Reduced Rank Regression Method Research Articles

Association between dietary patterns and depressive symptom based on reduced rank regression in people aged 55 and above in 4 provinces of China

To investigate the dietary patterns related to depressive symptoms based on reduced rank regression in people aged 55 and above in 4 provinces of China and the degree of association between this dietary pattern and depressive symptoms. Stratified, multi-stage, cluster and random sampling method was used to collect personal information such as demographic characteristics, behavioral lifestyles, disease history and medicine use in Chinese aged 55 and above who participated in the baseline survey of "Community-based Cohort Study on Nervous System Diseases" project conducted in 2018 and 2019 in Hebei, Zhejiang, Shaanxi and Hunan Provinces. Food frequency questionnaire was used to obtain dietary data. Depressive symptom was assessed by geriatric depression scale with a cut-off of 11. Participants who have incomplete demographic information, dietary data or scores of geriatric depression scale, and those whose intake frequency of each food-group >99. 5% were excluded. A total of 11 497 participants, 43. 1% of whom were male, were involved in this study with average age of(67. 3±7. 6) years. The reduced rank regression method was used to extract depressive symptoms-related dietary patterns by gender, and the degree of association between dietary patterns and depressive symptom was analyzed by logistic regression. Among males, the depressive symptoms-related dietary pattern was characterized by the higher intake frequency of fried flour-made food, meat, processed meat, animal offal, and preserved eggs, and the lower intake frequency of liquid milk/milk power/cheese, fresh eggs(except preserved eggs) and nut. Among females, the depressive symptoms-related dietary pattern was characterized by the higher intake frequency of fried flour-made food, meat, processed meat, animal offal and preserved eggs, and the lower intake frequency of coarse cereals, fruits, liquid milk/milk power/cheese and fresh eggs(except preserved eggs). The highest quartile group of the dietary pattern score had a significantly higher risk of depressive symptom than the lowest quartile group(OR=3. 498, 95% CI 2. 624-4. 663, P<0. 001 for males; OR=3. 853, 95% CI 3. 002-4. 944, P<0. 001 for females). The depressive symptoms-related dietary pattern is characterized by the higher intake frequency of fried flour-made food, meat, processed meat, animal offal and preserved eggs, and the lower intake frequency of liquid milk/milk power/cheese and fresh eggs(except preserved eggs) in the Chinese aged 55 and above. The score of this dietary pattern is significantly positively correlated with depressive symptom.

High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to rearrange the coefficient matrices of the model into a tensor form such that the parameter space can be restricted in three directions simultaneously via tensor decomposition. The proposed method substantially expands the capacity of vector autoregressive modeling for a large number of time series. In contrast, the widely used reduced-rank regression method can restrict the parameter space in only one direction. Moreover, to handle high-dimensional time series, this paper considers imposing sparsity on factor matrices to improve the interpretability and estimation efficiency, which leads to a sparsity-inducing estimator. For the low-dimensional case, we derive asymptotic properties of the proposed least squares estimator and introduce an alternating least squares algorithm. For the high-dimensional case, we establish non-asymptotic properties of the sparsity-inducing estimator and propose an ADMM-based algorithm for regularized estimation. Simulation experiments and a real data example demonstrate the advantages of the proposed approach over various existing methods.

Identification of dietary patterns associated with elevated blood pressure among Lebanese men: A comparison of principal component analysis with reduced rank regression and partial least square methods

