GeneRiskCalc

(I): What is Hardy-Weinberg Equilibrium?

The Hardy-Weinberg Equilibrium (HWE) is a fundamental concept in Population Genetics that describes how gene variants (alleles) are expected to be passed from one generation to the next in a stable population. This fundamental concept has various assumptions, such as that the population is large, mating is random, and there are no external influences such as mutation, natural selection, migration, or genetic drift. Under these ideal conditions, the genetic makeup of the population remains constant over time (no change)  (Relethford, 2012). 

(II): Why is HWE Testing Important?

HWE testing is a critical method in genetics and population biology because it provides a baseline expectation for how gene frequencies should behave in a stable, non-evolving population. 

By comparing observed genotype frequencies with those expected, calculated using the HWE equation, researchers can:

1. Detect evolutionary forces: Deviations from HWE can indicate that forces like natural selection, genetic drift, migration, or non-random mating are acting on the population.

2. Identify genotyping errors: Unexpected deviations may signal laboratory or data-entry mistakes, making HWE a common quality control check in genetic studies.

3. Support genetic association studies: In case-control studies, testing for HWE among groups helps to ensure the population is representative and not biased.

(III): The Hypothesis Behind HWE Testing?

When researchers test for HWE, they are applying the principles of hypothesis testing just like in any scientific experiment.

🔹 Null Hypothesis (H₀) (Shreffler & Huecker, 2023): The population is in Hardy-Weinberg Equilibrium. (In other words, the observed genotype frequencies are as expected frequencies.)

🔹 Alternative Hypothesis (H₁): The population is not in Hardy-Weinberg Equilibrium. (There’s a significant difference between observed and expected genotypes.)

(IV): Based on the p-value, we choose a hypothesis.

Before we see how the hypothesis is chosen, it is important to understand how the p-value is calculated? 

The p-value is derived from the Chi-square (χ²) test, which compares the observed genotype counts with the expected counts under Hardy-Weinberg Equilibrium (Relethford, 2012). 

A significant p-value suggests that the population deviates from Hardy-Weinberg expectations. This could be due to evolutionary forces (like selection, migration, or non-random mating) or technical errors. 

Interpreting the p-value:

• p-value > 0.05:  ✅ The population is in HWE. (No significant deviation; equilibrium holds.)

• p-value ≤ 0.05: ⚠️ The population is not in HWE. (There is a significant deviation; evolutionary forces may be at play or there may be genotyping errors.)

In a case-control study, the goal is to determine whether a specific factor, such as a genetic variant of a gene, e.g., the C667 variant of the MTHFR gene, is associated with a particular outcome, such as Migraine. Individuals with the condition (Migraine) are compared to those without it (healthy controls/ individuals without migraine or headache type), and their exposure to a potential risk factor is analyzed. 

The strength of the association is typically measured using statistical methods such as the odds ratio (OR) (Szumilas, 2010), which indicates how much more (or less) likely the cases are to have been exposed to the factor compared to the controls (Tenny & Hoffman, 2023). A significant association suggests that the factor may contribute to disease risk, while a non-significant result implies no meaningful link. 

Hypothesis Based on Genetic Variant

When studying the association between a genetic variant (C667) and a disease (migraine), researchers use hypothesis testing to determine if the variant is significantly associated with the outcome. This is especially common in case-control studies or genetic association analyses (Bush & Moore, 2012).

Hypotheses:

• Null Hypothesis (H₀): There is no association between the genetic variant and the trait or disease. (The frequency of the variant is the same in both cases and controls.)

• Alternative Hypothesis (H₁): There is an association between the genetic variant and the trait or disease. (The variant occurs at different frequencies in cases versus controls.)

To test these hypotheses, researchers analyze genotype or allele frequencies between groups using statistical methods such as the Chi-square test, Fisher's Exact Test, or logistic regression, depending on the study design and data type.

The p-value from these tests helps decide whether to reject the null hypothesis. A p-value ≤ 0.05 typically indicates a statistically significant association between the genetic variant and the outcome of interest.

In genetic association studies, association hypotheses can be tested under various genetic models, each of which assumes a different way in which alleles (e.g., A and a) affect disease risk.

Step 1: Understand the Genotypes

Assume a biallelic variant with two alleles:

• A (Major/Normal Allele/ Wild Allele/ W)

• a (Minor/Risk Allele/ R)

Possible genotypes:

• AA (Homozygous Major/ Homozygous Wild/ HW)

• Aa (Heterozygous/ HT)

• aa (Homozygous Minor/ Homozygous Recessive/ HR)

Step 2: Combination and Hypothesis under genetic models (Martorell-Marugan et al., 2017).

1. Dominant Model: Compares individuals carrying at least one copy of the risk allele (HR or HT) vs. those carrying none (HW).
Genotype Grouping: Case group: HT + HR, Reference group: HW 

Purpose: Tests if having at least one risk allele increases disease risk.

2. Recessive Model: Compares individuals homozygous for the risk allele (HR) vs. those with at least one wild allele (HT or HW).
Genotype Grouping: Case group: HR, Reference group: HW + HT
Purpose: Tests if two copies of the risk allele are needed for disease risk.

3. Allele Model (Allelic Association): Compares the frequency of the risk allele (R) vs. the wild-type allele (W) between cases and controls. 

Alleles Compared: R vs. W 

Purpose: Evaluates the overall contribution of the risk allele to disease, regardless of zygosity.

4. Overdominant Model: Compares heterozygotes (HT) to both homozygous groups (HW + HR).
Genotype Grouping: Case group: HT, Reference group: HW + HR
Purpose: Tests if heterozygosity confers a different risk than either homozygous genotype.

5. Codominant Model: Examines each genotype separately such as HT vs. HW, HR vs. HW, and HR vs. HT individually.
Genotype Comparisons: HR vs. HW, HT vs. HW, HR vs. HT
Purpose: Identifies specific genotype-related risks without grouping.
A). HR vs HW: Direct comparison of individuals homozygous for the risk allele (HR) to those homozygous for the wild-type allele (HW).
Purpose: Tests the effect of full risk allele presence compared to no risk allele.
B): HR vs HT: Compares homozygous risk genotype (HR) to heterozygous genotype (HT).
Purpose: Evaluates whether risk increases with two risk alleles over one.
C): HT vs HW: Compares heterozygous individuals (HT) to wild-type homozygotes (HW).
Purpose: Assesses whether one copy of the risk allele increases disease risk.

1. Martorell-Marugan, J., Toro-Dominguez, D., Alarcon-Riquelme, M. E., & Carmona-Saez, P. (2017). MetaGenyo: a web tool for meta-analysis of genetic association studies. BMC bioinformatics, 18(1), 563. https://doi.org/10.1186/s12859-017-1990-4 

2. Relethford, J. H. (2012). Human population genetics. John Wiley & Sons. 

3. Tenny, S., & Hoffman, M. R. (2023). Odds ratio. In StatPearls [Internet]. StatPearls Publishing.

4. Bush, W. S., & Moore, J. H. (2012). Chapter 11: Genome-wide association studies. PLoS computational biology, 8(12), e1002822. 

5. Szumilas M. (2010). Explaining odds ratios. Journal of the Canadian Academy of Child and Adolescent Psychiatry = Journal de l'Academie canadienne de psychiatrie de l'enfant et de l'adolescent, 19(3), 227–229.

6. Shreffler, J., & Huecker, M. R. (2023). Hypothesis testing, P values, confidence intervals, and significance. In StatPearls [Internet]. StatPearls Publishing.