Reduced Rank Regression Research Articles

The Relationship Between Dietary Patterns and Carotid Intima Media Thickness, as an Early Biomarker of Cardiovascular Disease: A Systematic Review and Narrative Synthesis

ObjectiveTo systematically review current literature on the association between empirically derived dietary patterns and carotid‐intima media thickness, an early marker of cardiovascular disease.BackgroundDietary pattern analysis has emerged as a complementary approach to single‐nutrient analysis for examining the relationship between diet and the risk of chronic diseases like cardiovascular disease (CVD). Carotid intima‐media thickness (CIMT) has been established as a robust early marker of CVD on the atherosclerotic pathway. Although a wealth of literature links dietary factors and traditional CVD markers, a limited number have investigated the relationship between dietary patterns, derived using empirical data, and CIMT, a novel CVD marker. This is a unique systematic review and narrative synthesis which investigates the association between dietary patterns and CIMT.MethodsA systematic search of MEDLINE, CINAHL and Web of Science (2000 to 2015) supplemented by manual searches of bibliographies was conducted. Studies that derived dietary patterns using a posteriori methods (principal component analysis (PCA)/factor analysis (FA)), a priori methods (investigator‐defined) or a combination (reduced rank regression (RRR)) were included with CIMT as the outcome. Most papers studied healthy adults (≥18 years) except two. The Critical Appraisal Skills Programme (CASP) checklist was adapted to assess each study for validity, methodology, and relevance. The narrative synthesis discusses the findings from each study according to the method used to derive the dietary patterns.ResultsOut of a total of 1582 papers, 15 papers were eligible for review. Six papers used empirical methods (PCA n=4, FA n=1, RRR n=1), while 9 papers used investigator‐defined methods to determine dietary patterns (refer to the figure). In general, of the papers using empirical methods, four reported a statistically significant association with increased CIMT. Overall, the dietary patterns identified in those studies were characterized by high consumption in ‘unhealthful’ food groups such as processed and red meat, soda and meal replacement drinks, refined grain and starchy foods. While two studies that identified dietary patterns empirically were associated with a decrease in CIMT, characterized by high consumption of ‘healthful’ foods namely fruits and vegetables, fish, and rice and low in the ‘unhealthful’ foods. Of the papers using investigator‐defined methods, four cross sectional studies showed that adherence to lacto‐vegetarian/low‐calorie vegan diets is associated with a decrease in CIMT. Dietary patterns derived from each study varied depending on derivation method and study design. When assessed for quality, RCTs scored the lowest, and cross sectional studies failed to provide sufficient information on the measurement of exposure variables. Cohort studies proved to be the most robust study design when assessed using the CASP criteria.ConclusionsFindings from this review are generally supportive of an association between greater adherence to dietary patterns characterised by higher consumption of ‘healthful’ foods and lower consumption of ‘unhealthful’ foods, and decreased CIMT. However, the evidence is heterogeneous as seen from the differences in CIMT measures with varying dietary patterns. Large‐scale prospective observational and interventional studies are needed to evaluate the association between dietary patterns and CIMT.Support or Funding Informationnone

The Early Life Predictors of a Dietary Pattern Linked With Greater Metabolic Risk in Adolescence and Tracking of Its Food Components

BackgroundGrowing evidence suggests that dietary behaviours linked with chronic diseases in adulthood may develop early in life. However, little is known on the tracking of food intakes during adolescence. This study examined predictors and tracking of key food groups in a dietary pattern (DP) associated with greater cardiometabolic risk among adolescents aged between 14 and 17 y in the Western Australian Pregnancy (Raine) Cohort study.MethodsA total of 860 adolescents reported their food consumption using a food frequency questionnaire (FFQ) at 14 and 17 y. Z‐scores for an ‘energy dense, high fat and low fibre’ DP were estimated using reduced rank regression (RRR) at both ages. Information on adolescents’ early life exposures and parental socio‐economic status at 14 and 17 y was collected using a detailed questionnaire. Tracking analysis was performed based on the predictive value (PV) of remaining in the same quartile of the DP z‐score between 14 and 17 y. Associations between the DP z‐scores, early life factors and SES were analysed using multiple linear regression.ResultsThe identified DP was prospectively associated with greater cardiometabolic risk factors, in boys and girls, between 14 and 17 y. Tracking was strongest amongst boys with the lowest consumption of vegetables, fruit, legumes, high‐fibre bread and yoghurt at 14 y. A high DP z‐score and high intake of processed meat, low‐fibre bread, crisps and savoury snack also tracked strongly among boys. Greater maternal education (β=0.09, p=0.002 at 14 y; β=0.14, p<0.001 at 17 y) and age at child birth (β=−0.09, p=0.003 at 14 y; β= −0.11, p=0.004 at 17 y) were consistently associated with a higher DP z‐score. Paternal smoking status during pregnancy was associated with a higher DP z‐score (β=0.10, p=0.049), at 14 y.ConclusionThese findings highlight subgroups of the population who may benefit the most from early interventions to improve dietary behaviors and reduce the risk of later chronic diseases.Support or Funding Information Medical Research Council, UK (U105960389) National Health and Medical Research Council of Australia National Heart Foundation of Australia Beyond Blue Cardiovascular Disease of Australia Depression Strategic Research Program of Australia

