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• W4313462465 abstract "Vol. 131, No. 1 Letter to the EditorOpen AccessComment on “A Permutation Test-Based Approach to Strengthening Inference on the Effects of Environmental Mixtures: Comparison between Single-Index Analytic Methods”is accompanied byA Permutation Test-Based Approach to Strengthening Inference on the Effects of Environmental Mixtures: Comparison between Single-Index Analytic Methodsis a letter which has replyResponse to “Comment on ‘A Permutation Test-Based Approach to Strengthening Inference on the Effects of Environmental Mixtures: Comparison between Single-Index Analytic Methods’” Alexander P. Keil, Jessie P. Buckley, Katie M. O’Brien, Kelly K. Ferguson, and Alexandra J. White Alexander P. Keil Address correspondence to Alexander P. Keil, 9609 Medical Center Dr., Rockville, MD 20892 USA. Email: E-mail Address: [email protected] https://orcid.org/0000-0002-0955-6107 Occupational and Environmental Epidemiology Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health (NIH), Department of Health and Human Services (DHHS), Bethesda, Maryland, USA Search for more papers by this author , Jessie P. Buckley Department of Environmental Health and Engineering, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA Search for more papers by this author , Katie M. O’Brien Epidemiology Branch, National Institute of Environmental Health Sciences, NIH, DHHS, Research Triangle Park, North Carolina, USA Search for more papers by this author , Kelly K. Ferguson Epidemiology Branch, National Institute of Environmental Health Sciences, NIH, DHHS, Research Triangle Park, North Carolina, USA Search for more papers by this author , and Alexandra J. White Epidemiology Branch, National Institute of Environmental Health Sciences, NIH, DHHS, Research Triangle Park, North Carolina, USA Search for more papers by this author Published:3 January 2023CID: 018001https://doi.org/10.1289/EHP12404AboutSectionsPDF ToolsDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InReddit Recently, Day et al.1 compared weighted quantile sum regression (WQSr) with quantile-based g-computation (QGC) using simulations and a worked example.2 They wrote that “mixture component-specific coefficients estimated by [QGC] were far more biased than those of any of the WQSr models.”1 Their results do not support this claim because bias was not assessed in isolation.Instead, Day et al. assessed mean absolute percent error (MAPE), a measure of accuracy that combines bias and variability. To assess bias, we repeated one of their simulations (correlated mixture, lowercase beta begin subscript 1 end subscript equals 0.2β1=0.2) and examined mean percent bias (MPB: average bias/truth) of the component-specific coefficients. MPB of their weighted quantile sum regression bootstrap sample permutation test (WQSBSPT) approach was 2.5–8 times higher than that for QGC (Table 1). MPB for the “mixture effect” was 80 times higher for WQSBSPT than QGC. Thus, the results support a countermanding claim: QGC was far less biased than WQSBSPT. We consequently disagree that their results suggest “caution when interpreting [QGC] coefficients.”1Table 1 Comparison of mean percent bias for QGC and WQSBSPT.Mean percent bias (%)(200 samples of lowercase italic n equals 500n=500)EstimandQGCWQSBSPTComponent coefficient, “high” effect size2negative 5−5Component coefficient, “low” effect size648Overall effect size0.18Note: Mean percent bias for two contrasting approaches (QGC without bootstrapping and weighted quantile sum regression using WQSBSPT) to estimate the effects of a mixture using the data simulation methods of Day et al.1 with a “correlated mixture” developed with the empirical covariance matrix reported in the appendix of their paper. QGC, quantile-based g-computation without bootstrapping; WQSBSPT, weighted quantile sum regression bootstrap sample permutation test.Day et al.’s simulations assume unidirectional causal exposures, an ideal setting for maximizing WQSr accuracy. A reanalysis using our previously published simulation2 with 1 causal exposure and 13 noise exposures yielded a 3-fold better component coefficient MAPE for QGC than WQSBS-Split (12% and 36%, respectively). Similar to Day et al.’s simulations, this simulation assumes no counteracting exposures. Thus, accuracy results do not generalize across different plausible scenarios.We also note a fundamental flaw in some simulations. When WQSr methods failed to return a result, Day et al. imputed lowercase beta hat begin subscript 1 end subscript equals 0β̂1=0. When analyzing data simulated with lowercase beta begin subscript 1 end subscript equals 0β1=0, the authors therefore imputed an estimate with perfect accuracy (no bias, no variability), which exaggerated WQSr performance. Because 86% of Weighted quantile sum regression, random subset, repeated holdout (WQSRS-RH) fits failed to return a result when lowercase beta begin subscript 1 end subscript equals 0β1=0, their WQSRS-RH results are not credible. Other WQSr results were also impacted.Finally, we respond to the authors’ coffee/alcohol analogy. The analogy says that the effects of coffee and alcohol would cancel out one another in a QGC regression such that QGC would erroneously report no joint effect of substance use. If the joint effect of coffee and alcohol on a health outcome of interest is truly null, QGC will tell us so2 and also estimate the independent effects of alcohol and coffee. That is no error; it is crucial to understand when therapeutic agents counteract hazardous agents in a mixture. Alternatively, WQSr will yield biased independent effects of alcohol and coffee and no joint effect.3AcknowledgmentsThis research was supported in part by grants from the National Institute of Environmental Health Sciences/National Institutes of Health (R01ES029531 and R01ES030078) (J.P. Buckley) and from the institute’s Intramural Research Program (Z01ES044005).References1. Day DB, Sathyanarayana S, LeWinn KZ, Karr CJ, Mason WA, Szpiro AAA. 2022. A permutation test-based approach to strengthening inference on the effects of environmental mixtures: comparison between single-index analytic methods. Environ Health Perspect 130(8):87010, PMID: 36040702, 10.1289/EHP10570. Link, Google Scholar2. Keil AP, Buckley JP, O’Brien KM, Ferguson KK, Zhao S, White AJ. 2020. A quantile-based g-computation approach to addressing the effects of exposure mixtures. Environ Health Perspect 128(4):47004, PMID: 32255670, 10.1289/EHP5838. Link, Google Scholar3. Keil AP, Buckley JP, O’Brien KM, Ferguson KK, Zhao S, White AJ. 2021. Response to “comment on ‘a quantile-based g-computation approach to addressing the effects of exposure mixtures.’” Environ Health Perspect 129(3):38002, PMID: 33688745, 10.1289/EHP8820. Link, Google ScholarAll authors declare they have no actual or potential competing financial interest.FiguresReferencesRelatedDetailsRelated articlesA Permutation Test-Based Approach to Strengthening Inference on the Effects of Environmental Mixtures: Comparison between Single-Index Analytic Methods30 August 2022Environmental Health PerspectivesResponse to “Comment on ‘A Permutation Test-Based Approach to Strengthening Inference on the Effects of Environmental Mixtures: Comparison between Single-Index Analytic Methods’”3 January 2023Environmental Health Perspectives Vol. 131, No. 1 January 2023Metrics About Article Metrics Publication History Manuscript received8 November 2022Manuscript accepted13 December 2022Originally published3 January 2023 Financial disclosuresPDF download License information EHP is an open-access journal published with support from the National Institute of Environmental Health Sciences, National Institutes of Health. All content is public domain unless otherwise noted. Note to readers with disabilities EHP strives to ensure that all journal content is accessible to all readers. However, some figures and Supplemental Material published in EHP articles may not conform to 508 standards due to the complexity of the information being presented. If you need assistance accessing journal content, please contact [email protected]. Our staff will work with you to assess and meet your accessibility needs within 3 working days." @default.
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