Statistical method scDEED for detecting dubious 2D single-cell embeddings and optimizing t-SNE and UMAP hyperparameters.

Two-dimensional (2D) embedding methods are crucial for single-cell data visualization. Popular methods such as t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP) are commonly used for visualizing cell clusters; however, it is well known that t-SNE and UMAP's 2D embeddings might not reliably inform the similarities among cell clusters. Motivated by this challenge, we present a statistical method, scDEED, for detecting dubious cell embeddings output by a 2D-embedding method. By calculating a reliability score for every cell embedding based on the similarity between the cell's 2D-embedding neighbors and pre-embedding neighbors, scDEED identifies the cell embeddings with low reliability scores as dubious and those with high reliability scores as trustworthy. Moreover, by minimizing the number of dubious cell embeddings, scDEED provides intuitive guidance for optimizing the hyperparameters of an embedding method. We show the effectiveness of scDEED on multiple datasets for detecting dubious cell embeddings and optimizing the hyperparameters of t-SNE and UMAP.

Polygenic Risk Score Modifies Prostate Cancer Risk of Pathogenic Variants in Men of African Ancestry.

Prostate cancer risk is influenced by rare and common germline variants. We examined the aggregate association of rare germline pathogenic/likely pathogenic/deleterious (P/LP/D) variants in ATM, BRCA2, PALB2, and NBN with a polygenic risk score (PRS) on prostate cancer risk among 1,796 prostate cancer cases (222 metastatic) and 1,424 controls of African ancestry. Relative to P/LP/D non-carriers at average genetic risk (33%-66% of PRS), men with low (0%-33%) and high (66%-100%) PRS had Odds Ratios (ORs) for overall prostate cancer of 2.08 [95% confidence interval (CI) = 0.58-7.49] and 18.06 (95% CI = 4.24-76.84) among P/LP/D carriers and 0.57 (95% CI = 0.46-0.71) and 3.02 (95% CI = 2.53-3.60) among non-carriers, respectively. The OR for metastatic prostate cancer was 2.73 (95% CI = 0.24-30.54) and 28.99 (95% CI = 4.39-191.43) among P/LP/D carriers and 0.54 (95% CI = 0.31-0.95) and 3.22 (95% CI = 2.20-4.73) among non-carriers, for men with low and high PRS, respectively. Lifetime absolute risks of overall prostate cancer increased with PRS (low to high) from 9.8% to 51.5% in P/LP/D carriers and 5.5% to 23.9% in non-carriers. Lifetime absolute risks of metastatic prostate cancer increased with PRS from 1.9% to 18.1% in P/LP/D carriers and 0.3% to 2.2% in non-carriers These findings suggest that assessment of prostate cancer risk for rare variant carriers should include PRS status. SIGNIFICANCE: These findings highlight the importance of considering rare and common variants to comprehensively assess prostate cancer risk in men of African ancestry.

Germline Sequencing Analysis to Inform Clinical Gene Panel Testing for Aggressive Prostate Cancer.