BackgroundTo examine the associations of dietary patterns with odds of elevated Blood Pressure (BP) among Lebanese adult males using principal component analysis (PCA), and compare the results to two other data reduction methods, including reduced rank regression (RRR) and partial least-squares (PLS) regression.MethodsData from the National Nutrition and Non-Communicable Disease Risk Factor Survey conducted in Lebanon between years 2008 and 2009 were used. Dietary intake data were collected by a 61-item food frequency questionnaire (FFQ). In addition, anthropometric and blood pressure measurements were obtained following standard techniques. For the purpose of this study, data of males older than 20 years with no history of chronic diseases were selected (n = 673). Elevated BP was indicated if the systolic blood pressure was > = 130mm Hg and/or the diastolic blood pressure > = 85 mm Hg. Dietary patterns were constructed using PCA, PLS and RRR and compared based on the performance to identify plausible patterns associated with elevated BP. For PLS and RR, the response variables were BMI, waist circumference and percent body fat. Multiple logistic regression was used to evaluate the associations between the dietary pattern scores of each method and risk of elevated BP.ResultsThree dietary patterns were identified using PCA: Western, Traditional Lebanese, and Fish and alcohol. Both the Western and the Traditional Lebanese patterns were associated with higher odds of elevated BP in the study population (OR = 1.23, CI 1.03, 1.46; OR = 1.29, CI 1.09, 1.52 respectively). The comparison among the three methods for dietary patterns derivation showed that PLS and RRR derived patterns explained greater variance in the outcome (PCA: 1.2%; PLS: 14.1%; RRR: 15.36%) and were significantly associated with elevated BP, while the PCA dietary patterns were descriptive of the study population’s real dietary habits (PCA: 23.6%; PLS: 19.8%; RRR: 11.3%).ConclusionsThe Western and Traditional Lebanese dietary patterns were associated with higher odds of elevated BP among Lebanese males. The findings of this study showed that, compared to PCA, the use of RRR method resulted in more significant associations with the outcome while the PCA-derived patterns were more related to the real habits in the study population.

A cohort study on the association between dietary patterns which benefit for normal kidney function and the cognitive performance in the Chinese elderly

Objective: To explore the association between dietary pattern which benefit for normal kidney function and the risk of cognitive decline or impairment in the elderly. Methods: In 2015, subjects aged 60 and over from four counties in the Nutrition and Chronic Disease Family Cohort project, were followed up in 2017. Cognitive function was repeatedly assessed, using the Mini Mental State Evaluation (MMSE) scale. Dietary pattern that benefit for normal kidney function was extracted, using the reduced rank regression method and followed by logistic regression models to explore the associations between scores that showing the kidney function on dietary patterns and the risk of cognitive deterioration and impairment in two years among those who were with normal cognition in 2015. Results: Dietary pattern that benefit for normal kidney function, was characterized by high consumption of cereal, vegetables, legume and fruits but with less meat and soy products. Comparing with the group with lowest score quartile on this dietary pattern, the risk of cognitive deterioration in the highest quartile group was significantly low (P<0.01) in two years, with an odds ratio as 0.57 (95%CI: 0.37-0.85). Linear trend was also obviously visible (P=0.007) in this group. The ones at the highest quartile group among the normal cognition ones in 2015, the risk of cognitive impairment also significantly reduced (P<0.05) in two years time, with an odds ratio as 0.52 (95%CI: 0.29-0.93). Also, linear trend could obviously be seen (P=0.01). Conclusion: Dietary pattern that benefit for normal kidney function was both inversely associated with cognitive deterioration and impairment, in two years.

A Diabetes-Related Dietary Pattern Is Associated with Incident Diabetes in Obese Men in the Korean Genome Epidemiology Study

Diet plays an important role in both the development and management of diabetes. Using data from the Korean Genome Epidemiology Study, we assessed dietary patterns associated with the clinical indicators of diabetes. This study included 7255 subjects aged 40-69 y. Individuals with chronic diseases were excluded. The daily intakes of specific food items were assessed using a dish-based semiquantitative food-frequency questionnaire comprising 103 items; the food items were then grouped into 26 food groups. Dietary patterns were analyzed by the reduced rank regression method using glycated hemoglobin, the homeostasis model of insulin resistance, and fasting glucose concentrations as dependent variables. We investigated the associations between dietary patterns and incident diabetes using the Cox proportional hazards model. During an 11.5-y follow-up, the incidence of diabetes was 11.8/1000 person-years. The dietary pattern related to selected biomarkers of diabetes was characterized by a relatively high intake of kimchi, beef, other meat, fish, and coffee in men and a high intake of rice, kimchi, and fruit in women. In men, the association of dietary patterns with incident diabetes was significant only in the obese group, and those in the top quartile of the dietary pattern score had a 1.72 times (95% CI: 1.15, 2.56 times) greater risk of incident diabetes than those in the bottom quartile. Conversely, dietary patterns in women were not associated with incident diabetes. Using reduced rank regression, we identified dietary patterns related to selected biomarkers of diabetes in a long-term study with follow-up data in Korea.

