Kohannim et al. Discovering genes that affect brain images missing genotype calls based on haplotype phasing was performed in the Brisbane young adult cohort. GENE-IMAGE ASSOCIATION SNP selection with the LASSO algorithm We incorporated all genotyped SNPs in a gene into LASSO regres- sion models and obtained coefﬁcients for each intragenic SNP. The LASSO (Tibshirani, 1996) is a form of regularized or “penalized” regression, where L1 regularization is introduced into the stan- dard multiple linear regression procedure, using a compound cost function to optimize the regression coefﬁcients: b D arg min y b X b 2 C lkbk1 Here, y represents the vector of our neuroimaging measure co-varied for age and sex (i.e., residuals of linear regression after adjustment for the covariates), X is the matrix of genotypes for a single gene coded additively for the number of minor alleles (i.e., 0, 1, or 2), and b represents the vector of ﬁtted regression coefﬁ- cients for each SNP’s effect on the neuroimaging measure. l is a positive, weighting parameter on the L1 penalty, which encourages sparsity in the resulting set of ﬁtted regression coefﬁcients. In other words, a regression model with a smaller number of coefﬁcients is favored, but this desirable characteristic is traded-off with the need for a model that offers a good ﬁt to the data (which is measured by the ﬁrst term above). Leave-one-out cross-validation was per- formed to determine the optimal penalty parameter with the mean squared error criterion. The LASSO analysis was performed gene by gene, and relatively sparse subsets of SNPs within each gene were obtained with non-zero coefﬁcients, by ﬁtting each LASSO model using optimal parameters. For our analyses, we used the “glm- net” package (Friedman et al., 2010) implemented in R17, which optimizes model ﬁtting parameters using a coordinate descent algorithm. We performed single leave-one-out cross-validation cycles with the coordinate descent algorithm for each fold and found regularization parameters that led to the smallest average mean squared errors across all folds. Multi-SNP partial F-tests Subsets of SNP genotypes within genes selected by the LASSO were incorporated into partial F -tests, and p-values were obtained for their joint effect on imaging phenotypes, after adjustment for age and sex. Partial F -tests were performed for each gene, where the full model included SNP genotypes selected by LASSO, along with covariates, and the reduced model contained only covariates. In ADNI, population structure parameters from MDS analysis were also included as covariates. For the Brisbane twin cohort, we used a version of the efﬁcient mixed-modeling association (EMMA; Kang et al., 2008) software, modiﬁed to allow for subject related- ness when ﬁtting multiple regressors in the regression model. The LASSO step used above serves as a ﬁlter to yield a less noisy and more sparse set of predictors, similarly to the data-adaptive col- lapsing method used in Chen et al. (2011) and the principal com- ponent regression method used in Hibar et al. (2011a). Although 17http://cran.r-project.org Frontiers in Neuroscience | Neurogenomics leave-one-out cross-validation is used to obtain the optimal para- meters for LASSO, the SNPs that remain in the optimized LASSO model are incorporated into partial F -tests in the same dataset. Correction for multiple comparisons In genetics, there is a notion of genome-wide signiﬁcance, based on the premise that credible results should surpass a very strin- gent statistical threshold that accounts for the very large number of separate statistical tests performed when imaging measure is asso- ciated with a large number of different variants on the genome. To compute an appropriate threshold to determine the genome-wide signiﬁcance level for our gene-centric tests, we used a Bonferroni correction: p D 0.05/(number of genes; i.e., 18,284), which yields a p-value threshold of 2.73 10 6. To perform post hoc, exploratory tests on the top genes, we created voxelwise statistical maps using partial F -tests from a multiple linear regression ﬁtted at each voxel. To correct for multiple spatial comparisons, we used a regional False Discovery Rate (FDR) method, which is now fairly standard in neuroimaging (Langers et al., 2007). RESULTS GENE-IMAGE ASSOCIATION RESULTS Sparse groups of SNPs within genes were selected by the LASSO algorithm and were subsequently incorporated into partial F -tests of association with the MRI-derived measure of temporal lobe volume (see Figure 1 for an example). We found a total of 22 genes to be genome-wide signiﬁcant (after Bonferroni correction for the total number of genes assessed). Remarkably, the top gene (MACROD2), had a p-value of 7.94 10 12 (Table 1; also see later for independent replication of this top hit). We compared F -test p-values for signiﬁcant genes with univariate p-values cor- responding to single top SNPs in the same genes (similarly to Figure 2 in Hibar et al., 2011a). In the standard, univariate GWAS (Stein et al., 2010a), two genes passed genome-wide multiple com- parison correction: GRIN2B and NRXN3. Here, we found the same two among our 22 signiﬁcant genes, and the whole-gene p-values we obtained for both were “more signiﬁcant” (i.e., had greater effect sizes) than their top SNP p-values reported in the GWAS (on the order of 10 9 and 10 8 instead of 10 7 and 10 6, respectively). The other 20 genes were undetectable with univari- ate GWAS as none of their SNPs attained an individual p-value that passed genome-wide signiﬁcance. We conﬁrmed that all top genes were expressed in the brain, using the Tissue-speciﬁc Gene Expression and Regulation (TIGER) database (Liu et al., 2008; Table 1). Although MACROD2 and GALNTL6 were not found in this database, their expression in the brain was evident from the GeneNote software (Shmueli et al., 2003). POST HOC, VOXELWISE ANALYSES To study the effects of the genes we identiﬁed in more spatial detail, we conducted post hoc, voxelwise analyses, where the par- tial F -test analysis is repeated at each voxel, and p-value maps are obtained for the gene effects, after correction for multiple com- parisons across all temporal lobe voxels. We note in advance that this type of follow-up analysis does not provide any additional sta- tistical veriﬁcation of the effects, above and beyond the evidence given to the gene for association with the overall temporal lobe August 2012 | Volume 6 | Article 115 | 4