Importance: Germline gene panel testing is recommended for men with advanced prostate cancer (PCa) or a family history of cancer. While evidence is limited for some genes currently included in panel testing, gene panels are also likely to be incomplete and missing genes that influence PCa risk and aggressive disease. Objective: To identify genes associated with aggressive PCa. Design, Setting, and Participants: A 2-stage exome sequencing case-only genetic association study was conducted including men of European ancestry from 18 international studies. Data analysis was performed from January 2021 to March 2023. Participants were 9185 men with aggressive PCa (including 6033 who died of PCa and 2397 with confirmed metastasis) and 8361 men with nonaggressive PCa. Exposure: Sequencing data were evaluated exome-wide and in a focused investigation of 29 DNA repair pathway and cancer susceptibility genes, many of which are included on gene panels. Main Outcomes and Measures: The primary study outcomes were aggressive (category T4 or both T3 and Gleason score ≥8 tumors, metastatic PCa, or PCa death) vs nonaggressive PCa (category T1 or T2 and Gleason score ≤6 tumors without known recurrence), and metastatic vs nonaggressive PCa. Results: A total of 17 546 men of European ancestry were included in the analyses; mean (SD) age at diagnosis was 65.1 (9.2) years in patients with aggressive PCa and 63.7 (8.0) years in those with nonaggressive disease. The strongest evidence of association with aggressive or metastatic PCa was noted for rare deleterious variants in known PCa risk genes BRCA2 and ATM (P ≤ 1.9 × 10-6), followed by NBN (P = 1.7 × 10-4). This study found nominal evidence (P < .05) of association with rare deleterious variants in MSH2, XRCC2, and MRE11A. Five other genes had evidence of greater risk (OR≥2) but carrier frequency differences between aggressive and nonaggressive PCa were not statistically significant: TP53, RAD51D, BARD1, GEN1, and SLX4. Deleterious variants in these 11 candidate genes were carried by 2.3% of patients with nonaggressive, 5.6% with aggressive, and 7.0% with metastatic PCa. Conclusions and Relevance: The findings of this study provide further support for DNA repair and cancer susceptibility genes to better inform disease management in men with PCa and for extending testing to men with nonaggressive disease, as men carrying deleterious alleles in these genes are likely to develop more advanced disease.

A novel scale for the evaluation of physician drawn medical illustrations.

Effective communication is a crucial component of patient-centered care and individuals with low health literacy face significant challenges in managing their health, leading to longer hospital stays and worse outcomes. Visual aids, such as medical illustrations and pictograms, can enhance patient understanding and memory retention; however, there is a lack in the medical field of tools for evaluating and improving a physician's ability to draw clinical illustrations for their patient. This article explores an aesthetic scale created in collaboration between Boston University Medical School and the Boston University Fine-Arts department. The scale scores basic design elements that could reasonably be improved in a clinical setting. A pilot study demonstrated interrater reliability between trained artists scoring images of varying concepts and visual quality with a Cronbach's alpha of 0.95. This scale has potential use in medical visual education and clinical evaluation.

scDEED: a statistical method for detecting dubious 2D single-cell embeddings and optimizing t-SNE and UMAP hyperparameters.

Two-dimensional (2D) embedding methods are crucial for single-cell data visualization. Popular methods such as t-SNE and UMAP are commonly used for visualizing cell clusters; however, it is well known that t-SNE and UMAP's 2D embedding might not reliably inform the similarities among cell clusters. Motivated by this challenge, we developed a statistical method, scDEED, for detecting dubious cell embeddings output by any 2D-embedding method. By calculating a reliability score for every cell embedding, scDEED identifies the cell embeddings with low reliability scores as dubious and those with high reliability scores as trustworthy. Moreover, by minimizing the number of dubious cell embeddings, scDEED provides intuitive guidance for optimizing the hyperparameters of an embedding method. Applied to multiple scRNA-seq datasets, scDEED demonstrates its effectiveness for detecting dubious cell embeddings and optimizing the hyperparameters of t-SNE and UMAP.

Genome-wide association study of abdominal MRI-measured visceral fat: The multiethnic cohort adiposity phenotype study.

