p-Value simulation for affected sib pair multiple testing

A standard approach to calculation of critical values for affected sib pair multiple testing is based on: (a) fully informative markers, (b) Haldane map function assumptions leading to a Markov chain model for inheritance vectors, (c) central limit approximation to averages of sampled inheritance vectors leading to an Ornstein-Uhlenbeck process approximation, and (d) simple approximations to the maximum of such a process. Under these assumptions, assuming equispaced or close to equispaced markers, if the sample size is large, an approximation is available that is easy to calculate and performs well. However, for small sample sizes, a large number of markers, and for small p-values, there is good reason to be cautious about the use of the Gaussian approximation. We develop an algorithm for calculation of multiple testing p-values based on the standard Markov chain model, avoiding the use of Gaussian (large sample) approximation. We illustrate the use of this algorithm by demonstrating some inadequacies of the Gaussian approximation.