Block coordinate descent algorithm improves variable selection and estimation in error-in-variables regression.

Medical research increasingly includes high-dimensional regression modeling with a need for error-in-variables methods. The Convex Conditioned Lasso (CoCoLasso) utilizes a reformulated Lasso objective function and an error-corrected cross-validation to enable error-in-variables regression, but requires heavy computations. Here, we develop a Block coordinate Descent Convex Conditioned Lasso (BDCoCoLasso) algorithm for modeling high-dimensional data that are only partially corrupted by measurement error. This algorithm separately optimizes the estimation of the uncorrupted and corrupted features in an iterative manner to reduce computational cost, with a specially calibrated formulation of cross-validation error. Through simulations, we show that the BDCoCoLasso algorithm successfully copes with much larger feature sets than CoCoLasso, and as expected, outperforms the naïve Lasso with enhanced estimation accuracy and consistency, as the intensity and complexity of measurement errors increase. Also, a new smoothly clipped absolute deviation penalization option is added that may be appropriate for some data sets. We apply the BDCoCoLasso algorithm to data selected from the UK Biobank. We develop and showcase the utility of covariate-adjusted genetic risk scores for body mass index, bone mineral density, and lifespan. We demonstrate that by leveraging more information than the naïve Lasso in partially corrupted data, the BDCoCoLasso may achieve higher prediction accuracy. These innovations, together with an R package, BDCoCoLasso, make error-in-variables adjustments more accessible for high-dimensional data sets. We posit the BDCoCoLasso algorithm has the potential to be widely applied in various fields, including genomics-facilitated personalized medicine research.

Improved prediction of fracture risk leveraging a genome-wide polygenic risk score.

BACKGROUND: Accurately quantifying the risk of osteoporotic fracture is important for directing appropriate clinical interventions. While skeletal measures such as heel quantitative speed of sound (SOS) and dual-energy X-ray absorptiometry bone mineral density are able to predict the risk of osteoporotic fracture, the utility of such measurements is subject to the availability of equipment and human resources. Using data from 341,449 individuals of white British ancestry, we previously developed a genome-wide polygenic risk score (PRS), called gSOS, that captured 25.0% of the total variance in SOS. Here, we test whether gSOS can improve fracture risk prediction. METHODS: We examined the predictive power of gSOS in five genome-wide genotyped cohorts, including 90,172 individuals of European ancestry and 25,034 individuals of Asian ancestry. We calculated gSOS for each individual and tested for the association between gSOS and incident major osteoporotic fracture and hip fracture. We tested whether adding gSOS to the risk prediction models had added value over models using other commonly used clinical risk factors. RESULTS: A standard deviation decrease in gSOS was associated with an increased odds of incident major osteoporotic fracture in populations of European ancestry, with odds ratios ranging from 1.35 to 1.46 in four cohorts. It was also associated with a 1.26-fold (95% confidence interval (CI) 1.13-1.41) increased odds of incident major osteoporotic fracture in the Asian population. We demonstrated that gSOS was more predictive of incident major osteoporotic fracture (area under the receiver operating characteristic curve (AUROC) = 0.734; 95% CI 0.727-0.740) and incident hip fracture (AUROC = 0.798; 95% CI 0.791-0.805) than most traditional clinical risk factors, including prior fracture, use of corticosteroids, rheumatoid arthritis, and smoking. We also showed that adding gSOS to the Fracture Risk Assessment Tool (FRAX) could refine the risk prediction with a positive net reclassification index ranging from 0.024 to 0.072. CONCLUSIONS: We generated and validated a PRS for SOS which was associated with the risk of fracture. This score was more strongly associated with the risk of fracture than many clinical risk factors and provided an improvement in risk prediction. gSOS should be explored as a tool to improve risk stratification to identify individuals at high risk of fracture.

Development of a polygenic risk score to improve screening for fracture risk: A genetic risk prediction study.

BACKGROUND: Since screening programs identify only a small proportion of the population as eligible for an intervention, genomic prediction of heritable risk factors could decrease the number needing to be screened by removing individuals at low genetic risk. We therefore tested whether a polygenic risk score for heel quantitative ultrasound speed of sound (SOS)-a heritable risk factor for osteoporotic fracture-can identify low-risk individuals who can safely be excluded from a fracture risk screening program. METHODS AND FINDINGS: A polygenic risk score for SOS was trained and selected in 2 separate subsets of UK Biobank (comprising 341,449 and 5,335 individuals). The top-performing prediction model was termed "gSOS", and its utility in fracture risk screening was tested in 5 validation cohorts using the National Osteoporosis Guideline Group clinical guidelines (N = 10,522 eligible participants). All individuals were genome-wide genotyped and had measured fracture risk factors. Across the 5 cohorts, the average age ranged from 57 to 75 years, and 54% of studied individuals were women. The main outcomes were the sensitivity and specificity to correctly identify individuals requiring treatment with and without genetic prescreening. The reference standard was a bone mineral density (BMD)-based Fracture Risk Assessment Tool (FRAX) score. The secondary outcomes were the proportions of the screened population requiring clinical-risk-factor-based FRAX (CRF-FRAX) screening and BMD-based FRAX (BMD-FRAX) screening. gSOS was strongly correlated with measured SOS (r2 = 23.2%, 95% CI 22.7% to 23.7%). Without genetic prescreening, guideline recommendations achieved a sensitivity and specificity for correct treatment assignment of 99.6% and 97.1%, respectively, in the validation cohorts. However, 81% of the population required CRF-FRAX tests, and 37% required BMD-FRAX tests to achieve this accuracy. Using gSOS in prescreening and limiting further assessment to those with a low gSOS resulted in small changes to the sensitivity and specificity (93.4% and 98.5%, respectively), but the proportions of individuals requiring CRF-FRAX tests and BMD-FRAX tests were reduced by 37% and 41%, respectively. Study limitations include a reliance on cohorts of predominantly European ethnicity and use of a proxy of fracture risk. CONCLUSIONS: Our results suggest that the use of a polygenic risk score in fracture risk screening could decrease the number of individuals requiring screening tests, including BMD measurement, while maintaining a high sensitivity and specificity to identify individuals who should be recommended an intervention.