Psychological disorders and dietary patterns by reduced-rank regression.

To determine the relationship between dietary patterns identified by reduced-rank regression method and psychological disorders in a large group of Iranian adults. A cross-sectional study was performed on 3363 Iranian adults between 20 and 55 years. Dietary intakes were assessed using a validated dish-based semi-quantitative food frequency questionnaire. Psychological health was examined through validated Iranian version of Hospital Anxiety and Depression Scale and General Health Questionnaires. Reduced-rank regression was applied to identify dietary patterns based on the ratio of omega-3/omega-6, zinc, magnesium, vitamin B6, and folic acid intake. Logistic regression was used to assess the relationship between dietary patterns and psychological disorders. Three major dietary patterns were derived: "healthy," "fish and poultry," and "transitional." After adjustment for potential confounders, "healthy" was associated with reduced depression (odds ratio (OR) for the highest vs. lowest quintile: 0.35; 95% confidence interval (CI): 0.25-0.50), anxiety (OR: 0.47; CI: 0.30-0.74), and psychological distress (OR: 0.52; CI: 0.36-0.75). Greater adherence to the "fish and poultry" was related with lower odds of depression (OR: 0.64; CI: 0.47-0.87). Participant in the third quintile of "fish and poultry" dietary pattern were less likely to be anxious (OR: 0.61; CI: 0.41-0.91). Additionally, we found an inverse significant correlation between adherence to the "transitional" dietary pattern and odds of depression (OR: 0.36; CI: 0.21-0.62), anxiety (OR: 0.43; CI: 0.21-0.88), and psychological distress (OR: 0.41; CI: 0.23-0.72). We found that "healthy," "fish and poultry," and "transitional" dietary patterns have inverse significant relationship with odds of psychological disorders, but prospective studies are needed for causal conclusion.

Dietary patterns related to exposure to persistent organic pollutants based on the Ewha Birth and Growth Cohort

Persistent organic pollutants (POPs) are endocrine disruptors that are typically ingested in food. Using data from the Ewha Birth and Growth Cohort study, we identified dietary patterns related to blood persistent organic pollutant (POP) levels in children. In total, 188 Korean children (95 boys and 93 girls) aged 7–9 years were included in this study. Daily food intake data derived from a semi-quantitative food-frequency questionnaire were grouped into 33 food groups. Dietary patterns were analyzed using the reduced rank regression method, with blood POP levels as dependent variables.The marker polychlorinated biphenyl (PCB) pattern showed more weighted loading factors in the intake of shellfish/salted seafood, cheese, nuts and seeds, and total PCBs showed similar results. The dioxin-like PCB pattern was characterized by a higher intake of yogurt, beverages, and fruit and a lower intake of grain, seaweeds, and processed meat. Additionally, the total organochlorine pesticide (OCP) pattern showed positive factor loading values in shrimp and beverages, and negative factor loading values in seaweeds and processed meat. Each dietary pattern accounted for 25.0% of total OCPs, 22.9% of dioxin-like PCBs, 21.6% of marker PCBs, and 21.3% of total PCBs in blood. Dietary pattern scores were linearly related to blood POP levels, and this association remained after adjusting for sex, age, follow-up survey year, maternal educational level, body mass index, and total energy. Dietary patterns differed slightly among the individual POPs. Further studies are needed to develop an intervention strategy for children.

Association between blood pressure related dietary patterns and identified cognitive performance in the elderly Chinese-a study by reduced rank regression method

