University of Washington - Department of Statistics
With pedigree data, genetic linkage can be detected using inheritance vector tests, which explore the discrepancy between the posterior distribution of the inheritance vectors given observed trait values and the prior distribution of the inheritance vectors. Marginal inheritance vector tests are useful for linkage detection. A marginal inheritance test, however, will show significance not only at the causal loci but also at positions linked to the causal loci, thus in general, a significant marginal test result does not provide specific localization information.
In this thesis, we propose a conditional inheritance vector test approach for linkage localization. In this approach, we perform an inheritance vector test conditioning on the inheritance vectors at two positions bounding a test region. The test will only show significance when there are one or more casual loci in the specified test region. When there is no causal locus in the test region, the test has the correct type-I error. The validity of the test does not rely on asymptotic results. Being focused on the distribution of the inheritance vectors, the conditional tests rely much less on trait model assumptions. The proposed conditional tests can be implemented for both quantitative traits and qualitative traits, and are applicable to general pedigrees.
When the inheritance vectors cannot be completely determined from genetic marker data, we can extend the marginal and conditional inheritance vector tests using an i.i.d or MCMC sample of inheritance vectors and summarize the test results using randomized p-values. Randomized p-values provide information about both the significance and the uncertainty in the test results.
We use simulation studies to compare and contrast the marginal and the conditional tests and to demonstrate that randomized p-values can capture both the significance and the uncertainty in the test results. We demonstrate the practicality and utility of the conditional tests for real data by using them to analyze lipid traits in the Framingham Heart Study.