Multiple augmented reduced rank regression for pan-cancer analysis.

Statistical approaches that successfully combine multiple datasets are more powerful, efficient, and scientifically informative than separate analyses. To address variation architectures correctly and comprehensively for high-dimensional data across multiple sample sets (ie, cohorts), we propose multiple augmented reduced rank regression (maRRR), a flexible matrix regression and factorization method to concurrently learn both covariate-driven and auxiliary structured variations. We consider a structured nuclear norm objective that is motivated by random matrix theory, in which the regression or factorization terms may be shared or specific to any number of cohorts. Our framework subsumes several existing methods, such as reduced rank regression and unsupervised multimatrix factorization approaches, and includes a promising novel approach to regression and factorization of a single dataset (aRRR) as a special case. Simulations demonstrate substantial gains in power from combining multiple datasets, and from parsimoniously accounting for all structured variations. We apply maRRR to gene expression data from multiple cancer types (ie, pan-cancer) from The Cancer Genome Atlas, with somatic mutations as covariates. The method performs well with respect to prediction and imputation of held-out data, and provides new insights into mutation-driven and auxiliary variations that are shared or specific to certain cancer types.

Association of a dietary pattern related to serum vitamin D levels with metabolic syndrome risk among Korean adults: based on the Korean national health and nutrition examination survey.

PURPOSE: Vitamin D has a crucial role in our metabolic health. We aimed to examine associations of vitamin D status and its related dietary pattern (DP) with prevalent risk of metabolic syndrome (MetS) in 9,237 Korean adults aged 19-64 years based on the National Health and Nutrition Examination Survey. METHODS: Vitamin D status was examined by serum 25-hydroxyvitamin D (25(OH)D). A vitamin D-related DP associated with 25(OH)D levels was derived using reduced rank regression (RRR). Associations of vitamin D status and its related DP with MetS prevalence were examined using multivariable logistic regression models adjusted for potential confounders. RESULTS: Men with sufficient vitamin D status had a 44% lower risk of MetS prevalence (OR: 0.56; 95%CI: 0.36-0.87) compared to those with deficiency. A vitamin D-related DP derived using RRR was characterized by high intakes of vegetables, fish, fruits, and nuts and low intakes of eggs, oils, and mushrooms in this study population. Among men, the DP was significantly associated with a lower risk of MetS prevalence, showing a 12% (95%CI: 4-20%) reduction in risk for a one-unit increase in the DP score. However, there was no significant association among women. CONCLUSION: The study's findings suggest that a sufficient vitamin D status and a related DP with high intakes of vegetables, fish, fruit, and nuts were associated with the risk of MetS, particularly in Korean male adults.

Development and validation of dietary depression index in Chinese adults.

Objective: Previous studies have suggested diet was associated with depressive symptoms. We aimed to develop and validate Dietary Depression Index (DDI) based on dietary prediction of depression in a large Chinese cancer screening cohort.Methods: In the training set (n = 2729), we developed DDI by using intake of 20 food groups derived from a food frequency questionnaire to predict depression as assessed by Patient Health Questionnaire-9 based on the reduced rank regression method. Sensitivity, specificity, positive predictive value, and negative predictive value were used to assess the performance of DDI in evaluating depression in the validation dataset (n = 1176).Results: Receiver operating characteristic analysis was constructed to determine the best cut-off value of DDI in predicting depression. In the study population, the DDI ranged from -3.126 to 1.810. The discriminative ability of DDI in predicting depression was good with the AUC of 0.799 overall, 0.794 in males and 0.808 in females. The best cut-off values of DDI for depression prediction were 0.204 overall, 0.330 in males and 0.034 in females. DDI was a validated method to assess the effects of diet on depression.Conclusion: Among individual food components in DDI, fermented vegetables, fresh vegetables, whole grains and onions were inversely associated, whereas legumes, pickled vegetables and rice were positively associated with depressive symptoms.

Trimethylamine N-oxide, ß-alanine, tryptophan index, and vitamin B6-related dietary patterns in association with stroke risk.

