Abstract
Restless legs syndrome (RLS) is a common multifactorial disease. Some genetic risk factors have been identified. RLS susceptibility also has been related to iron. We therefore asked whether known iron-related genes are candidates for association with RLS and, vice versa, whether known RLS-associated loci influence iron parameters in serum. RLS/control samples (n=954/1814 in the discovery step, 735/736 in replication 1, and 736/735 in replication 2) were tested for association with SNPs located within 4 Mb intervals surrounding each gene from a list of 111 iron-related genes using a discovery threshold of P=5 × 10−4. Two population cohorts (KORA F3 and F4 with together n=3447) were tested for association of six known RLS loci with iron, ferritin, transferrin, transferrin-saturation, and soluble transferrin receptor. Results were negative. None of the candidate SNPs at the iron-related gene loci was confirmed significantly. An intronic SNP, rs2576036, of KATNAL2 at 18q21.1 was significant in the first (P=0.00085) but not in the second replication step (joint nominal P-value=0.044). Especially, rs1800652 (C282Y) in the HFE gene did not associate with RLS. Moreover, SNPs at the known RLS loci did not significantly affect serum iron parameters in the KORA cohorts. In conclusion, the correlation between RLS and iron parameters in serum may be weaker than assumed. Moreover, in a general power analysis, we show that genetic effects are diluted if they are transmitted via an intermediate trait to an end-phenotype. Sample size formulas are provided for small effect sizes.
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For small effect sizes, the test statistics of linear and logistic regression analyses approximate standard normal distributions. Small effect sizes also imply that the variances under the alternative and the null hypothesis are approximately equal. The formulas in power calculations of necessary sample size n therefore simplify to
where t is the test statistic and Zα/2 and Zβ are quantiles of a standard normal distribution that correspond to the tolerated error rates α and β, that is, to the required significance and power (1−β), respectively.
(1) In the case of linear regression analysis, consider a set of independent individuals where each individual i displays a continuous trait yi that is influenced by an allele of a gene with effect size axy and frequency q. This allele occurs in xi ∈ {0,1,2} copies and is assumed to be in Hardy–Weinberg equilibrium. In the linear model, yi is given as yi=a0+axyxi+ɛi where a0 and axy are constants and ɛi is a noise parameter. The model is scaled so that ɛ has a standard normal distribution with zero mean and unit variance. The precise sample size determination30, 31 yields n=(Zα/2+Zβ)2/C(ρ)2+3 where C(ρ)=½ln((1+ρ)/(1−ρ)) is the Fisher transformation of the correlation coefficient ρ=axyσx/σy. For small axy (ie, small ρ), we can approximate C(ρ) by first-order expansion as C(ρ)≈ρ. Moreover, the variance of the noise term being unity and axy being small, the variance of y is σy2=axy2σx2+1≈1. To calculate ρ we also need σx. In Hardy–Weinberg equilibrium with we get σx2=Σ(xi−μx)2qxi(1−q)(2-xi)=2q(1−q). For small effect axy and, consequently, large sample size (» 3) we thus arrive at
(2) In logistic regression analysis,31, 32, 33 the association between a binary response (eg, disease present or absent) and an exposure variable y is modeled as logit(P(z|y))=log(P(1|y)/P(0|y))=b0+byzy where P(z|y), z ∈ {0,1}, is the conditional response probability, and b0 and byz are constants. The value of the effect parameter byz is estimated by maximum likelihood estimation. For a small effect byz, the variance of the estimator under the alternative hypothesis approximates the variance under the null hypothesis, [P(1−P)σy2]−1, where P is the average response probability with . If y has a standard normal distribution with σy2=1, equation (A1) yields the necessary sample size as
The same derivation applies to multiple logistic regression with logit(P(z|x,ɛ))=c0+cxzx+cɛzɛ+…, if the effects of the variates x, ɛ,… are small. Assuming that x ∈ {0,1,2} represents a genotype distribution in Hardy–Weinberg equilibrium with allele frequency q (implying σx2=2q(1−q), see above), the necessary sample size to estimate the effect size cxz then is
where P is the average response probability with P≈P(0|x=0,ɛ=0)=
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Oexle, K., Schormair, B., Ried, J. et al. Dilution of candidates: the case of iron-related genes in restless legs syndrome. Eur J Hum Genet 21, 410–414 (2013). https://doi.org/10.1038/ejhg.2012.193
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DOI: https://doi.org/10.1038/ejhg.2012.193
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