Efficient simulation of P values for linkage analysis

In many genetic linkage analyses, the P value is obtained through simulation since the underlying distribution of the test statistic is complex and unknown. However, this can be very computationally intensive. A "bootstrap/replicate pool" approach has been suggested that generates P values more efficiently in terms of computation by resampling sums from a small set of simulated replicates for each pedigree. The replicate pool idea has been successfully applied, but, to our knowledge, has never been theoretically studied. An entirely different method for increasing the computational efficiency of P value simulation is Besag and Clifford's sequential sampling method. We propose an algorithm which combines Besag and Clifford's method with the replicate pool method to efficiently estimate P values for linkage studies. We derive variance expressions for the P value estimates from the replicate pool method and from our proposed hybrid method, and use these to show that the hybrid estimator has a substantial advantage over the other methods in most situations.