Estimating the age of rare disease mutations: the example of Triple-A syndrome

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Abstract
We will first describe the principle of the method for two affected individuals who carry the studied mutation at the disease locus D, and then extend the method to a sample of N affected individuals. The basic assumption is that the two affected individuals descend from a common ancestor who introduced the mutation ngen generations ago. The problem is to estimate ngen from the size of the haplotype shared by the two individuals on each side of D. For simplicity, we will describe the method for only one side, the right side, as the treatment for the other side is completely analogous and independent. Let (M1,...,Mx,...,Mk), be a set of k ordered markers that have been typed on the right side of D, which are located at recombination fractions (θ1,...,θx,...,θk) from D. Mk is the first marker on the right side for which the two individuals have different alleles. The problem can be understood as a survival analysis problem in which the starting point is the disease locus, the discrete time scale is the genetic distance, and the event of interest is the occurrence of a recombination. Therefore, we define:

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