Free Sugars and Total Fat Are Important Characteristics of a Dietary Pattern Associated with Adiposity across Childhood and Adolescence

Background: The importance of dietary sugar compared with fat in the development of obesity is currently a topic of debate.Objective: We aimed to identify dietary patterns (DPs) characterized by high sugar content, high fat content, or both and their longitudinal associations with adiposity during childhood and adolescence.Methods: Participants were 6722 children from the ALSPAC (Avon Longitudinal Study of Parents and Children) who were born in 1991–1992. DPs were characterized by percentage of total energy intake (%E) from free sugars, %E from total fat, and dietary energy density (DED) and fiber density by using reduced rank regression at 7, 10, and 13 y of age. Total body fat mass was measured at 11, 13, and 15 y of age. Regression analyses were used to adjust for dietary misreporting, physical activity, and maternal social class.Results: Two major DPs were identified: higher z scores for DP1 were associated with greater DED, greater %E from free sugars and total fat, and lower fiber density; higher z scores for DP2 were associated with greater %E from free sugars but lower %E from total fat and DED. A 1-SD increase in z score for DP1 was associated with a mean increase in the fat mass index z score of 0.04 SD units (95% CI: 0.01, 0.07; P = 0.017) and greater odds of excess adiposity (OR: 1.12; 95% CI: 1.0, 1.25; P = 0.038). DP2 was not associated with adiposity.Conclusions: An energy-dense DP high in %E from total fat and free sugars is associated with greater adiposity in childhood and adolescence. This appears to confirm the role of both fat and sugar and provides a basis for food-based dietary guidelines to prevent obesity in children.

A high-fat, high-glycaemic index, low-fibre dietary pattern is prospectively associated with type 2 diabetes in a British birth cohort.

The combined association of dietary fat, glycaemic index (GI) and fibre with type 2 diabetes has rarely been investigated. The objective was to examine the relationship between a high-fat, high-GI, low-fibre dietary pattern across adult life and type 2 diabetes risk using reduced rank regression. Data were from the MRC National Survey of Health and Development. Repeated measures of dietary intake estimated using 5-d diet diaries were available at the age of 36, 43 and 53 years for 1180 study members. Associations between dietary pattern scores at each age, as well as longitudinal changes in dietary pattern z-scores, and type 2 diabetes incidence (n 106) from 53 to 60-64 years were analysed. The high-fat, high-GI, low-fibre dietary pattern was characterised by low intakes of fruit, vegetables, low-fat dairy products and whole-grain cereals, and high intakes of white bread, fried potatoes, processed meat and animal fats. There was an increasing trend in OR for type 2 diabetes with increasing quintile of dietary pattern z-scores at the age of 43 years among women but not among men. Women in the highest z-score quintile at the age of 43 years had an OR for type 2 diabetes of 5·45 (95 % CI 2·01, 14·79). Long-term increases in this dietary pattern, independently of BMI and waist circumference, were also detrimental among women: for each 1 sd unit increase in dietary pattern z-score between 36 and 53 years, the OR for type 2 diabetes was 1·67 (95 % CI 1·20, 2·43) independently of changes in BMI and waist circumference in the same periods. A high-fat, high-GI, low-fibre dietary pattern was associated with increased type 2 diabetes risk in middle-aged British women but not in men.

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.

Life Course Dietary Patterns and Bone Health in Later Life in a British Birth Cohort Study.