BACKGROUND AND AIMS: The aim of this study was to examine the associations of dietary patterns derived by reduced-rank regression (RRR) model reflecting variation in novel biomarkers (trimethylamine N-oxide, ß-alanine, tryptophan index, and vitamin B6) with stroke risk. METHODS AND RESULTS: We performed analyses based on a community-based cohort study "the Prospective Follow-up Study on Cardiovascular Morbidity and Mortality in China (PFS-CMMC)". Factor loadings were calculated by RRR using 11 food groups collected via a validated food frequency questionnaire and the four response variables based on its nested case-control data (393 cases of stroke vs. 393 matched controls). Dietary pattern scores were derived by applying the factor loadings to the food groups in the entire cohort (n = 15,518). The associations of dietary pattern with the stroke risk were assessed using Cox proportional hazards models. The dietary pattern characterized with higher intakes of red meat and poultry but lower intakes of fresh vegetables, fresh fruits, and fish/seafoods were identified for further analyses. The hazard ratios (HR) for the highest vs. lowest quartile was 1.55 [95 % confidence interval (CI): 1.18-2.03, P trend = 0.001] for total stroke, 2.96 [95 % CI: 1.53-5.71, P trend <0.001] for non-ischemic stroke, after adjustment for sex, age, educational attainment, current smoking, current drinking, body mass index, total energy intake, family history of stroke, hypertension, diabetes, hyperlipidemia, and estimated glomerular filtration rate. CONCLUSION: Our findings highlight the importance of limited meat intake and increased intakes of fresh vegetables, fruits, and fish/seafoods in the prevention of stroke among Chinese adults.

Dietary patterns derived by reduced rank regression are associated with lipid disorders among Korean adults: a cross-sectional analysis.

BACKGROUND: Lipid disorders are a potent risk factor for cardiovascular diseases. Moreover, the intake of dietary fatty acids has been closely related to blood lipid levels. Therefore, this cross-sectional study examined the associations between dietary patterns related to fatty acid intake and lipid disorders in Korean adults. METHODS: From the 2013-2019 Korea National Health and Nutrition Examination Surveys data, 8399 men and 11404 women (aged ≥ 19 years) were selected. Reduced rank regression was employed to identify dietary patterns from 26 food groups, aiming to explain the maximum variation in the intake of saturated fatty acids (SFA), polyunsaturated fatty acids (PUFA), omega-3 fatty acids, and the PUFA/SFA ratio. Associations of quintiles (Q) of dietary pattern scores with lipid disorders were examined using multiple logistic regression stratified by sex. RESULTS: Three dietary patterns were identified: dietary pattern 1 showed positive factor loadings for vegetable oils, seasonings, legumes, nuts, and fish; dietary pattern 2 was high in consumption of red meat, bread and snacks, and milk and dairy products; and dietary pattern 3 was rich in fish and milk and dairy products. In men, dietary pattern 3 was inversely associated with elevated triglycerides (Q5 vs. Q1: odds ratio [OR] = 0.82, 95% confidence interval [CI] = 0.69-0.97, P-trend = 0.008). In women, dietary pattern 2 was positively associated with elevated total cholesterol (OR = 1.31, 95% CI = 1.12-1.52, P-trend < 0.001) but inversely associated with low HDL-cholesterol (OR = 0.70, 95% CI = 0.59-0.83, P-trend < 0.001). CONCLUSION: In this study, dietary patterns explaining the intake of various types of fatty acids were differentially associated with lipid disorders in Korean adults. Dietary pattern characterized by higher intakes of red meat, bread and snacks and milk and dairy products were positively associated with elevated total cholesterol, whereas dietary pattern rich in fish consumption showed an inverse association with elevated triglycerides. These findings could be instrumental in developing dietary guidelines and strategies for preventing and managing lipid disorders in this population.

Associations Between Dietary Patterns and Kidney Health Assessed in the Population-Based CHRIS Study Using Reduced Rank Regression.

