Combining two-point genetic linkage analyses using mapping functions

A likelihood ratio statistic is proposed for combining two-point genetic linkage analyses when the two-point analyses are between a trait and a well-defined map of markers. It is assumed that the two-point analyses are independent, as in the case of choosing only the most informative marker per family. The asymptotic distribution of the likelihood ratio statistic is derived under the null hypothesis of no linkage of the trait with a map of 2 markers, with intermarker genetic distance delta. This distribution is shown to be a chi-square mixture distribution with mixing probability depending on delta and the assumed mapping function. We use this asymptotic result to approximate the distribution of the likelihood ratio statistic for the more general case of more than 2 markers. Simulation results indicate that this may be reasonable. Power is evaluated by simulations and results indicate that this approach, which constrains the intermarker distances to their known values, tends to be more powerful than other methods proposed in the literature.