A bootstrap approach to estimating power for linkage heterogeneity

We examined the power of detecting linkage heterogeneity when the null hypothesis is that all families are linked to one locus (A) and the two alternative hypotheses are either 1) a proportion of the families are linked to locus A and the remaining families are linked to a second locus B or 2) a proportion of the families are linked to locus A or B and a third proportion of the families are unlinked to either locus. The power of detecting linkage heterogeneity is estimated for various proportions of families linked to loci A, B or unlinked to either locus (sampling under the alternative hypothesis). To estimate the significance level, the data set is sampled under the null hypothesis. For sampling under both hypotheses, a bootstrap approach is employed, sampling the simulated pedigrees with replacement. The power to detect linkage heterogeneity is strongest when the recombination fraction is 0 and equal proportions of the families are linked to loci A and B. The power decreases as the recombination fraction increases, the proportion of unlinked families increases and the disparity between the proportion of the families linked to either locus A or B increases. In the data set of 32 Duke Familial Alzheimer Disease families, when equal proportions of families are linked to loci A and B, the power to detect linkage heterogeneity is 0.94 using a likelihood ratio criterion of 10:1. The p value that corresponds to the likelihood ratio of 10:1 is estimated as 0.013 with a 95% confidence interval for p ranging from 0.012 to 0.014.