The broad, long-term objective of this project is to develop new methodology for analyzing pedigree data with complex models. With the current explosion of genetic data, scientists have become more ambitious in their effort to locate disease susceptibility genes. Instead of being satisfied with mapping simple dominant or recessive d , more attention is directed towards complex traits such as diabetes or Alzheimer disease. At the same time, data on multiple markers may be used in a single analysis, either to increase the power in detecting linkage or to localize the gene after linkage has been found. These changes created two separate, but related, problems in data analysis. The first problem is computations. Because of the complex models fitted to the disease phenotype and/or the use of multiple markers, simply computing the lod score can be extremely time consuming and sometimes infeasible using existing techniques. The second problem concerns statistical inference. The current criterion for declaring linkage is to have a lod score of 3.0 or above. While this criterion is quite appropriate for a simple trait, it is clear that adjustments axe needed when the genetic models fitted have many parameters and when multiple diagnostics schemes are considered. Getting the lod score alone should not be considered as the end of an analysis. Other inference tools, such as P-values and posterior odds, are needed. The proposed research is directed towards the two problems mentioned. Computationally, efficient algorithms are developed by combining the strengths of several techniques. These include the traditional peeling algorithm, importance sampling, and Gibbs sampling. Algorithms are not just developed for computing lod scores, but also for obtaining P-values and posterior odds. In addition, probabilities of key recombination events can also be obtained as a bonus, which can sometimes greatly assist the task of understanding the data. The new methodology will be tested using both simulated and real data sets. The later include data sets on malignant melanoma, Alzheimer disease, a rare form of diabetes, and osteoporosis.