OBJECTIVE: While diet plays a key role in chronic kidney disease (CKD) management, the potential for diet to impact CKD prevention in the general population is less clear. Using a priori knowledge, we derived disease-related dietary patterns (DPs) through reduced rank regression (RRR) and investigated associations with kidney function, separately focusing on generally healthy individuals and those with self-reported kidney diseases, hypertension, or diabetes mellitus. METHODS: Eight thousand six hundred eighty-six participants from the population-based Cooperative Health Research in South Tyrol study were split into a group free of kidney disease, hypertension and diabetes (n = 6,133) and a group with any of the 3 conditions (n = 2,553). Diet was assessed through the self-administered Global Allergy and Asthma Network of Excellence food frequency questionnaire and DPs were derived through RRR selecting food frequency questionnaire-derived sodium, potassium, phosphorus, and protein intake as mediators. Outcomes were creatinine-based estimated glomerular filtration rate, urinary albumin-to-creatinine ratio, CKD and microalbuminuria. Multiple linear and logistic models were used to assess associations between RRR-based DPs and kidney outcomes separately in the 2 analytic groups. RESULTS: We identified 3 DPs, where high adherence reflected high levels of all nutrients (DP1), high potassium-phosphorus and low protein-sodium levels (DP2), and low potassium-sodium and high protein-phosphorus levels (DP3), respectively. We observed heterogeneous associations with kidney outcomes, varying by analytic group and sex. Kidney outcomes were much more strongly associated with DPs than with single nutrients. CONCLUSION: RRR is a feasible approach to estimate disease-related DPs and explore the combined effects of nutrients on kidney health. Heterogeneous associations across kidney outcomes suggest possible specificity to kidney function or damage. In individuals reporting kidney disease, hypertension or diabetes, specific dietary habits were associated with better kidney health, indicating that disease-specific dietary interventions can be effective for disease control.

Associations between an obesity-related dietary pattern and incidence of overall and site-specific cancers: a prospective cohort study.

BACKGROUND: A dietary pattern (DP) may impact on cancer incidence more strongly than individual foods, but this association remains uncertain. Here, we aimed to broadly explore the associations of an obesity-related DP with overall and 19 site-specific cancers. METHODS: This study included 114,289 cancer-free participants with at least two dietary assessments. A total of 210 food items were classified into 47 food groups, and the mean amount of each food group was used in reduced-rank regression to derive the obesity-related DP. Cox regressions were conducted to explore the associations of the obesity-related DP with overall and 19 site-specific cancers. The parallel mediation model was constructed to quantify the mediating roles of potential mediators. RESULTS: During a median follow-up period of 9.4 years, 10,145 (8.9%) incident cancer cases were documented. The derived-DP was characterized by a higher intake of beer and cider, processed meat, high sugar beverages, red meat, and artificial sweetener, and a lower intake of fresh vegetables, olive oil, tea, and high fiber breakfast cereals. Observational analysis showed that a higher obesity-related DP Z-score was linearly associated with an increased risk of overall cancer (adjusted hazard ratio (HR) = 1.02, 95% CI: 1.01, 1.04 per 1-SD increase, corrected P < 0.001). For site-specific cancer, positive linear associations for six cancer sites (oral, colorectal, liver, lung, endometrium, and thyroid) and nonlinear associations for six cancer sites (esophagus, malignant melanoma, prostate, kidney, bladder, and multiple myeloma) were observed. The paralleled mediation analysis suggested that the association between the obesity-related DP and overall cancer is mediated by the body mass index (BMI), the waist-to-hip ratio (WHR), C-reactive protein, high-density lipoproteins (HDLs), and triglycerides. CONCLUSIONS: The developed obesity-related DP is strongly associated with overall and multiple cancer sites. Our findings highlight the complicated and diverse associations between an obesity-related DP and cancers and provide clues for future research directions.

The associations of dietary patterns with depressive and anxiety symptoms: a prospective study.

