Score tests of genetic association in the presence of linkage based on the additive genetic gamma frailty model

Abstract

Nuclear families with multiple affected sibs are often collected for genetic linkage analysis of complex diseases. Once linkage evidence is established, dense markers are often typed in the linked region for genetic association analysis based on linkage disequilibrium (LD). Detection of association in the presence of linkage localizes disease genes more accurately than the methods that rely on linkage alone. However, test of association due to LD in the linked region needs to account for dependency of the allele transmissions to different sibs within a family. In this paper, we define a joint model for genetic linkage and association and derive the corresponding joint survival function of age of onset for the sibs within a sibship. The joint survival function is a function of both the inheritance vector and the genotypes at the candidate marker locus. Based on this joint survival function, we derive score tests for genetic association. The proposed methods utilize the phenotype data of all the sibs and have the advantages of family-based designs which can avoid the potential spurious association caused by population admixture. In addition, the methods can account for variable age of onset or age at censoring and possible covariate effects, and therefore provide important tools for modelling disease heterogeneity. Simulation studies and application to the data sets from the 12th Genetic Analysis Workshop indicate that the proposed methods have correct type 1 error rates and increased power over other existing methods for testing allelic association.

Survival Analysis Methods in Genetic Epidemiology

“…Li and Zhong (2004) define the additive genetic frailties due to the gene linked to locus d for the father and mother as…”

“…Based on this additive genetic gamma frailty model, Li and Zhong (2004) derived the joint survival function of age of onset data within a family as a function of the baseline hazard function, the covariate effects and the parameters related to the frailty. In addition, the null hypothesis that the disease locus is not linked to the candidate locus d can be reformulated as…”

“…Instead, Li and Zhong (2004) developed a retrospective likelihood ration test for this null hypothesis assuming that the baseline hazard function can be estimated from external data such as the SEER database for various types of cancers. Zhong and Li (2004) further extended the additive genetic gamma frailty model to simultaneously consider linkage to two unlinked loci and demonstrated that simultaneously searching for two loci can result in increased power to detect linkage when the disease risk is affected by two unlinked genes. Instead of assuming gamma frailty models, one can also assume a log-multivariate normal frailty where the variance-covariance matrix is specified by kinship coefficients and pairwise IBD-sharing proportions (Pankratz et al, 2005).…”

“…When the marker locus is not the DSL but is in LD with it, all sibling resemblance or lack of resemblance and within sibship correlation of age of onset cannot be fully accounted for by the genotypes at the marker locus. Motivated by this key difference between linkage and LD, Zhong and Li (2004) defined a joint model for the risk of disease to account for both the allele sharing information and the genotype information at the candidate marker locus by including the genetic frailties derived from the inheritance vector.…”

“…For these adult onset cancers, carriers of high-risk alleles were estimated to have an earlier onset of cancer than noncarriers (sporadic cases). Taking into account age of onset information has been shown to be important in studying disease correlation and aggregation Li and Thompson, 1997), in parametric linkage analysis (Morton and Kidd, 1980;Haynes et al, 1986), in segregation analysis (Li and Thompson, 1997;, and in allele-sharing based linkage analysis Zhong and Li, 2004;Li et al, 2002).…”