ABSTRACTEvidence for the contribution of individual foods and nutrients to bone health is weak. Few studies have considered hypothesis‐based dietary patterns and bone health. We investigated whether a protein‐calcium‐potassium–rich (PrCaK‐rich) dietary pattern over the adult life course, was positively associated with bone outcomes at 60 to 64 years of age. Diet diaries were collected at ages 36, 46, 53, and 60 to 64 years in 1263 participants (661 women) from the MRC National Survey of Health and Development. DXA and pQCT measurements were obtained at age 60 to 64 years, including size‐adjusted bone mineral content (SA‐BMC) and volumetric bone mineral density (vBMD). A food‐based dietary pattern best explaining dietary calcium, potassium, and protein intakes (g/1000 kcal) was identified using reduced rank regression. Dietary pattern Z‐scores were calculated for each individual, at each time point. Individual trajectories in dietary pattern Z‐scores were modeled to summarize changes in Z‐scores over the study period. Regression models examined associations between these trajectories and bone outcomes at age 60 to 64 years, adjusting for baseline dietary pattern Z‐score and other confounders. A consistent PrCaK‐rich dietary pattern was identified within the population, over time. Mean ± SD dietary pattern Z‐scores at age 36 years and age 60 to 64 years were –0.32 ± 0.97 and 2.2 ± 1.5 (women) and –0.35 ± 0.98 and 1.7 ± 1.6 (men), respectively. Mean trajectory in dietary pattern Z‐scores ± SD was 0.07 ± 0.02 units/year. Among women, a 0.02‐SD unit/year higher trajectory in dietary pattern Z‐score over time was associated with higher SA‐BMC (spine 1.40% [95% CI, 0.30 to 2.51]; hip 1.35% [95% CI, 0.48 to 2.23]), and vBMD (radius 1.81% [95% CI, 0.13 to 3.50]) at age 60 to 64 years. No statistically significant associations were found in men. During adulthood, an increasing score for a dietary pattern rich in protein, calcium, and potassium was associated with greater SA‐BMC at fracture‐prone sites in women. This study emphasizes the importance of these nutrients, within the context of the whole diet, to bone health. © 2016 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research (ASBMR).

Favorable outcome of intraoperative radiotherapy to the primary site in patients with metastatic prostate cancer.

The aim of this study was to determine whether local radiotherapy to the prostate by intraoperative radiotherapy (IORT) increases the overall and cancer-specific survival rates of patients with metastatic prostate cancer. Between 1993 and 2000, 102 patients with prostate cancer were treated with a combination of (a) IORT of the prostate (25 or 30Gy per fraction); (b) external beam radiotherapy of the prostate (30Gy in 10 fractions), starting approximately 1week post-operatively; and (c) endocrine treatment. Of these, 16 patients had stage D1 disease (D1 IORT group), 32 had stage D2 disease without visceral metastasis (D2 IORT group), and 38 had stage D2 disease without visceral metastasis and did not receive local therapy (D2 control group). Overall and cancer-specific survival rates were compared. The 5- and 10-year cancer-specific survival rates were 75.9 and 52.7%, respectively, in the (D1+D2) IORT group and 45.8 and 33.5%, respectively, in the D2 control group, with cancer-specific survival being significantly longer in the D2 IORT than in the D2 control group (P=0.030). Univariate and multivariate reduced-rank regression analyses showed that extent of skeletal disease Grade 4 and non-regional lymph node metastasis were significantly prognostic of poorer cancer-specific survival (P<0.001 each). Local radiotherapy to the prostate by IORT in patients with metastatic prostate cancer may contribute to better survival, especially in patients without extent of skeletal disease Grade 4 or non-regional lymph node metastasis.

Sparse Kernel Reduced-Rank Regression for Bimodal Emotion Recognition From Facial Expression and Speech

A novel bimodal emotion recognition approach from facial expression and speech based on the sparse kernel reduced-rank regression (SKRRR) fusion method is proposed in this paper. In this method, we use the openSMILE feature extractor and the scale invariant feature transform feature descriptor to respectively extract effective features from speech modality and facial expression modality, and then propose the SKRRR fusion approach to fuse the emotion features of two modalities. The proposed SKRRR method is a nonlinear extension of the traditional reduced-rank regression (RRR), where both predictor and response feature vectors in RRR are kernelized by being mapped onto two high-dimensional feature space via two nonlinear mappings, respectively. To solve the SKRRR problem, we propose a sparse representation (SR)-based approach to find the optimal solution of the coefficient matrices of SKRRR, where the introduction of the SR technique aims to fully consider the different contributions of training data samples to the derivation of optimal solution of SKRRR. Finally, we utilize the eNTERFACE ’05 and AFEW 4.0 bimodal emotion database to conduct the experiments of monomodal emotion recognition and bimodal emotion recognition, and the results indicate that our presented approach acquires the highest or comparable bimodal emotion recognition rate among some state-of-the-art approaches.