Objective: To study the association between blood pressure related dietary pattern and cognitive impairment in the elderly. Methods: In 2015, all participants who were aged ≥60 and participated in the Nutrition and Chronic disease family cohort were involved in the study. Information on demographic variables, lifestyle and health status was collected. Cognitive performance was assessed by the Mini Mental State Evaluation (MMSE) scale. Blood pressure, height and weight were measured by trained medical personnel and fasting venous blood samples were collected for testing on serum level of triglycerides and total cholesterol. Both SBP and DBP were used as response variables when dietary patterns were identified by reduced rank regression method. Logistic regression models were fit to explore the associations of scores on blood pressure-related dietary pattern and cognitive impairment. Results: Two blood related dietary patterns were identified. The first one was characterized by high consumption of vegetables and less meat, eggs and dessert (Pattern 1), while the second one was with high consumption of meat, soy products, wine and fried foods and less intake of dairy (Pattern 2). Data showed that the Pattern 1 was associated with the risk of cognitive impairment. Comparing with the lowest quartile of score of this dietary pattern, the risk of cognitive impairment in the highest quartile group showed a significant (P<0.01) increase, with OR=1.94 (1.21-3.11) and showing significant (P=0.002) linear trend. However, no significant association was observed (P>0.05) with cognitive impairment in the second dietary pattern. Conclusion: Blood pressure-related dietary pattern was positively associated with cognitive impairment.

Dietary Patterns and Its Associations with Adipokines (Adiponectin and Leptin) among Adults: A Narrative Review

To compile and analyse existing scientific evidence regarding the association of dietary patterns with adiponectin and leptin. Medline and PubMed electronic databases were searched for articles related to the association of dietary patterns with adiponectin and leptin from 2005 to 2015. Only full text articles using English as a language of publication were included. Studies were limited to the use of food frequency questionnaires in assessing dietary intake, factor analysis using principal component analysis, cluster analysis or reduced rank regression method in determining dietary pattern. A total of six relevant studies involving a total of 6467 subjects (47% men and 53% women) met the inclusion criteria from 1407 reviewed articles Twelve dietary patterns were extracted i.e. healthy pattern, meat and fat, sweet pattern, potatoes and refined grains, Japanese pattern, westernized pattern, mixed pattern, traditional pattern, vegetables, fruits and lean meat pattern, high alcohol, ‘Izakaya’ pattern and dieting. Two studies showed association with leptin which serum leptin concentration showed significantly higher in vegetables, fruits and lean meat compared to western pattern and lower circulating levels of leptin in westernized breakfast dietary pattern. Adiponectin concentration resulting significant positive relationship with fruits and vegetables, dieting, Japanese and healthy dietary pattern. Adherence to healthy dietary patterns plays an important role on serum adiponectin and leptin concentration. However, in most studies that resulted in a significant relationship, adiponectin, leptin and diet components were evaluated separately. Therefore, further well-designed studies were required to clarify the mechanism mediating relationship between dietary patterns and adipokines.

The Role of Cointegration for Optimal Hedging with Heteroscedastic Error Term

The role of cointegration is analysed for optimal hedging of an h-period portfolio.Prices are assumed to be generated by a cointegrated vector autoregressive model allowing for stationary martingale errors, satisfying a mixing condition and hence some heteroscedasticity. The risk of a portfolio is measured by the conditional variance of the h-period return given information at time t. If the price of an asset is nonstationary, the risk of keeping the asset for h periods diverges for large h. The h-period minimum variance hedging portfolio is derived, and it is shown that it approaches a cointegrating vector for large h, thereby giving a bounded risk. Taking the expected return into account, the portfolio that maximizes the Sharpe ratio is found, and it is shown that it also approaches a cointegration portfolio. For constant conditional volatility, the conditional variance can be estimated, using regression methods or the reduced rank regression method of cointegration. In case of conditional heteroscedasticity, however, only the expected conditional variance can be estimated without modelling the heteroscedasticity. The fi?ndings are illustrated with a data set of prices of two year forward contracts for electricity, which are hedged by forward contracts for fuel prices. The main conclusion of the paper is that for optimal hedging, one should exploit the cointegrating properties for long horizons, but for short horizons more weight should be put on the remaining dynamics.

Using reduced rank regression methods to identify dietary patterns associated with obesity: a cross-country study among European and Australian adolescents.