BACKGROUND: Diet is increasingly recognized as an important risk factor for mental health. However, evidence regarding the association between diet pattern and depressive and anxiety symptoms is limited. We aimed to investigate the associations of dietary patterns characterized by a set of nutrients of interest with depressive and anxiety symptoms. METHODS: The analyses included a total of 126,819 participants in the UK Biobank who had completed at least two dietary questionnaires. Dietary data were obtained through 24-h dietary assessment at baseline between 2006 and 2010 and four rounds of online follow-ups between 2011 and 2012. Reduced rank regression was applied to derive dietary patterns (DPs) explaining variability in energy density, free sugars, saturated fat, and fiber intakes. Depressive and anxiety symptoms were measured by the Patient Health Questionnaire-9 and General Anxiety Disorder-7 between 2016 and 2017, respectively. Logistic regression models were performed to investigate the associations between dietary patterns and depressive and anxiety symptoms. RESULTS: During a mean follow-up of 7.6 years, 2746 cases of depressive symptoms and 2202 cases of anxiety symptoms were recorded. Three major DPs were derived, explaining 74% of the variation in nutrients hypothesized to be related to depressive and anxiety symptoms. DP1 was characterized by high intakes of chocolate, confectionery, butter, and low vegetable/fruit intakes. Compared to the lowest quintile of DP1, the odds ratio (95% confidence interval) of depressive symptoms for Q2-Q5 was 0.82 (0.72-0.93), 0.86 (0.76-0.98), 1.02 (0.90-1.15), and 1.17 (1.03-1.32), respectively. Compared to the lowest quintile of DP1, the odds ratio (95% CI) of anxiety symptoms for Q2-Q5 was 0.84 (0.73-0.97), 0.91 (0.79-1.05), 1.01 (0.88-1.15), and 1.18 (1.03-1.35), respectively. DP2 featured high intakes of sugar-sweetened beverages, added sugars, and low intakes of butter/cheese but showed no significant links to depressive or anxiety symptoms. DP3 was characterized by high butter and milk desserts and low alcohol/bread intakes. Compared to the lowest quintile of DP3, the odds ratio (95% CI) of depressive symptoms for Q2-Q5 was 0.90 (0.79-1.01), 1.00 (0.88-1.13), 1.06 (0.94-1.20), and 1.17 (1.03-1.32), respectively. Compared to the lowest quintile of DP3, the odds ratio (95% CI) of anxiety symptoms for Q2-Q5 was 0.90 (0.78-1.04), 1.05 (0.91-1.20), 1.02 (0.89-1.17), and 1.21 (1.05-1.38), respectively. CONCLUSIONS: A DP characterized by high intakes of chocolate and confectionery, butter, high-fat cheese, added sugars, along with low intakes of fresh fruit and vegetables, is associated with a higher risk of depressive and anxiety symptoms.

Plasma Ferritin Concentrations in the General Population: A Cross-Sectional Analysis of Anthropometric, Metabolic, and Dietary Correlates.

BACKGROUND: Elevated concentrations of ferritin seem to be detrimental to human health while being quite common in the elderly. Data on dietary, anthropometric, and metabolic correlates of circulating ferritin levels in the elderly are scant. OBJECTIVES: We aimed to identify a dietary pattern, anthropometric, and metabolic traits associated with plasma ferritin status in an elderly cohort (n = 460, 57% male, age: 66 ± 12 y) from Northern Germany. METHODS: Plasma ferritin levels were measured by immunoturbidimetry. Reduced rank regression (RRR) yielded a dietary pattern explaining 13% of the variation in circulating ferritin concentrations. Cross-sectional associations of anthropometric and metabolic traits with plasma ferritin concentrations were assessed using multivariable-adjusted linear regression analysis. Restricted cubic spline regression was used to identify nonlinear associations. RESULTS: The RRR pattern was characterized by a high intake of potatoes, certain vegetables, beef, pork, processed meat, fats (frying and animal fat), and beer and a low intake of snacks, representing elements of the traditional German diet. BMI, waist circumference, and CRP were directly, HDL cholesterol inversely, and age nonlinearly associated with plasma ferritin concentrations (all P < 0.05). After additional adjustment for CRP, only the association of ferritin with age remained statistically significant. CONCLUSION: Higher plasma ferritin concentrations were associated with a traditional German dietary pattern. The associations of ferritin with unfavorable anthropometric traits and low HDL cholesterol were rendered statistically nonsignificant upon additional adjustment for chronic systemic inflammation (measured as elevated biomarker of the measurement of inflammation (CRP)), suggesting that these associations were largely driven by the proinflammatory role of ferritin (an acute-phase reactant).