Few studies have explored the genetic underpinnings of intra-abdominal visceral fat deposition, which varies substantially by sex and race/ethnicity. Among 1,787 participants in the Multiethnic Cohort (MEC)-Adiposity Phenotype Study (MEC-APS), we conducted a genome-wide association study (GWAS) of the percent visceral adiposity tissue (VAT) area out of the overall abdominal area, averaged across L1-L5 (%VAT), measured by abdominal magnetic resonance imaging (MRI). A genome-wide significant signal was found on chromosome 2q14.3 in the sex-combined GWAS (lead variant rs79837492: Beta per effect allele = -4.76; P = 2.62 × 10-8) and in the male-only GWAS (lead variant rs2968545: (Beta = -6.50; P = 1.09 × 10-9), and one suggestive variant was found at 13q12.11 in the female-only GWAS (rs79926925: Beta = 6.95; P = 8.15 × 10-8). The negatively associated variants were most common in European Americans (T allele of rs79837492; 5%) and African Americans (C allele of rs2968545; 5%) and not observed in Japanese Americans, whereas the positively associated variant was most common in Japanese Americans (C allele of rs79926925, 5%), which was all consistent with the racial/ethnic %VAT differences. In a validation step among UK Biobank participants (N = 23,699 of mainly British and Irish ancestry) with MRI-based VAT volume, both rs79837492 (Beta = -0.026, P = 0.019) and rs2968545 (Beta = -0.028, P = 0.010) were significantly associated in men only (n = 11,524). In the MEC-APS, the association between rs79926925 and plasma sex hormone binding globulin levels reached statistical significance in females, but not in males, with adjustment for total adiposity (Beta = -0.24; P = 0.028), on the log scale. Rs79837492 and rs2968545 are located in intron 5 of CNTNAP5, and rs79926925, in an intergenic region between GJB6 and CRYL1. These novel findings differing by sex and racial/ethnic group warrant replication in additional diverse studies with direct visceral fat measurements.

Clonal hematopoiesis and risk of prostate cancer in large samples of European ancestry men.

Little is known regarding the potential relationship between clonal hematopoiesis (CH) of indeterminate potential (CHIP), which is the expansion of hematopoietic stem cells with somatic mutations, and risk of prostate cancer, the fifth leading cause of cancer death of men worldwide. We evaluated the association of age-related CHIP with overall and aggressive prostate cancer risk in two large whole-exome sequencing studies of 75 047 European ancestry men, including 7663 prostate cancer cases, 2770 of which had aggressive disease, and 3266 men carrying CHIP variants. We found that CHIP, defined by over 50 CHIP genes individually and in aggregate, was not significantly associated with overall (aggregate HR = 0.93, 95% CI = 0.76-1.13, P = 0.46) or aggressive (aggregate OR = 1.14, 95% CI = 0.92-1.41, P = 0.22) prostate cancer risk. CHIP was weakly associated with genetic risk of overall prostate cancer, measured using a polygenic risk score (OR = 1.05 per unit increase, 95% CI = 1.01-1.10, P = 0.01). CHIP was not significantly associated with carrying pathogenic/likely pathogenic/deleterious variants in DNA repair genes, which have previously been found to be associated with aggressive prostate cancer. While findings from this study suggest that CHIP is likely not a risk factor for prostate cancer, it will be important to investigate other types of CH in association with prostate cancer risk.

Inverted genomic regions between reference genome builds in humans impact imputation accuracy and decrease the power of association testing.

Over the last two decades, the human reference genome has undergone multiple updates as we complete a linear representation of our genome. Two versions of human references are currently used in the biomedical literature, GRCh37/hg19 and GRCh38. Conversions between these versions are critical for quality control, imputation, and association analysis. In the present study, we show that single-nucleotide variants (SNVs) in regions inverted between different builds of the reference genome are often mishandled bioinformatically. Depending on the array type, SNVs are found in approximately 2-5 Mb of the genome that are inverted between reference builds. Coordinate conversions of these variants are mishandled by both the TOPMed imputation server as well as routine in-house quality control pipelines, leading to underrecognized downstream analytical consequences. Specifically, we observe that undetected allelic conversion errors for palindromic (i.e., A/T or C/G) variants in these inverted regions would destabilize the local haplotype structure, leading to loss of imputation accuracy and power in association analyses. Though only a small proportion of the genome is affected, these regions include important disease susceptibility variants that would be affected. For example, the p value of a known locus associated with prostate cancer on chromosome 10 (chr10) would drop from 2.86 × 10-7 to 0.0011 in a case-control analysis of 20,286 Africans and African Americans (10,643 cases and 9,643 controls). We devise a straight-forward heuristic based on the popular tool, liftOver, that can easily detect and correct these variants in the inverted regions between genome builds to locally improve imputation accuracy.

A Rare Germline HOXB13 Variant Contributes to Risk of Prostate Cancer in Men of African Ancestry.

