Use of r² measure in power and sample size calculations

In this link, we provide a mathematical explanation of how the r² measure is used in power and sample size calculations for our webtool, PAWE-3D (http://linkage.rockefeller.edu/pawe3d/).

Consider the following notation:

Probability parameters

= Frequency of disease or QTL increaser allele

= Frequency of SNP marker allele in coupling with disease allele

= Non-standardized disequilibrium:

Note that . For our purposes, we shall assume that .

c = Coefficient of maximal disequilibrium; note that .

Use of r² measure in definition of disequilibrium

We define to be . The two-locus haplotype frequencies then become:

These two-locus haplotype frequencies are used directly in the computation of the conditional genotype frequencies, which are used to determine power and sample size for the Allelic, Genotypic, and Linear Trend Tests of Association. For more information, click on the links: PAWE1 and PAWE2

It has been commented that the ratio (Sample size when )/(Sample size when )c for the Allelic, Genotypic, and Linear Trend Tests of Association on 2 x 3 contingency tables [see, e.g., (Gabriel et al., 2002)].

References

1. Gabriel, S.B., Schaffner, S.F., Nguyen, H., Moore, J.M., Roy, J., Blumenstiel, B., Higgins, J., DeFelice, M., Lochner, A., Faggart, M. et al. (2002) The structure of haplotype blocks in the human genome. Science. 296, 2225-9.