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Characterization of Weighted Quantile Sum Regression for Highly Correlated Data in a Risk Analysis Setting.

ABSTRACT: In risk evaluation, the effect of mixtures of environmental chemicals on a common adverse outcome is of interest. However, due to the high dimensionality and inherent correlations among chemicals that occur together, the traditional methods (e.g. ordinary or logistic regression) suffer from collinearity and variance inflation, and shrinkage methods have limitations in selecting among correlated components. We propose a weighted quantile sum (WQS) approach to estimating a body burden index, which identifies "bad actors" in a set of highly correlated environmental chemicals. We evaluate and characterize the accuracy of WQS regression in variable selection through extensive simulation studies through sensitivity and specificity (i.e., ability of the WQS method to select the bad actors correctly and not incorrect ones). We demonstrate the improvement in accuracy this method provides over traditional ordinary regression and shrinkage methods (lasso, adaptive lasso, and elastic net). Results from simulations demonstrate that WQS regression is accurate under some environmentally relevant conditions, but its accuracy decreases for a fixed correlation pattern as the association with a response variable diminishes. Nonzero weights (i.e., weights exceeding a selection threshold parameter) may be used to identify bad actors; however, components within a cluster of highly correlated active components tend to have lower weights, with the sum of their weights representative of the set.

SUBMITTER: Carrico C

PROVIDER: S-EPMC6261506 | biostudies-literature | 2015 Mar

REPOSITORIES: biostudies-literature

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Characterization of Weighted Quantile Sum Regression for Highly Correlated Data in a Risk Analysis Setting.

Carrico Caroline C Gennings Chris C Wheeler David C DC Factor-Litvak Pam P

Journal of agricultural, biological, and environmental statistics 20141224 1

In risk evaluation, the effect of mixtures of environmental chemicals on a common adverse outcome is of interest. However, due to the high dimensionality and inherent correlations among chemicals that occur together, the traditional methods (e.g. ordinary or logistic regression) suffer from collinearity and variance inflation, and shrinkage methods have limitations in selecting among correlated components. We propose a weighted quantile sum (WQS) approach to estimating a body burden index, which ...[more]

PMID: 30505142

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Project description:Studies of the health effects of the microbiome often measure overall associations by using diversity metrics, and individual taxa associations in separate analyses, but do not consider the correlated relationships between taxa in the microbiome. In this study, we applied random subset weighted quantile sum regression with repeated holdouts (WQSRSRH), a mixture method successfully applied to ‘omic data to account for relationships between many predictors, to processed amplicon sequencing data from the Human Microbiome Project. We simulated a binary variable associated with 20 operational taxonomic units (OTUs). WQSRSRH was used to test for the association between the microbiome and the simulated variable, adjusted for sex, and sensitivity and specificity were calculated. The WQSRSRH method was also compared to other standard methods for microbiome analysis. The method was further illustrated using real data from the Growth and Obesity Cohort in Chile to assess the association between the gut microbiome and body mass index. In the analysis with simulated data, WQSRSRH predicted the correct directionality of association between the microbiome and the simulated variable, with an average sensitivity and specificity of 75% and 70%, respectively, in identifying the 20 associated OTUs. WQSRSRH performed better than all other comparison methods. In the illustration analysis of the gut microbiome and obesity, the WQSRSRH analysis identified an inverse association between body mass index and the gut microbe mixture, identifying Bacteroides, Clostridium, Prevotella, and Ruminococcus as important genera in the negative association. The application of WQSRSRH to the microbiome allows for analysis of the mixture effect of all the taxa in the microbiome, while simultaneously identifying the most important to the mixture, and allowing for covariate adjustment. It outperformed other methods when using simulated data, and in analysis with real data found results consistent with other study findings.

Project description:Individuals are exposed to a large number of diverse environmental chemicals simultaneously and the evaluation of multiple chemical exposures is important for identifying cancer risk factors. The measurement of a large number of chemicals (the exposome) in epidemiologic studies is allowing for a more comprehensive assessment of cancer risk factors than was done in earlier studies that focused on only a few chemicals. Empirical evidence from epidemiologic studies shows that chemicals from different chemical classes have different magnitudes and directions of association with cancers. Given increasing data availability, there is a need for the development and assessment of statistical methods to model environmental cancer risk that considers a large number of diverse chemicals with different effects for different chemical classes. The method of grouped weighted quantile sum (GWQS) regression allows for multiple groups of chemicals to be considered in the model such that different magnitudes and directions of associations are possible for each group of chemicals. In this paper, we assessed the ability of GWQS regression to estimate exposure effects for multiple chemical groups and correctly identify important chemicals in each group using a simulation study. We compared the performance of GWQS regression with WQS regression, the least absolute shrinkage and selection operator (lasso), and the group lasso in estimating exposure effects and identifying important chemicals. The simulation study results demonstrate that GWQS is an effective method for modeling exposure to multiple groups of chemicals and compares favorably with other methods used in mixture analysis. As an application, we used GWQS regression in the California Childhood Leukemia Study (CCLS), a population-based case-control study of childhood leukemia in California to estimate exposure effects for many chemical classes while also adjusting for demographic factors. The CCLS analysis found evidence of a positive association between exposure to the herbicide dacthal and an increased risk of childhood leukemia.