A rare African ancestry-specific germline deletion variant in HOXB13 (X285K, rs77179853) was recently reported in Martinican men with early-onset prostate cancer. Given the role of HOXB13 germline variation in prostate cancer, we investigated the association between HOXB13 X285K and prostate cancer risk in a large sample of 22 361 African ancestry men, including 11 688 prostate cancer cases. The risk allele was present only in men of West African ancestry, with an allele frequency in men that ranged from 0.40% in Ghana and 0.31% in Nigeria to 0% in Uganda and South Africa, with a range of frequencies in men with admixed African ancestry from North America and Europe (0-0.26%). HOXB13 X285K was associated with 2.4-fold increased odds of prostate cancer (95% confidence interval [CI] = 1.5-3.9, p = 2 × 10-4), with greater risk observed for more aggressive and advanced disease (Gleason ≥8: odds ratio [OR] = 4.7, 95% CI = 2.3-9.5, p = 2 × 10-5; stage T3/T4: OR = 4.5, 95% CI = 2.0-10.0, p = 2 × 10-4; metastatic disease: OR = 5.1, 95% CI = 1.9-13.7, p = 0.001). We estimated that the allele arose in West Africa 1500-4600 yr ago. Further analysis is needed to understand how the HOXB13 X285K variant impacts the HOXB13 protein and function in the prostate. Understanding who carries this mutation may inform prostate cancer screening in men of West African ancestry. PATIENT SUMMARY: A rare African ancestry-specific germline deletion in HOXB13, found only in men of West African ancestry, was reported to be associated with an increased risk of overall and advanced prostate cancer. Understanding who carries this mutation may help inform screening for prostate cancer in men of West African ancestry.

Genome-wide association study of pancreatic fat: The Multiethnic Cohort Adiposity Phenotype Study.

Several studies have found associations between higher pancreatic fat content and adverse health outcomes, such as diabetes and the metabolic syndrome, but investigations into the genetic contributions to pancreatic fat are limited. This genome-wide association study, comprised of 804 participants with MRI-assessed pancreatic fat measurements, was conducted in the ethnically diverse Multiethnic Cohort-Adiposity Phenotype Study (MEC-APS). Two genetic variants reaching genome-wide significance, rs73449607 on chromosome 13q21.2 (Beta = -0.67, P = 4.50x10-8) and rs7996760 on chromosome 6q14 (Beta = -0.90, P = 4.91x10-8) were associated with percent pancreatic fat on the log scale. Rs73449607 was most common in the African American population (13%) and rs79967607 was most common in the European American population (6%). Rs73449607 was also associated with lower risk of type 2 diabetes (OR = 0.95, 95% CI = 0.89-1.00, P = 0.047) in the Population Architecture Genomics and Epidemiology (PAGE) Study and the DIAbetes Genetics Replication and Meta-analysis (DIAGRAM), which included substantial numbers of non-European ancestry participants (53,102 cases and 193,679 controls). Rs73449607 is located in an intergenic region between GSX1 and PLUTO, and rs79967607 is in intron 1 of EPM2A. PLUTO, a lncRNA, regulates transcription of an adjacent gene, PDX1, that controls beta-cell function in the mature pancreas, and EPM2A encodes the protein laforin, which plays a critical role in regulating glycogen production. If validated, these variants may suggest a genetic component for pancreatic fat and a common etiologic link between pancreatic fat and type 2 diabetes.

Germline Sequencing DNA Repair Genes in 5545 Men With Aggressive and Nonaggressive Prostate Cancer.

