Linkage disequilibrium and linkage information from one-child families

In linkage analysis a single-child family is usually considered to be completely uninformative. This article shows that such a family can provide information on linkage disequilibrium, even if it provides no information on linkage equilibrium. A transition matrix consisting of the recombination fraction and the phase proportion is proposed to study the genetic transmission from a pair of parents to their single child. The information about linkage for a single-child family is shown to be confounded by the phase proportion. This explains why such a family used to be considered uninformative under the assumption of linkage equilibrium. By reparametrizing the recombination fraction and the phase proportion into one parameter, it is demonstrated that extracting information on linkage disequilibrium is feasible. The study of power of the testing method proposed here is carried out by simulation.