Linkage disequilibrium is the nonrandom association of alleles at linked loci, which can be used as a gene mapping technique to refine the location of a disease susceptibility locus. Designing linkage disequilibrium studies have received very little attention in recent statistics literature, particularly when the cost of the study and the available sample size are limited. Here we address these issues by proposing two two-stage designs. An optimal design is one which maximizes the power or the chance of identifying the true disease susceptibility locus. The first design will be evaluated when the total cost of the study is the only constraint, for a given number of markers. The goal will be to determine the optimal allocation of sample size in a two-stage process. We will consider a second design when the constraints are on the total cost and the available sample size. The goal of this design will be to determine the number of markers to be genotyped in a two-stage process, and the intermarker spacing which will provide an optimal design. Finally, we will derive the critical value of a test statistics under these two designs. We will first obtain an approximation to the power function and the critical value under the two proposed designs. We will use Monte Carlo simulations to investigate how these values are affected by the choice of total number of markers, intermarker distance, and the total sample size. With increased attention on whole genome studies, the designs proposed here will permit researchers to allocate their limited resources in a manner whereby the power to identify the disease susceptibility locus, if any, is maximized.
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