Spectra in low-rank localized layers (SpeLLL) for interpretable time-frequency analysis.

The time-varying frequency characteristics of many biomedical time series contain important scientific information. However, the high-dimensional nature of the time-varying power spectrum as a surface in time and frequency limits its direct use by applied researchers and clinicians for elucidating complex mechanisms. In this article, we introduce a new approach to time-frequency analysis that decomposes the time-varying power spectrum in to orthogonal rank-one layers in time and frequency to provide a parsimonious representation that illustrates relationships between power at different times and frequencies. The approach can be used in fully nonparametric analyses or in semiparametric analyses that account for exogenous information and time-varying covariates. An estimation procedure is formulated within a penalized reduced-rank regression framework that provides estimates of layers that are interpretable as power localized within time blocks and frequency bands. Empirical properties of the procedure are illustrated in simulation studies and its practical use is demonstrated through an analysis of heart rate variability during sleep.

Dimension reduction for integrative survival analysis.

We propose a constrained maximum partial likelihood estimator for dimension reduction in integrative (e.g., pan-cancer) survival analysis with high-dimensional predictors. We assume that for each population in the study, the hazard function follows a distinct Cox proportional hazards model. To borrow information across populations, we assume that each of the hazard functions depend only on a small number of linear combinations of the predictors (i.e., "factors"). We estimate these linear combinations using an algorithm based on "distance-to-set" penalties. This allows us to impose both low-rankness and sparsity on the regression coefficient matrix estimator. We derive asymptotic results that reveal that our estimator is more efficient than fitting a separate proportional hazards model for each population. Numerical experiments suggest that our method outperforms competitors under various data generating models. We use our method to perform a pan-cancer survival analysis relating protein expression to survival across 18 distinct cancer types. Our approach identifies six linear combinations, depending on only 20 proteins, which explain survival across the cancer types. Finally, to validate our fitted model, we show that our estimated factors can lead to better prediction than competitors on four external datasets.

The association of obesity-related dietary patterns and main food groups derived by reduced-rank regression with cardiovascular diseases incidence and all-cause mortality: findings from 116,711 adults.

PURPOSE: Research about using reduced-rank regression (RRR) to simultaneously study the effects of both individual and combined consumption of foods on cardiovascular diseases (CVD) is scarce. METHODS: This study included 116,711 CVD-free participants (a median of 11.8 year follow-up) with 2 or more 24-h online dietary assessments. A total of 210 food items were classified into 45 food groups, and the mean amount of each food group was used in RRR to derive dietary patterns (DPs) explaining the maximum shared variation in obesity-related indicators. The associations of DPs and its main food groups (|factor loading| [Formula: see text] 0.2) with the incident CVD and all-cause mortality were examined by Cox model. In cross-sectional analyses, the associations of DP scores with cardiometabolic risk factors (biomarkers) were examined by linear regression. RESULTS: The derived DP was characterized by higher intakes of beer and cider, high-sugar beverages, processed meat, red meat, artificial sweetener, and crisps, chips and savory snacks, and lower intakes of olive oil, high fiber breakfast cereals, tea, and vegetable. Compared to the lowest dietary score quintile, those in the highest were associated with higher risks of total CVD (adjusted-HR: 1.45, 95% CI 1.33-1.57) and all-cause mortality (adjusted-HR 1.31, 95% CI 1.18-1.45). We observed consumption alone of these food groups had a consistent but limited health effect on total CVD and all-cause death incidence. These associations were modified by age and sex. Higher DP scores were related to adverse biomarkers profiles. CONCLUSIONS: We developed obesity-related DPs prospectively associated with increased risks of CVD and all-cause mortality.

Comparison of data-driven identified hypertension-protective dietary patterns among Chinese adults: based on a nationwide study.

