ArticleFrontiers in public health2023
A weighted quantile sum regression with penalized weights and two indices.
Article in Frontiers in public health, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 39 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
39 citing papers in PubMed, 54 citations in OpenAlex.
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- Air pollution mixtures and cognitive outcomes in children: associations with school-age exposure and sex differences.European journal of pediatrics · 2026Article
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- Associations of prenatal fine particulate matter mixtures with neurodevelopmental outcomes in early childhood: component- and source-specific insights.Particle and fibre toxicology · 2026Article
- Associations of volatile organic compounds with cancer: A cross-sectional analysis of single and mixture exposures.The Journal of international medical research · 2026Article
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- Environmental exposure to perchlorate, nitrate, and thiocyanate in relation to myopia in adolescents: a cross-sectional NHANES study.European journal of medical research · 2026Article
- Association Between Systemic Inflammation Indices and Recurrence Risk in Primary Budd-Chiari Syndrome.Journal of inflammation research · 2026Article
- Evaluating Missing Data Imputation Strategies for Environmental Mixture Models: A Simulation Study and Applied Analysis.Data science in science · 2026Article
- Metals and metal mixtures associated with the odds of uterine fibroid prevalence among African Caribbean women in the Tobago Health Study.Frontiers in reproductive health · 2026Article
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Corrections and comments
- Erratum issued
Authors and funding
3 authors at 2 institutions in 2 countries.
Funding
Abstract
Background: New 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. Objectives: In 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. Methods: To 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. Results: The 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. Discussion: Through 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.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the Socratic graph.