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Establishing a low-dimensional representation of the data leads to efficient data learning strategies. In many cases, the reduced dimension needs to be explicitly stated and estimated from the data. We explore the estimation of dimension in finite samples as a constrained optimization problem, where the estimated dimension is a maximizer of a penalized profile likelihood criterion within the framework of a probabilistic principal components analysis. Unlike other penalized maximization problems that require an "optimal" penalty tuning parameter, we propose a data-averaging procedure whereby the estimated dimension emerges as the most favourable choice over a range of plausible penalty parameters. The proposed heuristic is compared to a large number of alternative criteria in simulations and an application to gene expression data. Extensive simulation studies reveal that none of the methods uniformly dominate the other and highlight the importance of subject-specific knowledge in choosing statistical methods for dimension learning. Our application results also suggest that gene expression data have a higher intrinsic dimension than previously thought. Overall, our proposed heuristic strikes a good balance and is the method of choice when model assumptions deviated moderately.

It has been postulated that rare coding variants (RVs; MAF5%, with height having the highest h2RV at 21.9% (95% CI: 19.0-24.8%). The total heritability, including common and rare variants, recovered pedigree-based estimates for 11 traits. RARity can estimate gene-level h2RV, enabling the assessment of gene-level characteristics and revealing 12 novel gene-phenotype relationships. Finally, we demonstrated that in silico pathogenicity prediction (variant-level) and gene-level annotations do not generally enrich for RVs that over-contribute to complex trait variance, and thus, novel methods are needed to predict RV functionality.

Complex traits can share a substantial proportion of their polygenic heritability. However, genome-wide polygenic correlations between pairs of traits can mask heterogeneity in their shared polygenic effects across loci. We propose a novel method (weighted maximum likelihood-regional polygenic correlation [RPC]) to evaluate polygenic correlation between two complex traits in small genomic regions using summary association statistics. Our method tests for evidence that the polygenic effect at a given region affects two traits concurrently. We show through simulations that our method is well calibrated, powerful, and more robust to misspecification of linkage disequilibrium than other methods under a polygenic model. As small genomic regions are more likely to harbor specific genetic effects, our method is ideal to identify heterogeneity in shared polygenic correlation across regions. We illustrate the usefulness of our method by addressing two questions related to cardiometabolic traits. First, we explored how RPC can inform on the strong epidemiological association between high-density lipoprotein cholesterol and coronary artery disease (CAD), suggesting a key role for triglycerides metabolism. Second, we investigated the potential role of PPARγ activators in the prevention of CAD. Our results provide a compelling argument that shared heritability between complex traits is highly heterogeneous across loci.

BackgroundComplex traits can share a substantial proportion of their polygenic heritability. However, genome-wide polygenic correlations between pairs of traits can mask heterogeneity in their shared polygenic effects across loci. We propose a novel method (WML-RPC) to evaluate polygenic correlation between two complex traits in small genomic regions using summary association statistics. Our method tests for evidence that the polygenic effect at a given region affects two traits concurrently.ResultsWe show through simulations that our method is well calibrated, powerful and more robust to misspecification of linkage disequilibrium than other methods under a polygenic model. As small genomic regions are more likely to harbour specific genetic effects, our method is ideal to identify heterogeneity in shared polygenic correlation across regions. We illustrate the usefulness of our method by addressing two questions related to cardio-metabolic traits. First, we explored how regional polygenic correlation can inform on the strong epidemiological association between HDL cholesterol and coronary artery disease (CAD), suggesting a key role for triglycerides metabolism. Second, we investigated the potential role of PPARγ activators in the prevention of CAD.ConclusionsOur results provide a compelling argument that shared heritability between complex traits is highly heterogeneous across loci.

The advent of precision medicine is largely dependent on the availability of accurate and highly predictive gene scores. While progress has been made identifying genetic determinants of polygenic traits, the phenotypic variance explained by gene scores derived from genome-wide associations remains modest. Machine-learning techniques have proven very useful for solving a broad range of prediction problems, yet are not widely applied to complex traits prediction using gene scores. We propose a novel machine-learning heuristic (MLH) to improve the predictive performance of gene scores. It is based on two innovative features. We first apply gradient boosted regression trees models to leverage a large number of SNPs and optimize the weights of individual SNPs included in the gene scores. We show a calibration set sample size of ~200 individuals is sufficient for optimal performance. We then correct for linkage disequilibrium (LD) between SNPs using a novel procedure, enabling retention of all SNPs in the gene score irrespective of LD. Our novel heuristic yielded a prediction R2 of 0.237, 0.082 for height and BMI using GIANT summary association statistics in the UKBiobank study (N=130K; 1.98M SNPs), explaining 46.6% and 32.6% of the overall polygenic variance, respectively. Corresponding area under the ROC was 0.602 for diabetes in the UKBiobank using DIAGRAM association statistics. MLH outperformed other gene score heuristics for height and BMI and was equivalent to LDpred for diabetes. Results were independently validated in participants of the HRS (N=8,292) study. Our report demonstrates the potential of machine-learning methods for polygenic trait prediction. Our method has wide-ranging applications, from predicting medically important traits to creating stronger instrumental variables for Mendelian randomization studies.