BACKGROUND: There is an urgent need to identify factors specifically associated with aggressive prostate cancer (PCa) risk. We investigated whether rare pathogenic, likely pathogenic, or deleterious (P/LP/D) germline variants in DNA repair genes are associated with aggressive PCa risk in a case-case study of aggressive vs nonaggressive disease. METHODS: Participants were 5545 European-ancestry men, including 2775 nonaggressive and 2770 aggressive PCa cases, which included 467 metastatic cases (16.9%). Samples were assembled from 12 international studies and germline sequenced together. Rare (minor allele frequency < 0.01) P/LP/D variants were analyzed for 155 DNA repair genes. We compared single variant, gene-based, and DNA repair pathway-based burdens by disease aggressiveness. All statistical tests are 2-sided. RESULTS: BRCA2 and PALB2 had the most statistically significant gene-based associations, with 2.5% of aggressive and 0.8% of nonaggressive cases carrying P/LP/D BRCA2 alleles (odds ratio [OR] = 3.19, 95% confidence interval [CI] = 1.94 to 5.25, P = 8.58 × 10-7) and 0.65% of aggressive and 0.11% of nonaggressive cases carrying P/LP/D PALB2 alleles (OR = 6.31, 95% CI = 1.83 to 21.68, P = 4.79 × 10-4). ATM had a nominal association, with 1.6% of aggressive and 0.8% of nonaggressive cases carrying P/LP/D ATM alleles (OR = 1.88, 95% CI = 1.10 to 3.22, P = .02). In aggregate, P/LP/D alleles within 24 literature-curated candidate PCa DNA repair genes were more common in aggressive than nonaggressive cases (carrier frequencies = 14.2% vs 10.6%, respectively; P = 5.56 × 10-5). However, this difference was non-statistically significant (P = .18) on excluding BRCA2, PALB2, and ATM. Among these 24 genes, P/LP/D carriers had a 1.06-year younger diagnosis age (95% CI = -1.65 to 0.48, P = 3.71 × 10-4). CONCLUSIONS: Risk conveyed by DNA repair genes is largely driven by rare P/LP/D alleles within BRCA2, PALB2, and ATM. These findings support the importance of these genes in both screening and disease management considerations.

A Projection-based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models.

Measuring conditional dependence is an important topic in econometrics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution unveiled where the number of factors could be high-dimensional. It is also shown that the new test has control over the asymptotic type I error and can be calculated efficiently. A generic method for building dependency graphs without Gaussian assumption using the new test is elaborated. We show the superiority of the new method, implemented in the R package pgraph, through simulation and real data studies.

Replication and Genetic Risk Score Analysis for Pancreatic Cancer in a Diverse Multiethnic Population.

BACKGROUND: Genome-wide association studies (GWAS) have identified several SNPs associated with pancreatic cancer. No studies yet have attempted to replicate these SNPs in US minority populations. We aimed to replicate the associations of 31 GWAS-identified SNPs with pancreatic cancer and build and test a polygenic risk score (PRS) for pancreatic cancer in an ethnically diverse population. METHODS: We evaluated 31 risk variants in the Multiethnic Cohort and the Southern Community Cohort Study. We included 691 pancreatic ductal adenocarcinoma (PDAC) cases and 13,778 controls from African-American, Japanese-American, Latino, Native Hawaiian, and white participants. We tested the association between each SNP and PDAC, established a PRS using the 31 SNPs, and tested the association between the score and PDAC risk. RESULTS: Eleven of the 31 SNPs were replicated in the multiethnic sample. The PRS was associated with PDAC risk [OR top vs. middle quintile = 2.25 (95% confidence interval, 1.73-2.92)]. Notably, the PRS was associated with PDAC risk in all ethnic groups except Native Hawaiian (OR per risk allele ranged from 1.33 in Native Hawaiians to 1.91 in African Americans; P heterogeneity = 0.12). CONCLUSIONS: This is the first study to replicate 11 of the 31 GWAS-identified risk variants for pancreatic cancer in multiethnic populations, including African Americans, Japanese Americans, and Latinos. Our results also suggest a potential utility of PRS with GWAS-identified risk variants for the identification of individuals at increased risk for PDAC across multiple ethnic groups. IMPACT: PRS can potentially be used to stratify pancreatic cancer risk across multiple ethnic groups.

Genome-Wide Association Study of Liver Fat: The Multiethnic Cohort Adiposity Phenotype Study.

