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Genome-Wide Association Study (GWAS)

A statistical technique used to identify genetic variants associated with a particular trait or disease by examining genome-wide variations in a large population.
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The statement of the theorem

Consider a set of MM genetic variants (SNPs) G={G1,…,GM}\mathbf{G} = \{G_1, \dots, G_M\} and a quantitative trait Y=(Y1,…,YN)\mathbf{Y} = (Y_1, \dots, Y_N) measured across NN individuals. The association test for a single variant GjG_j is formulated as a linear regression model: Yi=β0+βjGij+βotherXi+τi+θiβcov+τiθiY_i = \beta_0 + \beta_j G_{ij} + \boldsymbol{\beta}_{other} \boldsymbol{X}_i + \boldsymbol{\tau}_i + \boldsymbol{\theta}_i \boldsymbol{\beta}_{cov} + \boldsymbol{\tau}_i \boldsymbol{\theta}_i where βj\beta_j is the effect size, Xi\boldsymbol{X}_i are covariates, and τi\boldsymbol{\tau}_i and θi\boldsymbol{\theta}_i represent population structure (e.g., principal components). The test statistic is the Wald ratio, and the significance is determined by the p-value pj=P(∣Zj∣≥∣Zobs∣)p_j = P(|Z_j| \ge |Z_{obs}|), where ZjZ_j is the standardized estimate of βj\beta_j under the null hypothesis H0:βj=0H_0: \beta_j = 0.
Source: Wikipedia