The multiple comparison problem arises in population-based studies when the association between phenotypes and multilocus genotypes is examined. Although Bonferroni's correction is often used to cope with such a problem, it may yield too conservative conclusions because all of the tests are assumed to be independent. We have developed new correction algorithms for the test of independence between phenotypes and multilocus genotypes at loci in linkage disequilibrium. In one of the algorithms, the exact type I error rate is calculated for the independency test. We found that such exact probabilities can be calculated using a 128 CPU PC cluster if the numbers of cases and controls are not more than 50. As an alternative method, we developed algorithms to calculate asymptotically the type I error rates using a Markov-chain Monte Carlo sampler that provided a good approximation to values calculated by the exact method. When the new algorithms were applied to both simulation and real data, the real overall type I error rates for the loci in linkage disequilibrium were from one-third to half as high as those obtained by Bonferroni's correction. These algorithms are likely to be useful for multilocus association studies for data obtained by case-control and cohort studies.
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