Linear mixed models (LMMs) are widely used for heritability estimation in genome-wide association studies (GWAS). In standard approaches to heritability estimation with LMMs, a genetic relationship matrix (GRM) must be specified. In GWAS, the GRM is frequently a correlation matrix estimated from the study population's genotypes, which corresponds to a normalized Euclidean distance kernel. In this paper, we show that reliance on the Euclidean distance kernel contributes to several unresolved modeling inconsistencies in heritability estimation for GWAS. These inconsistencies can cause biased heritability estimates in the presence of linkage disequilibrium (LD), depending on the distribution of causal variants. We show that these biases can be resolved (at least at the modeling level) if one adopts a Mahalanobis distance-based GRM for LMM analysis. Additionally, we propose a new definition of partitioned heritability -- the heritability attributable to a subset of genes or single nucleotide polymorphisms (SNPs) -- using the Mahalanobis GRM, and show that it inherits many of the nice consistency properties identified in our original analysis. Partitioned heritability is a relatively new area for GWAS analysis, where inconsistency issues related to LD have previously been known to be especially pernicious.
Recently, in independent work, @cite_0 proposed using the Mahalanobis kernel in a similar way for heritability esitmation with GWAS data. 's paper primarily focuses on empirical analysis, using both simulated and real datasets to illsutrate advantages of the Mahalanobis kernel. The present work contains more precise mathematical and statistical justification for much of the work in @cite_0 , and introduces statistical principles (e.g. @math -heritability in Section ) that can be extended to other targeted application areas and genetics (like partitioning heritability).
@cite_0
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Single nucleotide polymorphism (SNP)-heritability estimation is an important topic in several research fields, including animal, plant and human genetics, as well as in ecology. Linear mixed model estimation of SNP-heritability uses the structures of genomic relationships between individuals, which is constructed from genome-wide sets of SNP-markers that are generally weighted equally in their contributions. Proposed methods to handle dependence between SNPs include, “thinning” the marker set by linkage disequilibrium (LD)-pruning, the use of haplotype-tagging of SNPs, and LD-weighting of the SNP-contributions. For improved estimation, we propose a new conceptual framework for genomic relationship matrix, in which Mahalanobis distance-based LD-correction is used in a linear mixed model estimation of SNP-heritability. The superiority of the presented method is illustrated and compared to mixed-model analyses using a VanRaden genomic relationship matrix, a matrix used by GCTA and a matrix employing LD-weighting (as implemented in the LDAK software) in simulated (using real human, rice and cattle genotypes) and real (maize, rice and mice) datasets. Despite of the computational difficulties, our results suggest that by using the proposed method one can improve the accuracy of SNP-heritability estimates in datasets with high LD. Abstract Machine learning analysis of neuroimaging data can accurately predict chronological age in healthy people. Deviations from healthy brain ageing have been associated with cognitive impairment and disease. Here we sought to further establish the credentials of ‘brain-predicted age’ as a biomarker of individual differences in the brain ageing process, using a predictive modelling approach based on deep learning, and specifically convolutional neural networks (CNN), and applied to both pre-processed and raw T1-weighted MRI data. Firstly, we aimed to demonstrate the accuracy of CNN brain-predicted age using a large dataset of healthy adults (N = 2001). Next, we sought to establish the heritability of brain-predicted age using a sample of monozygotic and dizygotic female twins (N = 62). Thirdly, we examined the test-retest and multi-centre reliability of brain-predicted age using two samples (within-scanner N = 20; between-scanner N = 11). CNN brain-predicted ages were generated and compared to a Gaussian Process Regression (GPR) approach, on all datasets. Input data were grey matter (GM) or white matter (WM) volumetric maps generated by Statistical Parametric Mapping (SPM) or raw data. CNN accurately predicted chronological age using GM (correlation between brain-predicted age and chronological age r = 0.96, mean absolute error [MAE] = 4.16 years) and raw (r = 0.94, MAE = 4.65 years) data. This was comparable to GPR brain-predicted age using GM data (r = 0.95, MAE = 4.66 years). Brain-predicted age was a heritable phenotype for all models and input data (h 2 ≥ 0.5). Brain-predicted age showed high test-retest reliability (intraclass correlation coefficient [ICC] = 0.90–0.99). Multi-centre reliability was more variable within high ICCs for GM (0.83–0.96) and poor-moderate levels for WM and raw data (0.51–0.77). Brain-predicted age represents an accurate, highly reliable and genetically-influenced phenotype, that has potential to be used as a biomarker of brain ageing. Moreover, age predictions can be accurately generated on raw T1-MRI data, substantially reducing computation time for novel data, bringing the process closer to giving real-time information on brain health in clinical settings. It is commonly believed that the use of an individual patient's genetic information should be held to a slightly different legal standard than the use of general medical information. This article in the Genomic Medicine series provides examples of appropriate and inappropriate uses of genetic information. For physicians, the biggest dilemma is whether to inform the relatives of patients who have received a diagnosis of a heritable condition for which there is treatment and who are reluctant to share this information with their families. We consider statistical inference for the explained variance @math under the high-dimensional linear model @math in the semi-supervised setting, where @math is the regression vector and @math is the design covariance matrix. A calibrated estimator, which efficiently integrates both labelled and unlabelled data, is proposed. It is shown that the estimator achieves the minimax optimal rate of convergence in the general semi-supervised framework. The optimality result characterizes how the unlabelled data affects the minimax optimal rate. Moreover, the limiting distribution for the proposed estimator is established and data-driven confidence intervals for the explained variance are constructed. We further develop a randomized calibration technique for statistical inference in the presence of weak signals and apply the obtained inference results to a range of important statistical problems, including signal detection and global testing, prediction accuracy evaluation, and confidence ball construction. The numerical performance of the proposed methodology is demonstrated in simulation studies and an analysis of estimating heritability for a yeast segregant data set with multiple traits.