The global rise in fatty liver is a major public health problem. Thus, it is critical to identify both global and population-specific genetic variants associated with liver fat. We conducted a genome-wide association study (GWAS) of percent liver fat and nonalcoholic fatty liver disease (NAFLD) assessed by magnetic resonance imaging in 1,709 participants from the population-based Multiethnic Cohort Adiposity Phenotype Study. Our participants comprised older adults of five U.S. racial/ethnic groups: African Americans (n = 277), Japanese Americans (n = 424), Latinos (n = 348), Native Hawaiians (n = 274), and European Americans (n = 386). The established missense risk variant rs738409 located in patatin-like phospholipase domain containing 3 (PNPLA3) at 22q13 was confirmed to be associated with percent liver fat (P = 3.52 × 10-15) but more strongly in women than men (P heterogeneity = 0.002). Its frequency correlated with the prevalence of NAFLD across the five ethnic/racial groups. Rs738409 was also associated with homeostasis model assessment of insulin resistance (HOMA-IR) (beta = 0.028; P = 0.009) and circulating levels of insulin (beta = 0.022; P = 0.020) and alanine aminotransferase (beta = 0.016; P = 0.030). A novel association of percent liver fat with rs77249491 (located at 6q13 between limb region 1 domain containing 1 [LMBRD1] and collagen type XIX alpha 1 chain [COL19A1] (P = 1.42 × 10-8) was also observed. Rs7724941 was associated with HOMA-IR (beta = 0.12; P = 0.0005), insulin (beta = 0.11; P = 0.0003), triglycerides (beta = 0.059; P = 0.01), high-density lipoprotein (beta = -0.046; P = 0.04), and sex hormone binding globulin (beta = -0.084; P = 0.0012). This variant was present in Japanese Americans (minor allele frequency [MAF], 8%) and Native Hawaiians (MAF, 2%). Conclusion: We replicated the PNPLA3 rs738409 association in a multiethnic population and identified a novel liver fat risk variant in Japanese Americans and Native Hawaiians. GWASes of percent liver fat in East Asian and Oceanic populations are needed to replicate the rs77249491 association.

Pathogenic Variants in Cancer Predisposition Genes and Prostate Cancer Risk in Men of African Ancestry.

PURPOSE: In studies of men of European ancestry, rare pathogenic variants in DNA repair pathway genes have been shown to be associated with risk of aggressive prostate cancer. The contribution of rare coding variation to prostate cancer risk in men of African ancestry has not been established. METHODS: We sequenced a panel of 19 DNA repair and cancer predisposition genes in 2,453 African American and 1,151 Ugandan prostate cancer cases and controls. Rare variants were classified as pathogenic or putatively functionally disruptive and examined in association with prostate cancer risk and disease aggressiveness in gene and pathway-level association analyses. RESULTS: Pathogenic variants were found in 75 out of 2,098 cases (3.6%) and 31 out of 1,481 controls (2.1%) (OR=1.82, 95% CI=1.19 to 2.79, P=0.0044) with the association being stronger for more aggressive disease phenotypes (OR=3.10, 95% CI=1.54 to 6.23, P=0.0022). The highest risks for aggressive disease were observed with pathogenic variants in the ATM, BRCA2, PALB2 and NBN genes, with odds ratios ranging from ~4 to 15 in the combined study sample of African American and Ugandan men. Rare, non-pathogenic, non-synonymous variants did not have a major impact on risk of overall prostate cancer or disease aggressiveness. CONCLUSIONS: Rare pathogenic variants in DNA repair genes have appreciable effects on risk of aggressive prostate cancer in men of African ancestry. These findings have potential implications for panel testing and risk stratification in this high-risk population.

Strategies for Enriching Variant Coverage in Candidate Disease Loci on a Multiethnic Genotyping Array.