This study aims to examine repeatability of reduced rank regression (RRR) methods in calculating dietary patterns (DP) and cross-sectional associations with overweight (OW)/obesity across European and Australian samples of adolescents. Data from two cross-sectional surveys in Europe (2006/2007 Healthy Lifestyle in Europe by Nutrition in Adolescence study, including 1954 adolescents, 12-17 years) and Australia (2007 National Children's Nutrition and Physical Activity Survey, including 1498 adolescents, 12-16 years) were used. Dietary intake was measured using two non-consecutive, 24-h recalls. RRR was used to identify DP using dietary energy density, fibre density and percentage of energy intake from fat as the intermediate variables. Associations between DP scores and body mass/fat were examined using multivariable linear and logistic regression as appropriate, stratified by sex. The first DP extracted (labelled 'energy dense, high fat, low fibre') explained 47 and 31 % of the response variation in Australian and European adolescents, respectively. It was similar for European and Australian adolescents and characterised by higher consumption of biscuits/cakes, chocolate/confectionery, crisps/savoury snacks, sugar-sweetened beverages, and lower consumption of yogurt, high-fibre bread, vegetables and fresh fruit. DP scores were inversely associated with BMI z-scores in Australian adolescent boys and borderline inverse in European adolescent boys (so as with %BF). Similarly, a lower likelihood for OW in boys was observed with higher DP scores in both surveys. No such relationships were observed in adolescent girls. In conclusion, the DP identified in this cross-country study was comparable for European and Australian adolescents, demonstrating robustness of the RRR method in calculating DP among populations. However, longitudinal designs are more relevant when studying diet-obesity associations, to prevent reverse causality.

Cancer Subtype Discovery Based on Integrative Model of Multigenomic Data.

One major goal of large-scale cancer omics study is to understand molecular mechanisms of cancer and find new biomedical targets. To deal with the high-dimensional multidimensional cancer omics data (DNA methylation, mRNA expression, etc.), which can be used to discover new insight on identifying cancer subtypes, clustering methods are usually used to find an effective low-dimensional subspace of the original data and then cluster cancer samples in the reduced subspace. However, due to data-type diversity and big data volume, few methods can integrate these data and map them into an effective low-dimensional subspace. In this paper, we develop a dimension-reduction and data-integration method for indentifying cancer subtypes, named Scluster. First, Scluster, respectively, projects the different original data into the principal subspaces by an adaptive sparse reduced-rank regression method. Then, a fused patient-by-patient network is obtained for these subgroups through a scaled exponential similarity kernel method. Finally, candidate cancer subtypes are identified using spectral clustering method. We demonstrate the efficiency of our Scluster method using three cancers by jointly analyzing mRNA expression, miRNA expression, and DNA methylation data. The evaluation results and analyses show that Scluster is effective for predicting survival and identifies novel cancer subtypes of large-scale multi-omics data.

Dietary pattern, inflammation and cognitive decline: The Whitehall II prospective cohort study

SummaryBackground & aimsLow-grade inflammation appears to play an etiological role in cognitive decline. However the association between an inflammatory dietary pattern and cognitive decline has not been investigated. We aimed to investigate dietary patterns associated with inflammation and whether such diet is associated with cognitive decline.MethodsWe analyzed 5083 participants (28.7% women) from the Whitehall II cohort study. Diet and serum interleukin-6 (IL-6) were assessed in 1991–1993 and 1997–1999. We used reduced rank regression methods to determine a dietary pattern associated with elevated IL-6. Cognitive tests were performed in 1997–1999 and repeated in 2002–2004 and 2007–2009. The association between dietary pattern and cognitive decline between ages 45 and 79 was assessed using linear mixed models.ResultsWe identified an inflammatory dietary pattern characterized by higher intake of red meat, processed meat, peas and legumes, and fried food, and lower intake of whole grains which correlated with elevated IL-6 both in 1991–1993 and 1997–1999. A greater decline in reasoning was seen in participants in the highest tertile of adherence to the inflammatory dietary pattern (−0.37 SD; 95% confidence interval [CI] −0.40, −0.34) compared to those in the lowest tertile (−0.31; 95% CI −0.34, −0.28) after adjustment for age, sex, ethnicity, occupational status, education, and total energy intake (p for interaction across tertiles = 0.01). This association remained significant after multivariable adjustment. Similarly for global cognition, the inflammatory dietary pattern was associated with faster cognitive decline after multivariable adjustment (p for interaction across tertiles = 0.04). Associations were stronger in younger participants (<56 years), reducing the possibility of reverse causation.ConclusionsOur study found that a dietary pattern characterized as higher intake of red and processed meat, peas, legumes and fried food, and lower intake of whole grains was associated with higher inflammatory markers and accelerated cognitive decline at older ages. This supports the case for further research.

