Mixed Logistic Regression in Genome-Wide Association Studies

Abstract

Motivation:Mixed linear models (MLM) have been widely used to account for population structure in case-control genome-wide association studies, the status being analyzed as a quantitative phenotype.Chen et al. proved that this method is inappropriate and proposed a score test for the mixed logistic regression (MLR). However this test does not allow an estimation of the variants' effects. Results:We propose two computationally efficient methods to estimate the variants' effects. Their properties are evaluated on two simulations sets, and compared with other methods (MLM, logistic regression). MLR performs the best in all circumstances. The variants' effects are well evaluated by our methods, with a moderate bias when the effect sizes are large. Additionally, we propose a stratified QQ-plot, enhancing the diagnosis of p-values inflation or deflation, when population strata are not clearly identified in the sample.Availability: All methods are implemented in the R package milorGWAS available at https://github.com/genostats/milorGWAS.

Heterosis, inbreeding depression and genetic divergence in maize

“…Where g(.) represent any link function (commonly in the exponential family), pi the probability of success for individual i, X the incidence matrix for the fixed covariates, bi the set of non-marker fixed-effect including intercept, G the matrix of genotypes (coded as 0, 1, or 2), mi the marker fixed effect, and ui the random polygenic effects (Chen et al 2019;Milet and Perdry 2020;Stanhope and Abney 2012). Commonly the random effects are assumed to follow a multivariate normal distribution with mean zero and variance-covariance equal to 2 , where K represents the kinship matrix and 2 the polygenic additive variance (Chen et al 2019;Chen et al 2016;Stanhope and Abney 2012).…”

“…Gauss-Hermite Quadrature, Adaptive Gauss-Hermite Quadrature, or Laplace approximation, to find the marginal likelihood function (Christensen 2006;Cox and Snell 1981;Kim et al 2013;Kleinbaum 2010;Wang et al 2011;Whittemore and Halpern 2003). The logistic mixed regression model, using one of the numerical or approximated methods, can be implemented in SAS software (SAS Institute, Cary, NC), by using the "PROC GLIMMIX" or "PROC NLMIXED" procedures (Kim et al 2013;Milet and Perdry 2020;Shenstone et al 2018),…”