Importance sampling. I. Computing multimodel p values in linkage analysis.

In linkage analysis, when the lod score is maximized over multiple genetic models, standard asymptotic approximation of the significance level does not apply. Monte Carlo methods can be used to estimate the p value, but procedures currently used are extremely inefficient. We propose a Monte Carlo procedure based on the concept of importance sampling, which can be thousands of times more efficient than current procedures. With a reasonable amount of computing time, extremely accurate estimates of the p values can be obtained. Both theoretical results and an example of maturity-onset diabetes of the young (MODY) are presented to illustrate the efficiency performance of our method. Relations between single-model and multimodel p values are explored. The new procedure is also used to investigate the performance of asymptotic approximations in a single model situation.