Asymptotic properties of adaptive group Lasso for sparse reduced rank regression

This paper studies the asymptotic properties of the penalized least squares estimator using an adaptive group Lasso penalty for the reduced rank regression. The group Lasso penalty is defined in the way that the regression coefficients corresponding to each predictor are treated as one group. It is shown that under certain regularity conditions, the estimator can achieve the minimax optimal rate of convergence. Moreover, the variable selection consistency can also be achieved, that is, the relevant predictors can be identified with probability approaching one. In the asymptotic theory, the number of response variables, the number of predictors and the rank number are allowed to grow to infinity with the sample size. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Methods of a posteriori identification of food patterns in Brazilian children: a systematic review

The objective of this study is to provide guidance for identifying dietary patterns using the a posteriori approach, and analyze the methodological aspects of the studies conducted in Brazil that identified the dietary patterns of children. Articles were selected from the Latin American and Caribbean Literature on Health Sciences, Scientific Electronic Library Online and Pubmed databases. The key words were: Dietary pattern; Food pattern; Principal Components Analysis; Factor analysis; Cluster analysis; Reduced rank regression. We included studies that identified dietary patterns of children using the a posteriori approach. Seven studies published between 2007 and 2014 were selected, six of which were cross-sectional and one cohort, Five studies used the food frequency questionnaire for dietary assessment; one used a 24-hour dietary recall and the other a food list. The method of exploratory approach used in most publications was principal components factor analysis, followed by cluster analysis. The sample size of the studies ranged from 232 to 4231, the values of the Kaiser-Meyer-Olkin test from 0.524 to 0.873, and Cronbach's alpha from 0.51 to 0.69. Few Brazilian studies identified dietary patterns of children using the a posteriori approach and principal components factor analysis was the technique most used.

Corporate Capital Structure Actions

Existing empirical models of corporate leverage do a good job of predicting the cross section pattern of debt and equity repurchases. However, they do a poor job predicting debt and equity issuing. To improve the performance we use a large number of macroeconomic variables in reduced rank regression to estimate leverage targets based on firm-specific sensitivities to four common factors. This model gets the correct cross section patterns of issuing and repurchasing.The four factors load heavily on asset tangibility, taxation, corporate overhead, and volatility. The model performs particularly well for larger, profitable, and dividend paying firms.

Using both principal component analysis and reduced rank regression to study dietary patterns and diabetes in Chinese adults

Using both principal component analysis and reduced rank regression to study dietary patterns and diabetes in Chinese adults

%ERA: A SAS Macro for Extended Redundancy Analysis

A new approach to structural equation modeling based on so-called extended redundancy analysis has been recently proposed in the literature, enhanced with the added characteristic of generalizing redundancy analysis and reduced-rank regression models for more than two blocks. In this approach, the relationships between the observed exogenous variables and the observed endogenous variables are moderated by the presence of unobservable composites that were estimated as linear combinations of exogenous variables, permitting a great flexibility to specify and fit a variety of structural relationships. In this paper, we propose the SAS macro %ERA to specify and fit structural relationships in the extended redundancy analysis (ERA) framework. Two examples (simulation and real data) are provided in order to reproduce results appearing in the original article where ERA was proposed.

A visceral adiposity index-related dietary pattern and the cardiometabolic profiles in women with polycystic ovary syndrome

