Regression models for allele sharing: analysis of accumulating data in affected sib pair studies

Advances in human genome mapping have led to the identification of large numbers of genetic markers that allow systematic searches for multiple disease susceptibility genes for complex traits. A common design involves the recruitment of families with at least two children affected with the disease of interest. The objective is to find chromosomal regions that harbour susceptibility genes for the disease. The affected children, their parents if available, and sometimes other, unaffected, siblings are genotyped using sets of microsatellite DNA markers representing chromosomal sites distributed across the genome. Each marker can occur in several different variants known as alleles, and a pair of alleles constitutes the marker genotype. Each child randomly inherits one of their mother's two alleles and one of their father's two alleles. If a marker is close to a disease susceptibility gene, then affected siblings are expected to have more sharing of the same maternal and/or paternal marker alleles. Statistical methods are used to estimate the distribution of allele sharing in each affected sib pair (ASP) using the set of markers typed across each chromosome, and to test for the presence of excess sharing in the families as a group at each point across the genome. Regression models that allow the allele sharing proportions to depend on characteristics of the family such as diagnostic subtype or ethnic background have been developed to address the heterogeneity that is characteristic of complex disease, but these have not yet been widely applied. In this paper, we apply regression modelling to investigate variation associated with family-level covariates and with the order in which families are recruited and genotyped. We also discuss how some of the concepts of group sequential analysis apply to accumulating data from genome scans of complex disease.