gms | German Medical Science

51. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e. V. (gmds)

10. - 14.09.2006, Leipzig

A General Approach for Power Calculations for the Haseman-Elston Method

Meeting Abstract

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  • Oliver Hädicke - Universität zu Lübeck, Lübeck
  • Heping Zhang - Yale University School of Medicine, New Haven
  • Andreas Ziegler - Universität zu Lübeck, Lübeck

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e.V. (gmds). 51. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie. Leipzig, 10.-14.09.2006. Düsseldorf, Köln: German Medical Science; 2006. Doc06gmds227

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Published: September 1, 2006

© 2006 Hädicke et al.
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To unravel the genetic basis of complex genetic disorders, intermediate quantitative traits are often analyzed in practice instead of the clinically relevant outcome [1]. In family studies, these are often investigated with a sample of nuclear families, consisting in at least two offspring and their parents. Risch and Zhang [2] proposed a new approach for sample size and power calculations with the Haseman-Elston method [3] as tool for analysis. They started off with the simple Falconer model [4]

xit = μ + git + eit,

where xit is the trait value of offspring t, t = 1, 2, in family i, i = 1, …, n. μ is the general mean, git is the genetic effect attributed to the diallelic major locus. Polygenic and environmental effects are absorbed in the error term eit. The genetic effect g takes on values a, d, and –a, when the offspring is homozygous for the high allele, heterozygous, and homozygous for the low alleles, respectively. The Haseman-Elston method then regresses the sib-pairs squared trait difference on the proportion τi of alleles shared identical by descent (IBD) and the probability z1i for sib-pair i sharing one allele IBD:

yi = (xi1 – xi2)2 = α + β τi + γ z1i + εi

Haseman and Elston [3] have shown that the slope coefficient β is given by [3] β = -2(1-2θ)2 σg 2, where θ is the recombination fraction between the marker and the trait locus, and σg 2 is the genetic variance attributable to the trait locus. Formulae for σg 2 can be found elsewhere [see, e.g., [1]].

For power and sample size calculations, Risch and Zhang [2] considered an additive genetic model, i.e., γ = 0, and a completely informative genetic marker for the null hypothesis H0: σg 2 = 0 against the one-sided alternative H1: σg 2 > 0.

In this presentation, we firstly demonstrate in Monte-Carlo simulation studies that the power calculated by Risch and Zhang do not match their theoretical levels. We argue that the hypothesis σg 2 = 0 used by Risch and Zhang is inadequate. We next develop new formulae for power and sample size calculations for the Haseman-Elston method based on H0: θ = ½ versus H0: θ < ½. Finally, we illustrate the validity of our new formulae in Monte-Carlo simulation studies.

In conclusion, power and sample size calculations for the Haseman-Elston method should not be performed with the formulae developed by Risch and Zhang [2]. For this purpose, one should either utilize the approach proposed by Amos et al. [5] or our new method. For this, it is important to stress the limitations of these methods. Both are restricted to a single diallelic major trait locus. However, while Amos et al. assume absence of polygenic components and/or shared environmental effects, our approach is based on the existence of a completely informative genetic marker. We are convinced that the latter limitation is less crucial because today’s genome-wide linkage studies utilizing 10,000 or more single nucleotide polymorphisms lead to almost complete marker information at any chromosomal position.


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