Box 12.2Sample sizes needed to find a disease susceptibility locus by a whole genome scan using either affected sib pairs (ASP) or the transmission disequilibrium test (TDT)

Risch and Merikangas (1996) calculated the sample sizes needed to distinguish a genetic effect from the null hypothesis with power (1 - β) and significance level α. This Box summarizes their formulae and equations, but the original paper should be consulted for the derivations and for details.

A standard piece of statistics tells us that the sample size M required is given by

Image ch12e3.jpg

where Z refers to the standard normal deviate. The mean μ and variance σ2 are calculated as functions of the susceptibility allele frequency (p) and the relative risk γ conferred by one copy of the susceptibility allele. The model assumes that the relative risk for a person carrying two susceptibility alleles is γ2; that the marker used is always informative; and that there is no recombination with the susceptibility locus.

For ASP, the expected allele sharing at the susceptibility locus is given by

Image ch12e4.jpg

where w = [pq(γ - 1)2] /(pγ + q). μ = 2Y-1 and σ2 = 4Y(1-Y). The genome-wide threshold of significance (probability of a false positive anywhere in the genome = 0.05; testing for sharing IBD) requires a lod score of 3.6, corresponding to α = 3 × 10-5, and Zα = 4.014. For 80% power to detect an effect, 1 - β = 0.2 and Z1-β = -0.84.

For the TDT, the probability that a parent will be heterozygous for the allele in question is

Image ch12e5.jpg

The probability that such a heterozygous parent will transmit the high-risk allele to the affected child is

Image ch12e6.jpg

μ = √h(γ - 1)/(γ + 1), and σ2 = 1-[h(γ - 1)2/(γ + 1)2]. As discussed above, for an ultimate genome screen involving 1 000 000 tests, α = 5 × 10-8, Zα = 5.33 and, as before, Z1-β = -0.84.

In Table 12.3 the Zα, Z1-β, μ and σ2 values are used to calculate sample sizes by substituting in the formula

Image ch12e7.jpg

For the TDT, the answer is halved because each parent-child trio allows two tests, one on each parent.

From: Chapter 12, Genetic mapping of complex characters

Cover of Human Molecular Genetics
Human Molecular Genetics. 2nd edition.
Strachan T, Read AP.
New York: Wiley-Liss; 1999.
Copyright © 1999, Garland Science.

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