1. Hardy Weinberg Equilibrium?

The Hardy-Weinberg equilibrium is a cornerstone of population genetics, offering a theoretical model of a non-evolving population. It posits that in a large, randomly mating population, allele and genotype frequencies remain constant across generations, provided that certain conditions are met. These conditions include the absence of mutations, random mating, no gene flow (migration), no genetic drift (infinitely large population size), and no natural selection. The principle serves as a null hypothesis, allowing scientists to compare real-world populations against this theoretical baseline. Deviations from the expected Hardy-Weinberg frequencies suggest that evolutionary forces are actively shaping the population's genetic makeup. The equilibrium is mathematically represented by two key equations: p + q = 1, where p and q denote the frequencies of two alleles, and p² + 2pq + q² = 1, which describes the frequencies of homozygous dominant, heterozygous, and homozygous recessive genotypes, respectively. In essence, the Hardy-Weinberg principle provides a framework for understanding how allele and genotype frequencies behave in the absence of evolutionary influences, thereby highlighting the significance of evolutionary forces when observed deviations occur (Relethford, 2012). 

2. Genetic Association or Gene Association?

Genetic association studies are pivotal investigations that explore the relationship between genetic variations and the susceptibility to diseases or specific traits. These studies delve into the human genome to pinpoint genetic variants, such as single nucleotide polymorphisms (SNPs), that exhibit a statistical association with a particular condition. Rather than establishing direct causation, they illuminate regions within the genome that are more prevalent in individuals affected by the disease compared to those who are not. To achieve this, researchers conduct large-scale population studies, often employing case-control designs, where the genetic makeup of individuals with the disease is compared to that of healthy controls (Hirschhorn et al., 2002). These investigations utilize various genetic models such as dominant, recessive, allele, over-dominant, and codominant to find how different genetic variants contribute to disease risk. The significance of these studies lies in their potential to elucidate disease mechanisms, develop risk prediction tools, and pave the way for personalized medicine and targeted drug development. However, challenges such as multiple testing, population stratification, gene-environment interactions, and the small effect sizes of many genetic variants necessitate rigorous statistical analyses and careful interpretation of results. Ultimately, genetic association studies are instrumental in unraveling the intricate interplay between genetics and disease, fostering advancements in disease prevention, diagnosis, and treatment. 

3. Odds Ratio?

The odds ratio (OR) is a measure of association between an exposure and an outcome. It represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure (Tenny & Hoffman, 2023). 

The odds ratio (OR) measures the association between exposure and outcome. Here's how to interpret it:

• OR > 1: The exposure is associated with higher odds of the outcome. (e.g., OR = 2 means the outcome is twice as likely with the exposure).

• OR < 1: The exposure is associated with lower odds of the outcome (a protective effect). (e.g., OR = 0.5 means the outcome is half as likely with the exposure).

• OR = 1: There is no association between the exposure and the outcome.

Crucially, also consider the confidence interval (CI):

• If the CI includes 1, the association is not statistically significant.

• A narrow CI indicates a more precise estimate.

• A wide CI indicates a less precise estimate.

4. Bonferroni Correction?

The Bonferroni correction is a statistical method used to adjust the significance level (alpha) when performing multiple hypothesis tests. It aims to reduce the risk of false positives (Type I errors) by dividing the original alpha level by the number of tests conducted (Bonferroni, 1936).

Example for 7 Genetic Models: 

Here we are conducting a genetic association study and testing 7 different genetic models (dominant, recessive, over-dominant, allele, codominant such as HR vs HW, HR vs HT, & HT vs HW) for their association with a specific disease.

1. Original Alpha: We typically set our significance level (alpha) at 0.05. This means we are willing to accept a 5% chance of a false positive for a single test.

2. Multiple Tests: Because we are testing 7 models, we are performing 7 separate statistical tests. This increases the overall chance of a false positive.

3. Bonferroni Correction: To account for these multiple tests, we divide the original alpha (0.05) by the number of tests (7): Corrected alpha = 0.05 / 7 ≈ 0.00714

Interpretation: 

3. • Instead of using the standard p < 0.05, we now use p < 0.00714 to determine statistical significance.

   • If any of the 7 models shows a p-value less than 0.00714, we would consider that model's association with the disease to be statistically significant after Bonferroni correction.

   • Any p-values greater than 0.00714 would be considered not statistically significant.

In conclusion, using the Bonferroni correction, we are making it much harder to declare a result significant, ensuring that any significant findings are less likely to be due to random chance. This is particularly important when dealing with multiple tests, such as when comparing various genetic models.

References:

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

2. Tenny, S., & Hoffman, M. R. (2023). Odds Ratio. In StatPearls. StatPearls Publishing. 

3. Hirschhorn, J. N., Lohmueller, K., Byrne, E., & Hirschhorn, K. (2002). A comprehensive review of genetic association studies. Genetics in medicine : official journal of the American College of Medical Genetics, 4(2), 45–61. https://doi.org/10.1097/00125817-200203000-00002 

4. Bonferroni, C. (1936). Teoria statistica delle classi e calcolo delle probabilita. Pubblicazioni del R istituto superiore di scienze economiche e commericiali di firenze, 8, 3-62.