Machine-learning techniques have helped solve a broad range of prediction problems, yet are not widely used to build polygenic risk scores for the prediction of complex traits. We propose a novel heuristic based on machine-learning techniques (GraBLD) to boost the predictive performance of polygenic risk scores. Gradient boosted regression trees were first used to optimize the weights of SNPs included in the score, followed by a novel regional adjustment for linkage disequilibrium. A calibration set with sample size of ~200 individuals was sufficient for optimal performance. GraBLD yielded prediction R

Meta-analysis is a commonly used approach to increase the sample size for genome-wide association searches when individual studies are otherwise underpowered. Here, we present a meta-analysis procedure to estimate the heterogeneity of the quantitative trait variance attributable to genetic variants using Levene's test without needing to exchange individual-level data. The meta-analysis of Levene's test offers the opportunity to combine the considerable sample size of a genome-wide meta-analysis to identify the genetic basis of phenotypic variability and to prioritize single-nucleotide polymorphisms (SNPs) for gene–gene and gene–environment interactions. The use of Levene's test has several advantages, including robustness to departure from the normality assumption, freedom from the influence of the main effects of SNPs, and no assumption of an additive genetic model. We conducted a meta-analysis of the log-transformed body mass index of 5892 individuals and identified a variant with a highly suggestive Levene's test P-value of 4.28E-06 near the NEGR1 locus known to be associated with extreme obesity.

Despite considerable efforts, known genetic associations only explain a small fraction of predicted heritability. Regional associations combine information from multiple contiguous genetic variants and can improve variance explained at established association loci. However, regional associations are not easily amenable to estimation using summary association statistics because of sensitivity to linkage disequilibrium (LD). We now propose a novel method, LD Adjusted Regional Genetic Variance (LARGV), to estimate phenotypic variance explained by regional associations using summary statistics while accounting for LD. Our method is asymptotically equivalent to a multiple linear regression model when no interaction or haplotype effects are present. It has several applications, such as ranking of genetic regions according to variance explained or comparison of variance explained by two or more regions. Using height and BMI data from the Health Retirement Study (N = 7,776), we show that most genetic variance lies in a small proportion of the genome and that previously identified linkage peaks have higher than expected regional variance.

SummaryThe fat mass and obesity associated (FTO) gene has been implicated with obesity and dietary intake predominantly in European populations. We assessed the association between the FTO rs9939609 variant with body fat distribution and dietary intake in a multi-ethnic population. Aboriginal, Chinese, European and South Asian participants living in Canada (n=706) were assessed for body fat and inner-abdominal fat using imaging techniques, dietary intake and genotyped for the FTO rs9939609 variant. Linear regression was used to study the associations between the minor allele of the variant and measures of adiposity and dietary intake. Minor allele frequencies were: Aboriginals (17%), Chinese (17%), Europeans (39%) and South Asians (31%). The rs9939609 variant was associated with intake of dietary macronutrients in Aboriginals and Europeans only. In the total population, there were positive associations between the rs9939609 minor allele and greater fat mass (0·94±0·56 kg, P=0·045), per cent body fat (0·7±0·4%, P=0·031), relative greater subcutaneous abdominal adipose tissue (4·9±2·8%, P=0·039) and percent daily calories from fat (0·4±0·2%, P=0·064). Our findings suggest that the FTO rs9939609 minor allele may be associated with dietary intake in adults and is positively associated with regional fat deposition.

We agree with Professor Haft, in response to our article,1 that the prognostic significance of atrial arrhythmias lasting 17 000 electrograms for AF episodes lasting ≥6 …

Detection of gene-environment interactions using an exhaustive search necessarily raises the multiple hypothesis problem. While frequently used to control for experiment-wise type I error, Bonferroni correction is overly conservative and results in reduced statistical power. We have previously shown that prioritizing SNPs on the basis of heterogeneity in quantitative trait variance per genotype leads to increased power to detect genetic interactions. Our proposed method, variance prioritization (VP), selects SNPs having significant heterogeneity in variance per genotype using a pre-determined P-value threshold. We now suggest prioritizing SNPs individually such that the optimal heterogeneity of variance P-value is determined for each SNP. The large number of SNPs in genome-wide studies calls for a fast algorithm to output the optimal prioritization threshold for each SNP. In this report, we present such an algorithm, the Gene Environment Wide Interaction Search Threshold (GEWIST), and show that the use of GEWIST will increase power under a variety of interaction scenarios. Furthermore, by integrating over possible interaction effect sizes, we provide a framework to optimize prioritization in situations where interactions are a priori unknown.

Aims/hypothesis South Asians are up to four times more likely to develop type 2 diabetes than white Europeans. It is postulated that the higher prevalence results from greater genetic risk. To evaluate this hypothesis, we: (1) systematically reviewed the literature for single nucleotide polymorphisms (SNPs) predisposing to type 2 diabetes in South Asians; (2) compared risk estimates, risk alleles and risk allele frequencies of predisposing SNPs between South Asians and white Europeans; and (3) tested the association of novel SNPs discovered from South Asians in white Europeans. Methods MEDLINE, Embase, the Cumulative Index to Nursing and Allied Health Literature (CINAHL) and the Cochrane registry were searched for studies of genetic variants associated with type 2 diabetes in South Asians. Meta-analysis estimates for common and novel bi-allelic SNPs in South Asians were compared with white Europeans from the DIAbetes Genetics Replication And Meta-analysis (DIAGRAM) consortium. The population burden from predisposing SNPs was assessed using a genotype score. Results Twenty-four SNPs from 21 loci were associated with type 2 diabetes in South Asians after meta-analysis. The majority of SNPs increase odds of the disorder by 15–35% per risk allele. No substantial differences appear to exist in risk estimates between South Asians and white Europeans from SNPs common to both groups, and the population burden also does not differ. Eight of the 24 are novel SNPs discovered from South Asian genome-wide association studies, some of which show nominal associations with type 2 diabetes in white Europeans. Conclusions/interpretation Based on current literature there is no strong evidence to indicate that South Asians possess a greater genetic risk of type 2 diabetes than white Europeans. Electronic supplementary material The online version of this article (doi:10.1007/s00125-014-3354-1) contains peer-reviewed but unedited supplementary material, which is available to authorised users.