PURPOSE: Diet pattern (DP) is a key modifiable and cost-effective factor in hypertension (HTN) management. The current study aimed to identify and compare the hypertension-protective DPs among Chinese adults. METHODS: 52,648 participants aged over 18 years were included from China Nutrition and Health Surveillance (CNHS) 2015-2017. Reduced rank regression (RRR) and partial least square regression (PLS) was applied to identify the DPs. Multivariable-adjusted logistic regression was used to assess the association between the DPs and HTN. RESULTS: DPs derived by RRR and PLS were both featured by higher consumption of fresh vegetables and fruits, mushrooms and edible fungi, seaweeds, soybeans and related products, mixed legumes, dairy products, fresh eggs, and lower of refined grain consumption. Compared to the lowest quintile, participants in the highest quintile had lower odds of HTN (RRR-DP: OR = 0.77, 95% CI = 0.72-0.83; PLS-DP: OR = 0.76, 95% CI = 0.71-0.82; all p < 0.0001). Simplified DP scores were observed the same protective tendencies (Simplified RRR-DP: OR = 0.81, 95% CI = 0.75-0.87; Simplified PLS-DP: OR = 0.79, 95% CI = 0.74-0.85; all p < 0.0001) and showed effective extrapolation in subgroups defined by gender, age, location, lifestyle, and different metabolic conditions. CONCLUSIONS: The identified DPs had high conformity with East Asian dietary habits, and significantly negative associations with HTN among Chinese adults. The simplified DP technique also indicated the potential for improving the extrapolation of the results of DP analysis related to HTN.

Dietary patterns explaining variations in blood biomarkers in young adults are associated with the 30-year predicted cardiovascular disease risks in midlife: A follow-up study.

BACKGROUND AND AIMS: To examine a combined effect of dietary intakes, blood lipid and insulin resistance in young adulthood on the risk of predicted CVD through midlife. METHODS AND RESULTS: Data of young adults from a birth cohort study in Australia were used. Reduced rank regression (RRR) and partial least squares (PLS) methods identified dietary patterns rich in meats, refined grains, processed and fried foods, and high-fat dairy and low in whole grains and low-fat dairy from dietary intakes obtained at 21-years, and blood lipids and measures of insulin resistance measured at 30-years of age. Using standard CVD risk factors measured at 30-years of age, the Framingham Heart Study risk-prediction algorithms were used to calculate the 30-year predicted Framingham CVD risk scores. The scores represent Hard CVD events; coronary death, myocardial infarction and stroke and Full CVD events; Hard CVD plus coronary insufficiency and angina pectoris, transient ischaemic attack, intermittent claudication, and congestive heart failure in midlife. Sex-specific upper quartiles of CVD risk scores were used to define high-risk groups. Modified Poisson regression models were used to estimate relative risks (RRs) with 95% CI. Greater adherence to the diet identified applying RRR in young adulthood was associated with higher risks of predicted Hard CVD (RR: 1.60; 1.14, 2.25) and Full CVD (RR: 1.46; 1.04, 2.05) events in midlife. The diet from PLS showed similar trend of association for the risk of predicted Hard CVD events (RR: 1.49; 1.03, 2.16) in adjusted models. CONCLUSION: Dietary patterns associated with variations in blood lipids and insulin resistance in young adulthood are associated with increased risks of predicted CVD events in midlife. The findings suggest that diet induced altered blood lipids and insulin resistance in the life course of young adulthood could increase the risks of CVD events in later life.

Bayesian predictive modeling of multi-source multi-way data.

A Bayesian approach to predict a continuous or binary outcome from data that are collected from multiple sources with a multi-way (i.e., multidimensional tensor) structure is described. As a motivating example, molecular data from multiple 'omics sources, each measured over multiple developmental time points, as predictors of early-life iron deficiency (ID) in a rhesus monkey model are considered. The method uses a linear model with a low-rank structure on the coefficients to capture multi-way dependence and model the variance of the coefficients separately across each source to infer their relative contributions. Conjugate priors facilitate an efficient Gibbs sampling algorithm for posterior inference, assuming a continuous outcome with normal errors or a binary outcome with a probit link. Simulations demonstrate that the model performs as expected in terms of misclassification rates and correlation of estimated coefficients with true coefficients, with large gains in performance by incorporating multi-way structure and modest gains when accounting for differing signal sizes across the different sources. Moreover, it provides robust classification of ID monkeys for the motivating application.

