Examining the rare disease assumption used to justify HWE testing with control samples

Virginia L. Ma; Shili Lin; Virginia L. Ma; Shili Lin

doi:10.3934/mbe.2020004

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 1: 73-91. doi: 10.3934/mbe.2020004

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Examining the rare disease assumption used to justify HWE testing with control samples

Virginia L. Ma ¹,
Shili Lin ^{2
,
,}

1.
Columbus Academy, 4300 Cherry Bottom Road, Columbus, OH 43230, USA
2.
Department of Statistics, Ohio State University, Columbus, OH 43210, USA

Received: 21 February 2019 Accepted: 16 September 2019 Published: 25 September 2019

Many statistical methods for analyzing genetic data, such as those used in genome-wide association studies, assume Hardy-Weinberg Equilibrium (HWE). Therefore, to use such methods, one must check whether the HWE assumption is valid. For a case-control study, researchers have recognized that Hardy Weinberg proportions will be distorted if the marker being tested happens to be associated with the disease. To alleviate this problem, many studies carry out HWE testing on controls only. A number of papers in the literature have justified this practice by making the rare disease assumption without providing rigorous theoretical basis for this justification. Even though many of the diseases studied today are common, whether it is justifiable to use controls to test for HWE when the disease is indeed rare remains an outstanding issue. In this study, we address the rare disease assumption as well as potential problems associated with testing for HWE using controls only, regardless of the prevalence of the disease. We carried out theoretical derivations and numerical studies; the latter were performed using simulated genotypes as well as data from the 1000 Genomes Project. The results from our study are striking: the type Ⅰ error can be severely inflated, regardless of whether the disease being investigated is rare or common. This study shows that, based on the common practice of using controls only to test for HWE, many genetic variants will be discarded erroneously, wasting valuable information and hindering the ability to detect disease-associated variants.
- Hardy-Weinberg equilibrium,
- case-control study,
- rare disease assumption,
- genome-wide association studies,
- 1000 Genomes Project
Citation: Virginia L. Ma, Shili Lin. Examining the rare disease assumption used to justify HWE testing with control samples[J]. Mathematical Biosciences and Engineering, 2020, 17(1): 73-91. doi: 10.3934/mbe.2020004

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Abstract

Many statistical methods for analyzing genetic data, such as those used in genome-wide association studies, assume Hardy-Weinberg Equilibrium (HWE). Therefore, to use such methods, one must check whether the HWE assumption is valid. For a case-control study, researchers have recognized that Hardy Weinberg proportions will be distorted if the marker being tested happens to be associated with the disease. To alleviate this problem, many studies carry out HWE testing on controls only. A number of papers in the literature have justified this practice by making the rare disease assumption without providing rigorous theoretical basis for this justification. Even though many of the diseases studied today are common, whether it is justifiable to use controls to test for HWE when the disease is indeed rare remains an outstanding issue. In this study, we address the rare disease assumption as well as potential problems associated with testing for HWE using controls only, regardless of the prevalence of the disease. We carried out theoretical derivations and numerical studies; the latter were performed using simulated genotypes as well as data from the 1000 Genomes Project. The results from our study are striking: the type Ⅰ error can be severely inflated, regardless of whether the disease being investigated is rare or common. This study shows that, based on the common practice of using controls only to test for HWE, many genetic variants will be discarded erroneously, wasting valuable information and hindering the ability to detect disease-associated variants.

References

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