Abstract

Many linkage disequilibrium (LD) measures have been used to study LD patterns and for haplotype block partitioning. We examine the properties of one of these measures, Lewontin's D', in order to understand the dependency of its confidence interval (CI) to allele frequency and sample size as well as its applications in defining haplotype blocks. This measure and its CIs were used to partition haplotypes into blocks by Gabriel et al. as well as in many other applications. Gabriel et al. utilized a bootstrap approach to calculate the CI for D'. Under this method, over 1,000 bootstrap samples may be needed to obtain an accurate estimate of the CI for each pair of single nucleotide polymorphism (SNP) markers which can be very computationally intensive, particularly when many SNP markers are involved. We develop two alternative methods for calculating the CI for D' without bootstrap: one based on the approximate variance of D' given by Zapata et al. and the other based on a maximum likelihood estimate (MLE) of D' together with Fisher Information theory. Both methods depend on normal approximation for the estimates of D' for large sample sizes. We assess and compare the coverage of the CIs using the three methods through extensive simulations. We define the coverage as the fraction of times the estimated CI contains the true value of D'. In general, the average coverage of the bootstrap method is less than the pre-specified coverage. When the sample size is small (< or = 100), the remaining two methods slightly under estimate the coverage with MLE approach having smaller standard error compared to Zapata's method. When the sample size is large (> or = 200) , the estimated coverage from both Zapata's and MLE methods are very close to the pre-specified coverage with the MLE method having the smallest standard error among all three methods. In most typical scenarios, we recommend the use of MLE method for all sample sizes. Only under rare specific cases, would the bootstrap method be better suited for determining the CI, i.e. small sample size, at extreme allele frequencies and -3 < D' < 0.