A Polygenic Risk Score as a Risk Factor for Medication-Associated Fractures.

Some commonly prescribed drugs are associated with increased risk of osteoporotic fractures. However, fracture risk stratification using skeletal measures is not often performed to identify those at risk before these medications are prescribed. We tested whether a genomically predicted skeletal measure, speed of sound (gSOS) from heel ultrasound, which was developed in 341,449 individuals from UK Biobank and tested in a separate subset consisting of 80,027 individuals, is an independent risk factor for fracture in users of fracture-related drugs (FRDs). To do this, we first assessed 80,014 UK Biobank participants (including 12,678 FRD users) for incident major osteoporotic fracture (MOF, n = 1189) and incident hip fracture (n = 209). Effects of gSOS on incident fracture were adjusted for baseline clinical fracture risk factors. We found that each standard deviation decrease in gSOS increased the adjusted odds of MOF by 42% (95% confidence interval [CI] 1.34-1.51, p < 2 × 10-16 ) and of hip fracture by 31% (95% CI 1.15-1.50, p = 9 × 10-5 ). gSOS below versus above the mean increased the adjusted odds of MOF by 79% (95% CI 1.58-2.01, p < 2 × 10-16 ) and of hip fracture by 42% (95% CI 1.08-1.88, p = 1.3 × 10-2 ). Among FRD users, each standard deviation decrease in gSOS increased the adjusted odds of MOF by 29% (nMOF = 256, 95% CI 1.14-1.46, p = 7 × 10-5 ) and of hip fracture by 30% (nhip fracture = 68, 95% CI 1.02-1.65, p = 0.0335). FRD users with gSOS below versus above the mean had a 54% increased adjusted odds of MOF (95% 1.19-1.99, p = 8.95 × 10-4 ) and a twofold increased adjusted odds of hip fracture (95% 1.19-3.31, p = 8.5 × 10-3 ). We therefore showed that genomically predicted heel SOS is independently associated with incident fracture among FRD users. © 2020 American Society for Bone and Mineral Research.

Genetically Decreased Circulating Vascular Endothelial Growth Factor and Osteoporosis Outcomes: A Mendelian Randomization Study.

Vascular endothelial growth factor (VEGF) is important for bone formation and has been associated with osteoporosis in humans. Therefore, we conducted a two-sample Mendelian randomization study to test whether genetically decreased circulating VEGF was associated with decreased bone mineral density (BMD) and increased risk of fracture. Summary statistics from a genomewide association study (GWAS) meta-analysis of circulating VEGF level (n = 16,112) were used to identify 10 genetic variants explaining up to 52% of the variance in circulating VEGF levels. GWAS meta-analyses on dual-energy X-ray absorptiometry (DXA)-derived BMD of forearm, lumbar spine, and femoral neck (n = up to 32,735) and BMD estimated from heel calcaneus ultrasound (eBMD) (n = 426,824) were used to assess the effect of genetically lowered circulating VEGF levels on BMD. A GWAS meta-analysis including a total of 76,549 cases and 470,164 controls was used to assess the effect of genetically lowered circulating VEGF levels on risk of fracture. A natural log-transformed pg/mL decrease in circulating VEGF levels was not associated with a decrease in forearm BMD (0.02 standard deviation [SD], 95% confidence interval [CI] -0.024 to 0.064, p = 0.38), lumbar spine BMD (-0.005 SD, 95% CI -0.03 to 0.019, p = 0.67), femoral neck BMD (0.004 SD, 95% CI -0.017 to 0.026, p = 0.68), eBMD (-0.006 SD, 95% CI -0.012 to -0.001, p = 0.031) or risk of fracture (odds ratio = 0.99, 95% CI 0.98 to 1.0, p = 0.37) in inverse-variance-weighted Mendelian randomization analyses. Sensitivity analyses did not provide evidence that our results were influenced by pleiotropy. Genetically lowered circulating VEGF was not associated with a decrease in BMD or increased risk of fracture, suggesting that efforts to influence circulating VEGF level are unlikely to have beneficial effects on osteoporosis outcomes and that previous observational associations of circulating VEGF with BMD were influenced by confounding or reverse causation. © 2019 American Society for Bone and Mineral Research.