Association of maternal dietary patterns derived by multiple approaches with gestational diabetes mellitus: a prospective cohort study.

We used two a priori diet scores [Mediterranean diet (aMed) and Diet Balance Index (DBI)] and two a posteriori approaches [principal components analysis (PCA) and reduced-rank regression (RRR)] to examine the association of maternal dietary patterns with risk of gestational diabetes mellitus (GDM) and blood glucose among 2202 pregnant women in the Tongji Birth Cohort. Compared to the highest quartile of the aMed and legumes-vegetables-fruits (derived by PCA) scores, the fasting blood glucose (FBG) levels were higher in the lower quartiles (p-trend < 0.05). Lower scores of the meats-eggs-dairy (derived by PCA) and eggs-fish patterns (derived by RRR; characterised by higher intakes of freshwater fish, eggs, and lower intakes of leafy and cruciferous vegetables and fruits) were associated with decreased FBG levels (p-trend < 0.05). Similarities were found across approaches that some dietary patterns were associated with FBG, but not with postprandial glucose and GDM risk.

A Poisson reduced-rank regression model for association mapping in sequencing data.

BACKGROUND: Single-cell RNA-sequencing (scRNA-seq) technologies allow for the study of gene expression in individual cells. Often, it is of interest to understand how transcriptional activity is associated with cell-specific covariates, such as cell type, genotype, or measures of cell health. Traditional approaches for this type of association mapping assume independence between the outcome variables (or genes), and perform a separate regression for each. However, these methods are computationally costly and ignore the substantial correlation structure of gene expression. Furthermore, count-based scRNA-seq data pose challenges for traditional models based on Gaussian assumptions. RESULTS: We aim to resolve these issues by developing a reduced-rank regression model that identifies low-dimensional linear associations between a large number of cell-specific covariates and high-dimensional gene expression readouts. Our probabilistic model uses a Poisson likelihood in order to account for the unique structure of scRNA-seq counts. We demonstrate the performance of our model using simulations, and we apply our model to a scRNA-seq dataset, a spatial gene expression dataset, and a bulk RNA-seq dataset to show its behavior in three distinct analyses. CONCLUSION: We show that our statistical modeling approach, which is based on reduced-rank regression, captures associations between gene expression and cell- and sample-specific covariates by leveraging low-dimensional representations of transcriptional states.

Is glycaemic control associated with dietary patterns independent of weight change in people newly diagnosed with type 2 diabetes? Prospective analysis of the Early-ACTivity-In-Diabetes trial.

