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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.

Using Importance Sampling to Improve Simulation in Linkage Analysis