Carotenoid-rich dietary patterns during midlife and subsequent cognitive function

Carotenoids may help to prevent the ageing of the brain. Previous findings regarding β-carotene alone are not consistent. In the present study, we evaluated the cross-time association between a carotenoid-rich dietary pattern (CDP) and subsequent cognitive performance using a sample of 2983 middle-aged adults participating in the SU.VI.MAX (Supplémentation en Vitamines et Minéraux Antioxydants) study. Cognitive performance was assessed in 2007-9 using six neuropsychological tests, and a composite cognitive score was computed. The cognitive data were related to dietary data obtained by repeated 24 h dietary records (1994-6) and to measurements of baseline plasma concentrations of carotenoids (lutein, zeaxanthin, β-cryptoxanthin, lycopene, α-carotene, trans-β-carotene and cis-β-carotene). DP were extracted using the reduced rank regression method for 381 participants and then extrapolated to the whole sample using plasma carotenoid concentrations as response variables. Associations between a CDP and cognitive function measured 13 years later were estimated with ANCOVA providing mean difference values and 95 % CI across the tertiles of CDP. A correlation between CDP and consumption of orange- and green-coloured fruits and vegetables, vegetable oils and soup was observed. CDP was found to be associated with a higher composite cognitive score (mean difference 1·04, 95 % CI 0·20, 1·87, P for trend 0·02), after adjustment for sociodemographic, lifestyle and health factors. Similar findings were obtained for scores obtained in the cued recall task, backward digit span task, trail making test and semantic fluency task (all P for trend < 0·05). Further studies ought to confirm whether a diet providing sufficient quantity and variety of coloured fruits and vegetables may contribute to the preservation of cognitive function during ageing.

A maternal dietary pattern characterised by fish and seafood in association with the risk of congenital heart defects in the offspring

To identify maternal dietary patterns related to biomarkers of methylation and to investigate associations between these dietary patterns and the risk of congenital heart defects (CHDs) in the offspring. Case-control study. Western part of the Netherlands, 2003-08. One hundred and seventy-nine mothers of children with CHD and 231 mothers of children without a congenital malformation. Food intake was obtained by food frequency questionnaires. The reduced rank regression method was used to identify dietary patterns related to the biomarker concentrations of methylation in blood. Dietary patterns, vitamin B and homocysteine concentrations, biomarkers of methylation (S-adenosylmethionine [SAM] and S-adenosylhomocysteine [SAH]) and the risk of CHD estimated by odds ratios and 95% confidence intervals. The one-carbon-poor dietary pattern, comprising a high intake of snacks, sugar-rich products and beverages, was associated with SAH (β = 0.92, P < 0.001). The one-carbon-rich dietary pattern with high fish and seafood intake was associated with SAM (β = 0.44, P < 0.001) and inversely with SAH (β =-0.08, P < 0.001). Strong adherence to this dietary pattern resulted in higher serum (P <0.05) and red blood cell (P < 0.01) folate and a reduced risk of CHD in offspring: odds ratio, 0.3 (95% confidence interval, 0.2-0.6). The one-carbon-rich dietary pattern, characterised by the high intake of fish and seafood, is associated with a reduced risk of CHD. This finding warrants further investigation in a randomised intervention trial.

Specific food group combinations explaining the variation in intakes of nutrients and other important food components in the European Prospective Investigation into Cancer and Nutrition: an application of the reduced rank regression method