Visceral adiposity index (VAI), an indicator of visceral adiposity, has been found to be associated with cardiometabolic disturbances in women with polycystic ovary syndrome (PCOS). The association of dietary intakes with VAI, and subsequently cardiometabolic variables is still unclear. The aims of this study were to identify a dietary pattern associated with VAI and to investigate whether this pattern is associated with cardiometabolic variables in PCOS women. The study was conducted on 53 PCOS women, aged 18-45 years, diagnosed according to National Institutes of Health (NIH) criteria, and 167 age-matched normo-ovulatory women who were recruited from the Tehran Lipid and Glucose Study. Reduced rank regression was applied to determine a dietary pattern that explains the maximum variation of the VAI. Associations between the dietary pattern and cardiometabolic profiles were investigated using linear and logistic regression, adjusted for age and BMI. A VAI dietary pattern was identified characterized by high consumption of fried vegetables, vegetable oils (except olive oil), salty snacks, legumes, eggs, fast foods and low consumption of traditional sweets, high and low fat dairy, cruciferous vegetables, sugars and honey. A one standard deviation (SD) increase in dietary pattern score was significantly associated with higher triglycerides (TGs) (βcontrol=0.22, p=0.003; βcase=0.48, p=0.001) and TGs/HDL-C ratio (βcontrol=0.23, p=0.002; βcase=0.52, p=0.001) in both groups. After adjusting for age and BMI, a 1-SD increase in dietary pattern score was associated with increased risk of VAD in PCOS (OR 2.77; 95% CI 1.15, 6.66) and control groups (OR 2.41; 95% CI 1.41-4.12). In the control group, the risk of hypercholesterolemia, hypertriglyceridemia, high LDL-C, low HDL-C, hyperglycemia and IGT+IFG increased significantly per 1-SD increase in dietary pattern score, which all remained significant after adjusting for age and BMI, except for the risk of high LDL-C. Among the cardiometabolic abnormalities, only the risk of hypertriglyceridemia was significantly associated with dietary pattern score in women with PCOS, which lost its significance after adjusting for age and BMI. The VAI dietary pattern affects most cardiometabolic variables in controls, but to a lesser extent in PCOS women. Our study suggests that relationships between diet and cardiometabolic risk profiles may be modified by PCOS status.

Bayes and empirical Bayes methods for reduced rank regression models in matched case-control studies.

Matched case-control studies are popular designs used in epidemiology for assessing the effects of exposures on binary traits. Modern studies increasingly enjoy the ability to examine a large number of exposures in a comprehensive manner. However, several risk factors often tend to be related in a nontrivial way, undermining efforts to identify the risk factors using standard analytic methods due to inflated type-I errors and possible masking of effects. Epidemiologists often use data reduction techniques by grouping the prognostic factors using a thematic approach, with themes deriving from biological considerations. We propose shrinkage-type estimators based on Bayesian penalization methods to estimate the effects of the risk factors using these themes. The properties of the estimators are examined using extensive simulations. The methodology is illustrated using data from a matched case-control study of polychlorinated biphenyls in relation to the etiology of non-Hodgkin's lymphoma.

Dietary Patterns during Pregnancy Are Associated with Risk of Gestational Diabetes Mellitus.

Maternal dietary patterns before and during pregnancy play important roles in the development of gestational diabetes mellitus (GDM). We aimed to identify dietary patterns during pregnancy that are associated with GDM risk in pregnant U.S. women. From a 24 h dietary recall of 253 pregnant women (16–41 years) included in the National Health and Nutrition Examination Survey (NHANES) 2003–2012, food items were aggregated into 28 food groups based on Food Patterns Equivalents Database. Three dietary patterns were identified by reduced rank regression with responses including prepregnancy body mass index (BMI), dietary fiber, and ratio of poly- and monounsaturated fatty acids to saturated fatty acid: “high refined grains, fats, oils and fruit juice”, “high nuts, seeds, fat and soybean; low milk and cheese”, and “high added sugar and organ meats; low fruits, vegetables and seafood”. GDM was diagnosed using fasting plasma glucose levels ≥5.1 mmol/L for gestation <24 weeks. Multivariable logistic regression models were used to estimate adjusted odds ratio (AOR) and 95% confidence intervals (CIs) for GDM, after controlling for maternal age, race/ethnicity, education, family poverty income ratio, marital status, prepregnancy BMI, gestational weight gain, energy intake, physical activity, and log-transformed C-reactive protein (CRP). All statistical analyses accounted for the appropriate survey design and sample weights of the NHANES. Of 249 pregnant women, 34 pregnant women (14%) had GDM. Multivariable AOR (95% CIs) of GDM for comparisons between the highest vs. lowest tertiles were 4.9 (1.4–17.0) for “high refined grains, fats, oils and fruit juice” pattern, 7.5 (1.8–32.3) for “high nuts, seeds, fat and soybean; low milk and cheese” pattern, and 22.3 (3.9–127.4) for “high added sugar and organ meats; low fruits, vegetables and seafood” pattern after controlling for maternal sociodemographic variables, prepregnancy BMI, gestational weight gain, energy intake and log-transformed CRP. These findings suggest that dietary patterns during pregnancy are associated with risk of GDM after controlling for potential confounders. The observed connection between a high consumption of refined grains, fat, added sugars and low intake of fruits and vegetables during pregnancy with higher odds for GDM, are consistent with general health benefits of healthy diets, but warrants further research to understand underlying pathophysiology of GDM associated with dietary behaviors during pregnancy.

