Am J Epidemiol 2003; 158:404-405.
Copyright © 2003 by Johns
Hopkins Bloomberg School of Public Health
ORIGINAL CONTRIBUTIONS |
Lee Responds to "Testing for Hardy-Weinberg Disequilibrium"
From the Graduate Institute of Epidemiology, College of Public Health, National Taiwan University, Taipei, Taiwan.
Received for publication April 28, 2003; accepted for publication May 8, 2003.
Abbreviations: Abbreviation: HWT, Hardy-Weinberg disequilibrium test.
I appreciate Weinberg and Morris’ thoughtful commentary (1) on my paper (2). In their article, they put my work under the perspective of gene mapping in the postgenomic era. I share the same view with them that the method proposed in my paper amounts to a tree-shaking approach to harvesting the high-hanging fruit (a low-cost approach to generating hypotheses aimed at localizing disease-susceptibility genes for complex human diseases). However, some issues raised by Weinberg and Morris (1) deserve scrutiny. These are 1) the power of the Hardy-Weinberg disequilibrium test (HWT) when a single-nucleotide polymorphism is a "marker" but is not a disease-susceptibility "gene" itself; 2) the utility of the proposed method as a gene-localization tool; and 3) the false alarm due to unmeasured ethnicity.
To address the first issue, consider a marker, M, which is in linkage disequilibrium with a disease-susceptibility gene, A. Jiang et al. (3) showed that, for the M marker, the Hardy-Weinberg disequilibrium coefficient in the affected population is (with the notations changed to be consistent with my paper (2)):
,
where f is the allele frequency of M in the source population, 
is the recombination fraction between M and A, t is the generation elapsed since the A gene was first introduced to the population, and q, R, 
1, and 2 are defined the same as in my paper (2). The equation shows that the Hardy-Weinberg disequilibrium coefficient of the M marker decays according to the function, (1 – )2t. However, the 
term still appears in the equation, meaning that the effect of the mode of inheritance of the A gene is largely preserved even though we are looking at the M marker. Weinberg and Morris’ assertion that "[s]uch a marker will display a gene-dose relation to risk, even if the linked risk-related gene for which it serves as a surrogate works according to a recessive or a dominant model" (1, p. 401), is therefore incorrect.
A second consequence of the above equation is that the Hardy-Weinberg disequilibrium coefficient, D, decays more quickly than the linkage disequilibrium coefficient, 
= q(1 – f) x (1 – )t, as the genomic distance between M and A increases (3). Thus, if a disease gene is not of too recent origin, a marker has to be closer to the gene to reach statistical significance using the HWT more than a marker has to be using the transmission/disequilibrium test. This implies that, in a Hardy-Weinberg population, a genome-wide HWT scan can fine map the putative disease-susceptibility gene(s), because in the very vicinity of the marker(s) with significant HWT, there may exist disease-susceptibility gene(s). This fine-mapping ability should be better for a HWT scan as compared with a transmission/disequilibrium test scan.
As for the problem of unmeasured ethnicity (hidden stratification), the "genomic control" method of Reich and Goldstein (4) can be used for a correction of the HWT. (Their method was proposed originally to correct the allelic chi-square statistic of a case-control design.) To be precise, a number of markers (e.g., 50 markers) are to be selected at random throughout the genome. It is unlikely that any such randomly selected marker will be tightly linked to a disease-susceptibility gene. Therefore, the mean square HWT (denoted as 
) of these "null markers" will be close to one if the population is a Hardy-Weinberg population. (A chi-square distribution with 1 df has the expectation of one.) On the other hand, will tend to be greater than one if the population is stratified. By the principle of multiplicative scaling of chi-square distribution (4), one refers the adjusted statistic, HWT2/, to a 1-df chi-square distribution for each and every marker typed in the study. Such a correction procedure should reduce the number of false positive results.
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Reprint requests to Dr. Wen-Chung Lee, Graduate Institute of Epidemiology, National Taiwan University, No. 1, Jen-Ai Road, Section 1, Taipei, Taiwan (e-mail: wenchung{at}ha.mc.ntu.edu.tw).
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REFERENCES |
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 TOP REFERENCES |
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- Weinberg CR, Morris RW. Invited commentary: testing for Hardy-Weinberg disequilibirum using a genome single-nucleotide polymorphism scan based on cases only. Am J Epidemiol 2003;158:401–3.
[Free Full Text] - Lee W-C. Searching for disease-susceptibility loci by testing for Hardy-Weinberg disequilibirum in a gene bank of affected individuals. Am J Epidemiol 2003;158:397–400.
[Abstract/Free Full Text] - Jiang R, Dong J, Wang D, et al. Fine-scale mapping using Hardy-Weinberg disequilibrium. Ann Hum Genet 2001;65:207–19.[CrossRef][Web of Science][Medline]
- Reich DE, Goldstein DB. Detecting association in a case-control study while correcting for population stratification. Genet Epidemiol 2001;20:4–16.[CrossRef][Web of Science][Medline]
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Related articles in Am. J. Epidemiol.:
- Searching for Disease-Susceptibility Loci by Testing for Hardy-Weinberg Disequilibrium in a Gene Bank of Affected Individuals
- Wen-Chung Lee
Am. J. Epidemiol. 2003 158: 397-400.[Abstract] [FREE Full Text] - Invited Commentary: Testing for Hardy-Weinberg Disequilibrium Using a Genome Single-Nucleotide Polymorphism Scan Based on Cases Only
- Clarice R. Weinberg and Richard W. Morris
Am. J. Epidemiol. 2003 158: 401-403.[Extract] [FREE Full Text]
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