I propose attacking several methodological and mathematical problems relating to the genetic epidemiology of common and/or complex diseases. As each problem is resolved and new methodologies are developed, I will apply theresulting solution to available data on four diseases: insulin-dependent diabetes IDDM), multiple sclerosis, ankylosing spondylitis, and coeliac disease. I will begin with four problems relating to gene linkage analysis: disease-marker associations (HLA and disease), two-locus linkage analysis, reduced penetrance, and incorrectly specified or unknown models. Then I will turn to theoretical and practical issues (sample size, robustness, asymptotic behavior) associated with the use of likelihood methods in genetic epidemiology. The rationale for concentrating on linkage methods is that the common diseases exhibit familial aggregation but do not fit simple Mendelian patterns of inheritance. Presumably, genes and environment both contribute to the occurrence of these diseases. Since genes act in only a few, well understood ways in pedigrees, it seems logical to identify genetic factors first, then use them to sort out environmental contributions. Gene linkage analysis represents a powerful tool for identifying specific genes, detecting genetic heterogeneity, and predicting recurrence risks.
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