On the Univariate Representation of BEKK Models with Common Factors

AbstractSimple low order multivariate GARCH models imply marginal processes with a lot of persistence in the form of high order lags. This is not what we find in many situations however, where parsimonious univariate GARCH(1,1) models for instance describe quite well the conditional volatility of some asset returns. In order to explain this paradox, we show that in the presence of common GARCH factors, parsimonious univariate representations can result from large multivariate models generating the conditional variances and conditional covariances/correlations. The diagonal model without any contagion effects in conditional volatilities gives rise to similar conclusions though. Consequently, after having extracted a block of assets representing some form of parsimony, remains the task of determining if we have a set of independent assets or instead a highly dependent system generated with a few factors. To investigate this issue, we first evaluate a reduced rank regressions approach for squared returns that we extend to cross-returns. Second we investigate a likelihood ratio approach, where under the null the matrix parameters have a reduced rank structure. It emerged that the latter approach has quite good properties enabling us to discriminate between a system with seemingly unrelated assets (e.g. a diagonal model) and a model with few common sources of volatility.

Locally Efficient Semiparametric Estimators for Proportional Hazards Models with Measurement Error.

We propose a new class of semiparametric estimators for proportional hazards models in the presence of measurement error in the covariates, where the baseline hazard function, the hazard function for the censoring time, and the distribution of the true covariates are considered as unknown infinite dimensional parameters. We estimate the model components by solving estimating equations based on the semiparametric efficient scores under a sequence of restricted models where the logarithm of the hazard functions are approximated by reduced rank regression splines. The proposed estimators are locally efficient in the sense that the estimators are semiparametrically efficient if the distribution of the error-prone covariates is specified correctly, and are still consistent and asymptotically normal if the distribution is misspecified. Our simulation studies show that the proposed estimators have smaller biases and variances than competing methods. We further illustrate the new method with a real application in an HIV clinical trial.

Identification of a dietary pattern prospectively associated with bone mass in Australian young adults

Relatively little is known about the relations between dietary patterns and bone health in adolescence, which is a period of substantial bone mass accrual. We derived dietary patterns that were hypothesized to be related to bone health on the basis of their protein, calcium, and potassium contents and investigated their prospective associations with bone mineral density (BMD), bone area, and bone mineral content (BMC) in a cohort of young adults. The study included 1024 young adults born to mothers who were participating in the Western Australian Pregnancy Cohort (Raine) Study. Dietary information was obtained from food-frequency questionnaires at 14 and 17 y of age. Dietary patterns were characterized according to protein, calcium, and potassium intakes with the use of reduced-rank regression. BMD, bone area, and BMC were estimated with the use of a total body dual-energy X-ray absorptiometry scan at 20 y of age. We identified 2 major dietary patterns. The first pattern was positively correlated with intakes of protein, calcium, and potassium and had high factor loadings for low-fat dairy products, whole grains, and vegetables. The second pattern was positively correlated with protein intake but negatively correlated with intakes of calcium and potassium and had high factor loadings for meat, poultry, fish, and eggs. After adjustment for anthropometric, sociodemographic, and lifestyle factors, a higher z score for the first pattern at 14 y of age was positively associated with BMD and BMC at 20 y of age [differences: 8.6 mg/cm(2) (95% CI: 3.0, 14.1 mg/cm(2)) and 21.9 g (95% CI: 6.5, 37.3 g), respectively, per SD increase in z score]. The z score for this same pattern at 17 y of age was not associated with bone outcomes at 20 y of age. The second pattern at 14 or 17 y of age was not associated with BMD, BMC, or bone area. A dietary pattern characterized by high intakes of protein, calcium, and potassium in midadolescence was associated with higher BMD and BMC at 20 y of age. Our results indicate that high consumption of low-fat dairy products, whole grains, and vegetables in adolescence are associated with beneficial effects on bone development.

Nonconvex penalized reduced rank regression and its oracle properties in high dimensions

Sparse reduced rank regression achieves dimension reduction and variable selection simultaneously. In this paper, for a class of nonconvex penalties, we give sufficient conditions that guarantee the oracle estimator is a local minimizer and stronger conditions that guarantee it is a global minimizer, with probability tending to one in an ultra-high dimensional setting. We carry out simulations to investigate the performance of the estimator. A real data set is analyzed for illustration.