Statistical Methods to Map Disease Genes in Populations

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Variation in DNA sequences reflects their relationships. The relationships can tell us about individual predisposition to inherited traits, and so are of use in mapping the genomic location of disease genes. The function of the mapped genes and their biochemical pathways can lead to personalized treatments for disease. The research program focuses on mapping the genomic location of genes that influence disease traits, using data on traits and on genetic variation in homologous DNA sequences. Statistical gene mapping looks for genomic regions with excess relatedness and excess trait similarity. To characterize the relatedness in a sample of DNA sequences, the research program will use their gene genealogy. The gene genealogy is a set of correlated ancestral trees across the genomic region. At trait-influencing locations on the genome, we expect excess clustering of similar trait values on the genealogical tree. Genealogical clustering of trait values is thus a basis for mapping disease genes. A short-term objective is to investigate the statistical properties of different measures of clustering on the genealogy. To cluster trait values on the genealogy, we must reconstruct it, either as a parameter or as a latent random variable. Cladistic methods view the genealogy as a parameter. However, mapping approaches that rely on cladistic reconstructions are potentially biased because they ignore uncertainty in the genealogy. A short-term goal is to characterize the bias and other statistical properties of clustering approaches applied to cladistic reconstructions. Instead of being viewed as parameters, genealogies may be viewed as latent random variables, and sampled from their posterior distribution given the genetic data. However, currently-available, MCMC samplers rely on approximations that break down for a larger number of sequences. A medium-term goal is to develop improved sampling methods with faster mixing, through the use of particle-marginal Metropolis-Hastings algorithms. To reduce the complexity of the state space, we will consider only partial genealogies going back 100 generations before present. Little information about the genomic location of low-frequency causal variants is likely to be gained from going further back in time. In the mapping of disease genes, accurate phenotyping is critical. For brain disorders, 3-dimensional imaging measurements provide objective assessments of cognitive capacity that are thought to be closer to genetic influences than questionnaire scores. Each image typically has millions of measurements, but the information on changes due to disease is thought to reside in only a subset. A second and longer-term focus of the research is to work closely with our brain-imaging collaborators to develop clinically-meaningful measures of trait similarities between individuals that can be integrated into the proposed gene-mapping methods.