Using importance sampling to improve simulation in linkage analysis

In this article we describe and discuss implementation of a weighted simulation procedure, importance sampling, in the context of nonparametric linkage analysis. The objective is to estimate genome-wide p-values, i.e. the probability that the maximal linkage score exceeds given thresholds under the null hypothesis of no linkage. In order to reduce variance of the estimate for large thresholds, we simulate linkage scores under a distribution different from the null with an artificial disease locus positioned somewhere along the genome. To compensate for the fact that we simulate under the wrong distribution, the simulated scores are reweighted using a certain likelihood ratio. If the sampling distribution are properly chosen the variance of the corresponding estimate is reduced. This results in accurate genome-wide p-value estimates for a wide range of large thresholds with a substantially smaller cost adjusted relative efficiency with respect to standard unweighted simulation. We illustrate the performance of the method for several pedigree examples, discuss implementation including the amount of variance reduction and describe some possible generalizations.