Assessing genetic effects in survival data by correlating martingale residuals with an application to age at onset of Huntington disease

Genetic models for survival data are hard to formulate and hard to fit. For example, the popular gamma-frailty model for sib-pair data does not generalize easily to extended pedigrees and is not easy to fit. In this paper we show how martingale residuals from a (marginal) Cox model can be employed to estimate the presence of a genetic effect and to estimate genetic correlations depending on the genetic distance (kinship). The methodology is applied to age at onset of Huntington disease (HD) in carriers of the HD gene. The number of CAG repeats in the HD gene is a well-known predictor for age at onset of the disease. However, there is an indication that other genes might be involved as well; leading to unexplained familial clustering. Using our methodology, we found a clearly significant genetic association between the martingale residuals with correlations of about 0.6 for relatives that share 50 per cent of their genes (sib-pairs and parent-child) and about 0.3 for relatives that share 25 per cent of their genes (grandparent-grandchild, uncle/aunt-niece/nephew)