Linear mixed models (LMMs) are widely used in genome-wide association studies (GWASs) to account for population structure and relatedness, for both continuous and binary traits. Motivated by the failure of LMMs to control type I errors in a GWAS of asthma, a binary trait, we show that LMMs are generally inappropriate for analyzing binary traits when population stratification leads to violation of the LMM's constant-residual variance assumption. To overcome this problem, we develop a computationally efficient logistic mixed model approach for genome-wide analysis of binary traits, the generalized linear mixed model association test (GMMAT). This approach fits a logistic mixed model once per GWAS and performs score tests under the null hypothesis of no association between a binary trait and individual genetic variants. We show in simulation studies and real data analysis that GMMAT effectively controls for population structure and relatedness when analyzing binary traits in a wide variety of study designs.

BACKGROUND Genetic variants influencing lung function in children and adults may ultimately lead to the development of chronic obstructive pulmonary disease (COPD), particularly in high-risk groups. METHODS We tested for an association between single-nucleotide polymorphisms (SNPs) in the gene encoding matrix metalloproteinase 12 (MMP12) and a measure of lung function (prebronchodilator forced expiratory volume in 1 second [FEV1]) in more than 8300 subjects in seven cohorts that included children and adults. Within the Normative Aging Study (NAS), a cohort of initially healthy adult men, we tested for an association between SNPs that were associated with FEV1 and the time to the onset of COPD. We then examined the relationship between MMP12 SNPs and COPD in two cohorts of adults with COPD or at risk for COPD. RESULTS The minor allele (G) of a functional variant in the promoter region of MMP12 (rs2276109 [−82A→G]) was positively associated with FEV1 in a combined analysis of children with asthma and adult former and current smokers in all cohorts (P=2×10−6). This allele was also associated with a reduced risk of the onset of COPD in the NAS cohort (hazard ratio, 0.65; 95% confidence interval [CI], 0.46 to 0.92; P = 0.02) and with a reduced risk of COPD in a cohort of smokers (odds ratio, 0.63; 95% CI, 0.45 to 0.88; P = 0.005) and among participants in a family-based study of early-onset COPD (P = 0.006). CONCLUSIONS The minor allele of a SNP in MMP12 (rs2276109) is associated with a positive effect on lung function in children with asthma and in adults who smoke. This allele is also associated with a reduced risk of COPD in adult smokers.