BACKGROUND: It is unclear whether diet affects glycaemic control in type 2 diabetes (T2D), over and above its effects on bodyweight. We aimed to assess whether changes in dietary patterns altered glycaemic control independently of effects on bodyweight in newly diagnosed T2D. METHODS: We used data from 4-day food diaries, HbA1c and potential confounders in participants of the Early-ACTivity-In-Diabetes trial measured at 0, 6 and 12 months. At baseline, a 'carb/fat balance' dietary pattern and an 'obesogenic' dietary pattern were derived using reduced-rank regression, based on hypothesised nutrient-mediated mechanisms linking dietary intake to glycaemia directly or via obesity. Relationships between 0 and 6 month change in dietary pattern scores and baseline-adjusted HbA1c at 6 months (n = 242; primary outcome) were assessed using multivariable linear regression. Models were repeated for periods 6-12 months and 0-12 months (n = 194 and n = 214 respectively; secondary outcomes). RESULTS: Reductions over 0-6 months were observed in mean bodyweight (- 2.3 (95% CI: - 2.7, - 1.8) kg), body mass index (- 0.8 (- 0.9, - 0.6) kg/m2), energy intake (- 788 (- 953, - 624) kJ/day), and HbA1c (- 1.6 (- 2.6, -0.6) mmol/mol). Weight loss strongly associated with lower HbA1c at 0-6 months (ß = - 0.70 [95% CI - 0.95, - 0.45] mmol/mol/kg lost). Average fat and carbohydrate intakes changed to be more in-line with UK healthy eating guidelines between 0 and 6 months. Dietary patterns shifting carbohydrate intakes higher and fat intakes lower were characterised by greater consumption of fresh fruit, low-fat milk and boiled/baked potatoes and eating less of higher-fat processed meats, butter/animal fats and red meat. Increases in standardised 'carb/fat balance' dietary pattern score associated with improvements in HbA1c at 6 months independent of weight loss (ß = - 1.54 [- 2.96, - 0.13] mmol/mol/SD). No evidence of association with HbA1c was found for this dietary pattern at other time-periods. Decreases in 'obesogenic' dietary pattern score were associated with weight loss (ß = - 0.77 [- 1.31, - 0.23] kg/SD) but not independently with HbA1c during any period. CONCLUSIONS: Promoting weight loss should remain the primary nutritional strategy for improving glycaemic control in early T2D. However, improving dietary patterns to bring carbohydrate and fat intakes closer to UK guidelines may provide small, additional improvements in glycaemic control. TRIAL REGISTRATION: ISRCTN92162869 . Retrospectively registered on 25 July 2005.

Measuring, comparing and interpreting phenotypic selection on floral scent.

Natural selection on floral scent composition is a key element of the hypothesis that pollinators and other floral visitors drive scent evolution. The measure of such selection is complicated by the high-dimensional nature of floral scent data and uncertainty about the cognitive processes involved in scent-mediated communication. We use dimension reduction through reduced-rank regression to jointly estimate a scent composite trait under selection and the strength of selection acting on this trait. To assess and compare variation in selection on scent across species, time and space, we reanalyse 22 datasets on six species from four previous studies. The results agreed qualitatively with previous analyses in terms of identifying populations and scent compounds subject to stronger selection but also allowed us to evaluate and compare the strength of selection on scent across studies. Doing so revealed that selection on floral scent was highly variable, and overall about as common and as strong as selection on other phenotypic traits involved in pollinator attraction or pollen transfer. These results are consistent with an important role of floral scent in pollinator attraction. Our approach should be useful for further studies of plant-animal communication and for studies of selection on other high-dimensional phenotypes. In particular, our approach will be useful for studies of pollinator-mediated selection on complex scent blends comprising many volatiles, and when no prior information on the physiological responses of pollinators to scent compounds is available.

Negative binomial factor regression with application to microbiome data analysis.

The human microbiome provides essential physiological functions and helps maintain host homeostasis via the formation of intricate ecological host-microbiome relationships. While it is well established that the lifestyle of the host, dietary preferences, demographic background, and health status can influence microbial community composition and dynamics, robust generalizable associations between specific host-associated factors and specific microbial taxa have remained largely elusive. Here, we propose factor regression models that allow the estimation of structured parsimonious associations between host-related features and amplicon-derived microbial taxa. To account for the overdispersed nature of the amplicon sequencing count data, we propose negative binomial reduced rank regression (NB-RRR) and negative binomial co-sparse factor regression (NB-FAR). While NB-RRR encodes the underlying dependency among the microbial abundances as outcomes and the host-associated features as predictors through a rank-constrained coefficient matrix, NB-FAR uses a sparse singular value decomposition of the coefficient matrix. The latter approach avoids the notoriously difficult joint parameter estimation by extracting sparse unit-rank components of the coefficient matrix sequentially, effectively delivering interpretable bi-clusters of taxa and host-associated factors. To solve the nonconvex optimization problems associated with these factor regression models, we present a novel iterative block-wise majorization procedure. Extensive simulation studies and an application to the microbial abundance data from the American Gut Project (AGP) demonstrate the efficacy of the proposed procedure. In the AGP data, we identify several factors that strongly link dietary habits and host life style to specific microbial families.