shared. Moreover, we find that the likelihood polynomials of different pedigrees also often share terms. This term-sharing feature leads us to an evaluation strategy where shared terms are evaluated only once and reused by all the polynomials that share them. The reuse of shared terms in polynomial evaluation greatly decreases the re- computation in calculation of large numbers of LOD scores and improves the computing efficiency. Our results show that this approach can speed up the traditional genetic linkage computation by 10~1200 times. This approached has been applied to the computation of the posterior probability of linkage (PPL) where calculation of large numbers of LOD scores is required.