A likelihood-based trait-model-free approach for linkage detection of binary trait

Abstract

Trait-model-free (or "allele-sharing") approach to linkage analysis is a popular tool in genetic mapping of complex traits, because of the absence of explicit assumptions about the underlying mode of inheritance of the trait. The likelihood framework introduced by Kong and Cox (1997, American Journal of Human Genetics 61, 1179-1188) allows calculation of accurate p-values and LOD scores to test for linkage between a genomic region and a trait. Their method relies on the specification of a model for the trait-dependent segregation of marker alleles at a genomic region linked to the trait. Here we propose a new such model that is motivated by the desire to extract as much information as possible from extended pedigrees containing data from individuals related over several generations. However, our model is also applicable to smaller pedigrees, and has some attractive features compared with existing models (Kong and Cox, 1997), including the fact that it incorporates information on both affected and unaffected individuals. We illustrate the proposed model on simulated and real data, and compare its performance with the existing approach (Kong and Cox, 1997). The proposed approach is implemented in the program lm_ibdtests within the framework of MORGAN 2.8 (http://www.stat.washington.edu/thompson/Genepi/MORGAN/Morgan.shtml).

Figure 1

Figure shows the empirical distribution of the 21og(LR) test statistic (equation 2) for PTM under the null hypothesis. The solid line shows the cumulative distribution function of the mixture of chi-square $0.20{\chi }_2^2+0.50{\chi }_1^2+0.30{\chi }_0^2$. The proportions are computed using equation A.3 in Appendix. The dashed line shows the empirical cumulative distribution function of the 21og(LR) statistic.

Figure 2

Figure shows the power for linkage detection of the likelihood-ratio test under PTM, PTM aff-only and Kong and Cox (1997)'s one parameter linear allele-sharing model with S_pairs for (a) Model 4, (b) Model 5, and (c) Model 6. The solid line in each graph shows the power to detect linkage at recombination fractions 0, .05, .1 under PTM. The dashed line and the dotted line in each graph show the power at different recombination fractions for PTM aff-only and for KC δ-model with S_pairs respectively.

Figure 3

Figure shows the performance of the likelihood-ratio test under PTM (dark solid line), PTM aff-only (solid line) and Kong and Cox (1997)'s one parameter linear allele-sharing model for (a) S_pairs (dashed line), (b) S_all (dotted line) for linkage detection of obesity trait in NHLBI Family Heart Study. We have reported the linkage signals on Chromosome 1, 7, 13 and 22.