Mathematical bounds on r 2 and the effect size in case-control genome-wide association studies

Area of Science:

• Population Genetics
• Statistical Genetics
• Genomic Epidemiology

Background:

• Case-control genome-wide association studies (GWAS) are fundamental for identifying genetic variants linked to diseases.
• Study design decisions, particularly the ratio of cases to controls, significantly influence the statistical power of GWAS.
• Allele frequencies and linkage disequilibrium (LD) impact association statistics, and these are affected by the case fraction.

Purpose of the Study:

• To investigate how varying the proportion of cases in a case-control GWAS affects the statistical power to detect genetic associations.
• To extend existing knowledge on bounds of LD statistics to understand the impact of case fraction on power.
• To provide a framework for optimizing study design based on allele characteristics.

Main Methods:

• Analysis of a mathematical model incorporating allele frequencies and LD.
• Simulations to evaluate a quantity proportional to the non-centrality parameter of association tests.
• Exploration of effects under varying conditions of dominance, penetrance, and allele frequency.

Main Results:

• The case fraction significantly influences the non-centrality parameter and, consequently, statistical power.
• The impact of case fraction on power is dependent on the specific genetic architecture of the risk allele (dominance, penetrance, frequency).
• Observed power asymmetries for risk versus protective alleles and non-optimal power with balanced samples for certain allele types are explained.

Conclusions:

• The optimal case fraction in GWAS is not always 1:1 and depends on the genetic properties of the variant.
• This framework offers insights into optimizing GWAS design for enhanced detection of disease-associated genetic variants.
• The findings are applicable as a guide for statistical power in various association tests beyond chi-squared tests.