From: Chapter 12, Genetic mapping of complex characters

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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

where *Z* refers to the standard normal deviate. The mean
μ and variance σ^{2} 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 γ^{2}; 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

where *w* = [*pq*(γ -
1)^{2}] /(*p*γ + *q*).
μ = 2*Y*-1 and σ^{2}
= 4*Y*(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 *Z*_{α} =
4.014. For 80% power to detect an effect, 1 - β = 0.2
and *Z*_{1-β} = -0.84.

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

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

μ = √h(γ - 1)/(γ + 1), and
σ^{2} = 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},
*Z*_{α} = 5.33 and, as
before, *Z*_{1-β} = -0.84.

In Table 12.3 the
*Z*_{α},
*Z*_{1-β}, μ and
σ^{2} values are used to calculate sample sizes by
substituting in the formula

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

Copyright © 1999, Garland Science.

NCBI Bookshelf. A service of the National Library of Medicine, National Institutes of Health.