Computation of the posterior probability of linkage using 'high effect' genetic model priors

The posterior probability of linkage, or PPL, directly measures the probability that a disease gene is linked to a marker. By placing a Bayesian prior on the elements of the genetic model, it allows for an unknown genetic model without the inflationary effects of maximization. The standard technique uses essentially uniform priors over the elements of the penetrance vector. However, much of the parameter space corresponds to models that seem unlikely to yield substantial evidence for linkage: for example, models with very high phenocopy rates.

A new class of priors on the elements of the genetic model is examined both theoretically and in simulations. These priors place 0% probability over models with low sibling relative risk, lambda(s).

Focusing the prior probability on high lambda(s) models does tend to increase the mean PPL for linked markers, and to decrease the mean PPL for unlinked markers. However, the power to detect linkage remains virtually unchanged. Moreover, under these priors, the PPL occasionally yields unacceptably high values under no linkage.

It appears important to retain prior probability over apparently 'uninformative' genetic models to accurately characterize the amount of evidence for linkage represented by the data.