Project description:BackgroundNew statistical methodologies were developed in the last decade to face the challenges of estimating the effects of exposure to multiple chemicals. Weighted Quantile Sum (WQS) regression is a recent statistical method that allows estimating a mixture effect associated with a specific health effect and identifying the components that characterize the mixture effect.ObjectivesIn this study, we propose an extension of WQS regression that estimates two mixture effects of chemicals on a health outcome in the same model through the inclusion of two indices, one in the positive direction and one in the negative direction, with the introduction of a penalization term.MethodsTo evaluate the performance of this new model we performed both a simulation study and a real case study where we assessed the effects of nutrients on obesity among adults using the National Health and Nutrition Examination Survey (NHANES) data.ResultsThe method showed good performance in estimating both the regression parameter and the weights associated with the single elements when the penalized term was set equal to the magnitude of the Akaike information criterion of the unpenalized WQS regression. The two indices further helped to give a better estimate of the parameters [Positive direction Median Error (PME): 0.022; Negative direction Median Error (NME): -0.044] compared to the standard WQS without the penalization term (PME: -0.227; NME: 0.215). In the case study, WQS with two indices was able to find a significant effect of nutrients on obesity in both directions identifying sodium and magnesium as the main actors in the positive and negative association, respectively.DiscussionThrough this work, we introduced an extension of WQS regression that improved the accuracy of the parameter estimates when considering a mixture of elements that can have both a protective and a harmful effect on the outcome; and the advantage of adding a penalization term when estimating the weights.

Project description:IntroductionPhthalates are a group of high production chemicals, generally used as plasticizers and odor enhancers. Phthalates cross the blood-placenta barrier and are associated with deficits in cognitive functions and behavior problems in offspring. We previously reported sex-specific associations with motor function when phthalates are considered singly. Because exposure to phthalates usually occurs as mixtures, here we assess these associations between a mixture of phthalates and motor function at age 11 years.MethodsData come from the prospective cohort study of mothers and offspring who participated in the Columbia Center for Children's Environmental Health birth cohort (CCCEH). Seven phthalate metabolites were measured in maternal spot urine obtained during the third trimester and motor function was evaluated using the short form of the Bruininks-Oseretsky Test of Motor Proficiency, 2nd edition (BOT-2) at the age of 11 years. We used Weighted Quartile Sum (WQS) regression models to examine the effect of phthalate metabolites in males and females separately. The models were adjusted for child age in months, child BMI, maternal race (African-American vs. Dominican), prenatal alcohol consumption, maternal demoralization score, HOME score, and urine specific gravity. In a secondary analysis we used linear regression models to examine the association between the sum of molar concentrations of both DEHP and non-DEHP metabolites, and outcomes of gross and fine motor functions.Results209 mother-child pairs were eligible for this analysis. A significant decrease in fine-motor functions was observed among females, but not among males, following exposure to high levels of weighted quartile sum of seven phthalate metabolites (Covariates-adjusted coefficient estimate B = -2.7, 95% Confidence Interval [CI] -4.64 to -0.75, p = 0.01 for females [n = 116] and B = -1.63, 95%CI -3.94 to 0.69, p = 0.16 for males [n = 93]). The most highly weighted phthalate metabolites, associated with fine-motor functions among females, were MBP, MBZP, and MIBP, all non-DEHP phthalates. No significant associations were found between the weighted quartile sum of seven phthalate metabolites and gross-motor functions at the age of 11 years for males (B = -0.81, 95%CI -1.17 to 1.96, p = 0.23). With the molar sum of four non-DEHP phthalates as main predictor of linear regression models, we found significant decrease in gross and fine motor functions among females prenatally exposed to non-DEHP phthalates B = -0.98, 95%CI -1.98 to 0.03, p = 0.05 and B = -0.85, 95%CI -1.49 to -0.20, p = 0.01, respectively).ConclusionsPhthalate exposure during pregnancy was associated with decreased motor functions among 11-year-old girls.

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Characterization of Weighted Quantile Sum Regression for Highly Correlated Data in a Risk Analysis Setting.

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Characterization of Weighted Quantile Sum Regression for Highly Correlated Data in a Risk Analysis Setting.

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