Bayesian Intervals for Linkage Location

Ritwik Sinha , Shiv K. Saini , Robert C. Elston , Yuqun Luo

In positional cloning of disease susceptibility genes, identification of a linked chromosomal region
via linkage studies is often followed by fine mapping with association studies. Efficiency can be
gained via an intermediate step where confidence regions for the locations of disease genes are
constructed. In this article, we propose a novel Bayesian method for constructing such intervals
using affected sibling pair data. While a number of approaches are available for constructing con-
fidence intervals for disease gene locations, the empirical coverage of all methods tend to deviate
from the nominal level. This motivates us to explore a Bayesian approach, that formulates the
disease gene location as a parameter, to seek possible improvements. For the problem of disease
gene location, credible intervals with a uniform prior on the location are confidence regions. A
Metropolis-Hastings algorithm is implemented to sample from the posterior distribution and High-
est Posterior Density Intervals of the disease gene location are constructed. The proposed Bayesian
method is shown to provide precise confidence sets with correct coverage probabilities when com-
pared to competing methods in a wide range of simulated data sets and a real data for localization
of disease genes for Rheumatoid Arthritis.