Dataset Information

Application of copulas to improve covariance estimation for partial least squares.

ABSTRACT: Dimension reduction techniques, such as partial least squares, are useful for computing summary measures and examining relationships in complex settings. Partial least squares requires an estimate of the covariance matrix as a first step in the analysis, making this estimate critical to the results. In addition, the covariance matrix also forms the basis for other techniques in multivariate analysis, such as principal component analysis and independent component analysis. This paper has been motivated by an example from an imaging study in Alzheimer's disease where there is complete separation between Alzheimer's and control subjects for one of the imaging modalities. This separation occurs in one block of variables and does not occur with the second block of variables resulting in inaccurate estimates of the covariance. We propose the use of a copula to obtain estimates of the covariance in this setting, where one set of variables comes from a mixture distribution. Simulation studies show that the proposed estimator is an improvement over the standard estimators of covariance. We illustrate the methods from the motivating example from a study in the area of Alzheimer's disease.

SUBMITTER: D'Angelo GM

PROVIDER: S-EPMC3543761 | biostudies-literature | 2013 Feb

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Application of copulas to improve covariance estimation for partial least squares.

D'Angelo Gina M GM Weissfeld Lisa A LA

Statistics in medicine 20120910 4

Dimension reduction techniques, such as partial least squares, are useful for computing summary measures and examining relationships in complex settings. Partial least squares requires an estimate of the covariance matrix as a first step in the analysis, making this estimate critical to the results. In addition, the covariance matrix also forms the basis for other techniques in multivariate analysis, such as principal component analysis and independent component analysis. This paper has been mot ...[more]

PMID: 22961807

Similar Datasets

Project description:In a large cohort of older women, a mechanism-driven statistical technique for assessing dietary patterns that considers a potential nutrient pathway found two dietary patterns associated with lumbar spine and femoral neck bone mineral density. A "healthy" dietary pattern was observed to be beneficial for bone mineral density.IntroductionDietary patterns represent a broader, more realistic representation of how foods are consumed, compared to individual food or nutrient analyses. Partial least-squares (PLS) is a data-reduction technique for identifying dietary patterns that maximizes correlation between foods and nutrients hypothesized to be on the path to disease, is more hypothesis-driven than previous methods, and has not been applied to the study of dietary patterns in relation to bone health.MethodsWomen from the Aberdeen Prospective Osteoporosis Screening Study (2007-2011, n = 2129, age = 66 years (2.2)) provided dietary intake using a food frequency questionnaire; 37 food groups were created. We applied PLS to the 37 food groups and 9 chosen response variables (calcium, potassium, vitamin C, vitamin D, protein, alcohol, magnesium, phosphorus, zinc) to identify dietary patterns associated with bone mineral density (BMD) cross-sectionally. Multivariable regression was used to assess the relationship between the retained dietary patterns and BMD at the lumbar spine and femoral neck, adjusting for age, body mass index, physical activity level, smoking, and national deprivation category.ResultsFive dietary patterns were identified, explaining 25% of the variation in food groups and 77% in the response variables. Two dietary patterns were positively associated with lumbar spine (per unit increase in factor 2: 0.012 g/cm2 [95% CI: 0.006, 0.01]; factor 4: 0.007 g/cm2 [95% CI: 0.00001, 0.01]) and femoral neck (factor 2: 0.006 g/cm2 [95% CI: 0.002, 0.01]; factor 4: 0.008 g/cm2 [95% CI: 0.003, 0.01)]) BMD. Dietary pattern 2 was characterized by high intakes of milk, vegetables, fruit and vegetable juices, and wine, and low intakes of processed meats, cheese, biscuits, cakes, puddings, confectionary, sweetened fizzy drinks and spirits while dietary pattern 4 was characterized by high intakes of fruits, red and white meats, and wine, and low intakes of vegetables and sweet spreads.ConclusionOur findings using a robust statistical technique provided important support to initiatives focusing on what constitutes a healthy diet and its implications.

Project description:BackgroundSurvival analysis is the most appropriate method of analysis for time-to-event data. The classical accelerated failure-time model is a more powerful and interpretable model than the Cox proportional hazards model, provided that model imposed distribution and homoscedasticity assumptions satisfied. However, most of the real data are heteroscedastic which violates the fundamental assumption and consequently, the statistical inference could be erroneous in accelerated failure-time modeling. The weighted least-squares estimation for the accelerated failure-time model is an efficient semi-parametric approach for time-to-event data without the homoscedasticity assumption, which is developed recently and not often utilized for real data analysis. Thus, this study was conducted to ascertain the better performance of the weighted least-squares estimation method over the classical methods.MethodsWe analyzed a REAL dataset on Antiretroviral Therapy patients we recently collected. We compared the results from classical methods of estimation for the accelerated failure-time model with the results revealed from the weighted least-squares estimation.ResultsWe found that the data are heteroscedastic and indicated that the weighted least-square method should be used to analyze this data. The weighted least-squares estimation revealed more accurate, and efficient estimates of covariates effect since its confidence intervals were shorter and it identified more significant covariates. Accordingly, the survival of HIV positives was found to be significantly linked with age, weight, functional status, CD4 (Cluster of Differentiation agent 4 glycoproteins), and clinical stages.ConclusionsThe weighted least-squares estimation performed the best in providing more significant effects and precise estimates than the classical accelerated failure-time methods of estimation if data are heteroscedastic. Thus, we recommend future researchers should utilize weighted least-squares estimation rather than the classical methods when the homoscedasticity assumption is violated.

Dataset Information

Application of copulas to improve covariance estimation for partial least squares.

Publications

Application of copulas to improve covariance estimation for partial least squares.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets