A likelihood-based procedure for obtaining confidence intervals of disease loci with general pedigree data

We proposed a confidence interval method for disease gene localization by testing every position on each chromosome of interest for its possibility of being a disease locus and including those not rejected into the interval. Three test statistics were proposed to perform the tests, including one based on LOD and two generalized likelihood ratio tests with or without model averaging (GLRT/MA and GLRT). For the statistic based on LOD, an integrated procedure was proposed with an adaptive and an importance sampling component. We also proposed asymptotic approaches based on GLRT and GLRT/MA as alternatives that are much more efficient computationally but depends on the reliability of the limiting distributions. Besides its efficiency, the asymptotic procedure based on GLRT/MA also takes model uncertainty into consideration. Applications of these methods to the Genetic Analysis Workshop 15 (GAW15) rheumatoid arthritis data from the French population gave results that successfully captured the well recognized susceptibility gene HLA*DRB1 to a less than 6 cM, 99% confidence interval with the two asymptotic approaches.