To identify combinations of food groups that explain as much variation in absolute intakes of 23 key nutrients and food components as possible within the country-specific populations of the European Prospective Investigation into Cancer and Nutrition (EPIC). The analysis covered single 24-h dietary recalls (24-HDR) from 36,034 subjects (13,025 men and 23,009 women), aged 35-74 years, from all 10 countries participating in the EPIC study. In a set of 39 food groups, reduced rank regression (RRR) was used to identify those combinations (RRR factors) that explain the largest proportion of variation in intake of 23 key nutrients and food components, namely, proteins, saturated fatty acids, monounsaturated fatty acids, polyunsaturated fatty acids, cholesterol, sugars (sum of mono- and disaccharides), starch, fibre, alcohol, calcium, iron, potassium, phosphorus, magnesium, vitamin D, beta-carotene, retinol and vitamins E, B1, B2, B6, B12 and C (RRR responses). Analyses were performed at the country level and for all countries combined. In the country-specific analyses, the first RRR factor explained a considerable proportion of the total nutrient intake variation in all 10 countries (27.4-37.1%). The subsequent RRR factors were much less important in explaining the variation (<or=6%). Strong similarities were observed for the first country-specific RRR factor between the individual countries, largely characterized by consumption of bread, vegetable oils, red meat, milk, cheese, potatoes, margarine and processed meat. The highest explained variation was seen for protein, potassium, phosphorus and magnesium (50-70%), whereas sugars, beta-carotene, retinol and alcohol were only marginally explained (<or=5%). The explained proportion of the other nutrients ranged between these extremes. A combination of food groups was identified that explained a considerable proportion of the nutrient intake variation in 24-HDRs in every country-specific EPIC population in a similar manner. This indicates that, despite the large variability in food and nutrient intakes reported in the EPIC, the variance of intake of important nutrients is explained, to a large extent, by similar food group combinations across countries.

Dietary patterns, insulin resistance, and incidence of type 2 diabetes in the Whitehall II Study.

OBJECTIVE—The aim of this study was to identify a dietary pattern associated with insulin resistance and investigate whether this pattern was prospectively associated with type 2 diabetes.RESEARCH DESIGN AND METHODS—Analysis was based on 7,339 participants of the Whitehall II study. Dietary intake was measured using a 127-item food frequency questionnaire. We used the reduced rank regression method to determine dietary patterns using the homeostasis model assessment of insulin resistance as the intermediate or response variable. The association between the dietary pattern identified and incidence of type 2 diabetes was investigated using Cox proportional hazard regression models.RESULTS—We identified a dietary pattern characterized by high consumption of low-calorie/diet soft drinks, onions, sugar-sweetened beverages, burgers and sausages, crisps and other snacks, and white bread and low consumption of medium-/high-fiber breakfast cereals, jam, French dressing/vinaigrette, and wholemeal bread. Higher dietary pattern scores were associated with increased risk of type 2 diabetes (hazard ratio for top quartile 2.95 [95% CI 2.19–3.97]; adjusted for age, sex, and energy misreporting). This relationship was attenuated after adjustment for ethnicity, employment grade, health behaviors (smoking, alcohol use, and physical activity) but remained significant after further adjustment for blood pressure and BMI (1.51 [1.10–2.09]).CONCLUSIONS—A dietary pattern associated with insulin resistance predicts type 2 diabetes risk after adjustment for a range of confounders. This study adds to the evidence that dietary patterns are an important risk factor for type 2 diabetes.

Identification of a Food Pattern Characterized by High-Fiber and Low-Fat Food Choices Associated with Low Prospective Weight Change in the EPIC-Potsdam Cohort

The aim of the study was to identify a dietary pattern predictive of subsequent annual weight change by using dietary composition information. Study subjects were 24,958 middle-aged men and women of the European Prospective Investigation into Cancer and Nutrition-Potsdam cohort. To derive dietary patterns, we used the reduced rank regression method with 3 response variables presumed to affect weight change: fat density, carbohydrate density, and fiber density. Annual weight change was computed by fitting a linear regression line to each person's body weight data (baseline, and 2- and 4-y follow-up) and determining the slope. In linear regression models, the pattern score was related to annual weight change. We identified a food pattern of high consumption of whole-grain bread, fruits, fruit juices, grain flakes/cereals, and raw vegetables, and of low consumption of processed meat, butter, high-fat cheese, margarine, and meat to be predictive of subsequent weight change. Mean annual weight gain gradually decreased with increasing pattern score (P for trend < 0.0001), i.e., subjects scoring high for the pattern maintained their weight or gained significantly less weight over time compared with subjects with an opposite pattern. However, the prediction of annual weight change by the food pattern was significant only in nonobese subjects. In this study population, we identified a food pattern characterized by high-fiber and low-fat food choices that can help to maintain body weight or at least prevent excess body weight gain.