Investigating genetic architecture of complex traits in ancestrally diverse populations is imperative to understand the etiology of disease. However, the current paucity of genetic research in people of African and Latin American ancestry, Hispanic and indigenous peoples in the United States is likely to exacerbate existing health disparities for many common diseases. The Population Architecture using Genomics and Epidemiology, Phase II (PAGE II), Study was initiated in 2013 by the National Human Genome Research Institute to expand our understanding of complex trait loci in ethnically diverse and well characterized study populations. To meet this goal, the Multi-Ethnic Genotyping Array (MEGA) was designed to substantially improve fine-mapping and functional discovery by increasing variant coverage across multiple ethnicities at known loci for metabolic, cardiovascular, renal, inflammatory, anthropometric, and a variety of lifestyle traits. Studying the frequency distribution of clinically relevant mutations, putative risk alleles, and known functional variants across multiple populations will provide important insight into the genetic architecture of complex diseases and facilitate the discovery of novel, sometimes population-specific, disease associations. DNA samples from 51,650 self-identified African ancestry (17,328), Hispanic/Latino (22,379), Asian/Pacific Islander (8,640), and American Indian (653) and an additional 2,650 participants of either South Asian or European ancestry, and other reference panels have been genotyped on MEGA by PAGE II. MEGA was designed as a new resource for studying ancestrally diverse populations. Here, we describe the methodology for selecting trait-specific content for use in multi-ethnic populations and how enriching MEGA for this content may contribute to deeper biological understanding of the genetic etiology of complex disease.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.

A meta-analysis of 87,040 individuals identifies 23 new susceptibility loci for prostate cancer.

Genome-wide association studies (GWAS) have identified 76 variants associated with prostate cancer risk predominantly in populations of European ancestry. To identify additional susceptibility loci for this common cancer, we conducted a meta-analysis of > 10 million SNPs in 43,303 prostate cancer cases and 43,737 controls from studies in populations of European, African, Japanese and Latino ancestry. Twenty-three new susceptibility loci were identified at association P < 5 × 10(-8); 15 variants were identified among men of European ancestry, 7 were identified in multi-ancestry analyses and 1 was associated with early-onset prostate cancer. These 23 variants, in combination with known prostate cancer risk variants, explain 33% of the familial risk for this disease in European-ancestry populations. These findings provide new regions for investigation into the pathogenesis of prostate cancer and demonstrate the usefulness of combining ancestrally diverse populations to discover risk loci for disease.

Exome-wide association study of endometrial cancer in a multiethnic population.

Endometrial cancer (EC) contributes substantially to total burden of cancer morbidity and mortality in the United States. Family history is a known risk factor for EC, thus genetic factors may play a role in EC pathogenesis. Three previous genome-wide association studies (GWAS) have found only one locus associated with EC, suggesting that common variants with large effects may not contribute greatly to EC risk. Alternatively, we hypothesize that rare variants may contribute to EC risk. We conducted an exome-wide association study (EXWAS) of EC using the Infinium HumanExome BeadChip in order to identify rare variants associated with EC risk. We successfully genotyped 177,139 variants in a multiethnic population of 1,055 cases and 1,778 controls from four studies that were part of the Epidemiology of Endometrial Cancer Consortium (E2C2). No variants reached global significance in the study, suggesting that more power is needed to detect modest associations between rare genetic variants and risk of EC.

Genome-wide association study of endometrial cancer in E2C2.

Endometrial cancer (EC), a neoplasm of the uterine epithelial lining, is the most common gynecological malignancy in developed countries and the fourth most common cancer among US women. Women with a family history of EC have an increased risk for the disease, suggesting that inherited genetic factors play a role. We conducted a two-stage genome-wide association study of Type I EC. Stage 1 included 5,472 women (2,695 cases and 2,777 controls) of European ancestry from seven studies. We selected independent single-nucleotide polymorphisms (SNPs) that displayed the most significant associations with EC in Stage 1 for replication among 17,948 women (4,382 cases and 13,566 controls) in a multiethnic population (African America, Asian, Latina, Hawaiian and European ancestry), from nine studies. Although no novel variants reached genome-wide significance, we replicated previously identified associations with genetic markers near the HNF1B locus. Our findings suggest that larger studies with specific tumor classification are necessary to identify novel genetic polymorphisms associated with EC susceptibility.