Risk prediction with linked markers: pedigree analysis

Bayesian statistics in genetics: a guide for the uninitiated

Statistical analyses are used in many fields of genetic research. Most geneticists are taught classical statistics, which includes hypothesis testing, estimation and the construction of confidence intervals; this framework has proved more than satisfactory in many ways. What does a Bayesian framework have to offer geneticists? Its utility lies in offering a more direct approach to some questions and the incorporation of prior information. It can also provide a more straightforward interpretation of results. The utility of a Bayesian perspective, especially for complex problems, is becoming increasingly clear to the statistics community; geneticists are also finding this framework useful and are increasingly utilizing the power of this approach.

A Bayesian characterization of Hardy-Weinberg disequilibrium

A Bayesian method for determining if there are large departures from independence between pairs of alleles at a locus, Hardy-Weinberg equilibrium (HWE), is presented. We endorse the view that a population will never be exactly in HWE and that there will be occasions when there is a need for an alternative to the usual hypothesis-testing setting. Bayesian methods provide such an alternative, and our approach differs from previous Bayesian treatments in using the disequilibrium and inbreeding coefficient parameterizations. These are easily interpretable but may be less mathematically tractable than other parameterizations. We examined the posterior distributions of our parameters for evidence that departures from HWE were large. For either parameterization, when a conjugate prior was used, the prior probability for small departures was itself small, i.e., the prior was weighted against small departures from independence. We could avoid this uneven weighting by using a step prior which gave equal weighting to both small and large departures from HWE. In most cases, the Bayesian methodology makes it clear that there are not enough data to draw a conclusion.

Utility of linked markers in genetic counseling: estimation of carrier risks in X-linked ocular albinism

We apply a method proposed by Rogatko et al. [1995: Am J Med Genet 59:24-32] to estimate carrier risks using genetic linkage data. The method is illustrated for X-linked ocular albinism. Linkage data from pedigrees were combined with genome mapping data to compute carrier risks for individuals with unknown carrier status based on pedigree data alone. We considered two situations. First, a linkage map with some ambiguity in the gene order was considered. This analysis allows us to examine the effect of incomplete genetic map information on risk computations. Second, published physical and meiotic mapping information was used to derive a linkage map that could be assumed known without ambiguity. In both situations, the mean and median estimate of carrier risk differed significantly from that obtained using pedigree relationships only, in that the computed risk was significantly different from the a priori value of 0.5. The 95% CI's associated with point estimates of risk made using the known map or an map with ambiguity did not overlap in some cases. These results suggest that the risk estimate and the confidence with which a risk estimate can be imparted may depend on the genetic map and marker data used in the risk estimation procedure. We conclude that the method presented here can be used to estimate genetic risk under a variety of analytical conditions.

Risk prediction with linked markers: theory

A Bayesian method to predict disease recurrence risks based on distance information between loci and allowing for uncertain gene location is presented. The methodology allows derivation of the posterior distribution of recurrence risks, from which point estimates and associated precision measures can be calculated. The resulting risk distribution accounts for all available information concerning location and relative distance, and can be updated as additional data become available.