Comparison of two statistical approaches to predict all-cause mortality by dietary patterns in German elderly subjects

Dietary patterns are comprehensive variables of dietary intake appropriate to model the complex exposure in nutritional research. The objectives of this study were to identify dietary patterns by applying two statistical methods, principal component analysis (PCA) and reduced rank regression (RRR), and to assess their ability to predict all-cause mortality. Motivated by previous studies we chose percentages of energy from different macronutrients as response variables in the RRR analysis. We used data from 9356 German elderly subject enrolled in the European Prospective Investigation into Cancer and Nutrition study. The first RRR pattern, subjects which explained 30.8 % of variation in energy sources and especially much variation in intake of saturated fat, monounsaturated fat and carbohydrates was a significant predictor of all-cause mortality. The pattern score had high positive loadings in all types of meat, butter, sauces and eggs, and was inversely associated with bread and fruits. After adjustment for other known risk factors, the relative risks from the lowest to highest quintiles of the first RRR pattern score were 1.0, 1.01, 0.96, 1.32, 1.61 (P for trend: 0.0004). In contrast, the first two PCA patterns explaining 19.7 % of food intake variation but only 7.0 % of variation in energy sources were not related to mortality. These results suggest that variation in macronutrients is meaningful for mortality and that the RRR method is more appropriate than the classic PCA method to identify dietary patterns relevant to mortality.

Predicting Multivariate Response in Linear Regression Model

Predicting a multivariate response vector in a linear multivariate regression model requires the estimate of the matrix of regression parameters. Stein (Stein, C. (1973). Estimation of the mean of a multivariate normal distribution. Proc. Prague Symp. Asymp. Statist. 345–381), van der Merwe and Zidek (van der Merwe, A., Zidek, J.V. (1980). Multivariate regression analysis and canonical variates. Canadian Journal of Statistics 8:27–39), Bilodeau and Kariya (Bilodeau, M., Kariya, T. (1989). Minimax estimators in the normal MANOVA model. Journal of Multivariate Analysis 28:260–270) and Konno (Konno, Y. (1990). On estimation of a matrix of mean. Unpublished manuscript; Konno, Y. (1991). On estimation of a matrix of normal means with unknown covariance matrix. J. Multi. Analysis 36:44–55) have shown that their shrinkage estimators perform better than the least squares estimator. Recently, Breiman and Friedman (Breiman, L., Friedman, J. H. (1997). Predicting multivariate responses in multiple regression. J. Roy. Statist. Soc. Ser. B 59:3–54) proposed another class of shrinkage estimators, called C&W-GCV estimators. Through extensive simulations, they have showed that their C&W-GCV estimator performs better than the FICYREG estimator of van der Merwe and Zidek (van der Merwe, A., Zidek, J. V. (1980). Multivariate regression analysis and canonical variates. Canadian Journal of Statistics 8:27–39), the reduced rank regression method of Anderson (Anderson, T. W. (1951). Estimating linear restrictions on regression coefficients for multivariate normal distribution. Ann. Math. Statist., 22:327–351 (Correction in Ann. Statist. (1980), 8, 1400). Estimating linear restrictions on regression coefficients for multivariate normal distribution. Ann. Math. Statist. 22:327–351. (Correction in Ann. Statist. (1980), 8, 1400)), the component-wise ridge regression and the partial least squares. They, however, did not include in their comparisons, the minimax estimators of Bilodeau and Kariya (Bilodeau, M., Kariya, T. (1989). Minimax estimators in the normal MANOVA model. Journal of Multivariate Analysis 28:260–270) and Konno (Konno, Y. (1990). On estimation of a matrix of mean. Unpublished manuscript; Konno, Y. (1991). On estimation of a matrix of normal means with unknown covariance matrix. J. Multi. Analysis 36:44–55). In this article, we compare C&W-GCV estimator with two invariant minimax estimators and show that C&W-GCV does not perform as well as the two minimax estimators unless the number of response variables is fairly small compared to the number of independent variables and the sample size is small.