Convergent evidence associates exposure to endocrine disrupting chemicals (EDCs) with major human diseases, even at regulation-compliant concentrations. This might be because humans are exposed to EDC mixtures, whereas chemical regulation is based on a risk assessment of individual compounds. Here, we developed a mixture-centered risk assessment strategy that integrates epidemiological and experimental evidence. We identified that exposure to an EDC mixture in early pregnancy is associated with language delay in offspring. At human-relevant concentrations, this mixture disrupted hormone-regulated and disease-relevant regulatory networks in human brain organoids and in the model organisms Xenopus leavis and Danio rerio , as well as behavioral responses. Reinterrogating epidemiological data, we found that up to 54% of the children had prenatal exposures above experimentally derived levels of concern, reaching, for the upper decile compared with the lowest decile of exposure, a 3.3 times higher risk of language delay.

Weighted Quantile Sum (WQS) regression is a method commonly used in environmental epidemiology to assess the impact of chemical mixtures in relation to a health outcome of interest. Data are partitioned into a single training and test set to reduce sample-specific chemical weights. However, in typical epidemiology sample sizes, this may produce unstable chemical weights and WQS index estimates, and investigators may resort to training and testing on the same data. To solve this problem, we propose repeated holdout validation whereby data are randomly partitioned 100 times, producing a distribution of validated results. Taking the mean as the final estimate, confidence estimates may also be calculated for inference. Further, this method helps characterize the variability in chemical weights, aiding in the identification of chemicals of concern. This is important since it may direct future research into specific chemicals. Using data from 718 mother-child pairs in the Swedish Environmental Longitudinal, Mother and Child, Asthma and Allergy (SELMA) study, we assessed the association between prenatal exposure to 26 endocrine disrupting chemicals and child Intelligence Quotient (IQ). Results using a single partition were unstable, varying by random seed. The WQS index estimate was significant when all data was used (e.g. no partition) (β = -2.2 CI = -3.43, -0.98), but attenuated and nonsignificant using repeated holdout validation (β = -0.82 CI = -2.11, 0.45). When implementing WQS in epidemiologic studies with limited sample sizes, repeated holdout validation is a viable alternative to using a single, or no partitioning. Repeated holdout can both stabilize results and help characterize the uncertainty in identifying chemicals of concern, while maintaining some of the the rigor of holdout validation. •Repeated holdout validation improves the stability of WQS estimates in finite study samples•Uncertainty in identifying toxic chemicals of concern is acknowledged and characterized.

Humans are exposed to a diverse mixture of chemical and non-chemical exposures across their lifetimes. Well-designed epidemiology studies as well as sophisticated exposure science and related technologies enable the investigation of the health impacts of mixtures. While existing statistical methods can address the most basic questions related to the association between environmental mixtures and health endpoints, there were gaps in our ability to learn from mixtures data in several common epidemiologic scenarios, including high correlation among health and exposure measures in space and/or time, the presence of missing observations, the violation of important modeling assumptions, and the presence of computational challenges incurred by current implementations. To address these and other challenges, NIEHS initiated the Powering Research through Innovative methods for Mixtures in Epidemiology (PRIME) program, to support work on the development and expansion of statistical methods for mixtures. Six independent projects supported by PRIME have been highly productive but their methods have not yet been described collectively in a way that would inform application. We review 37 new methods from PRIME projects and summarize the work across previously published research questions, to inform methods selection and increase awareness of these new methods. We highlight important statistical advancements considering data science strategies, exposure-response estimation, timing of exposures, epidemiological methods, the incorporation of toxicity/chemical information, spatiotemporal data, risk assessment, and model performance, efficiency, and interpretation. Importantly, we link to software to encourage application and testing on other datasets. This review can enable more informed analyses of environmental mixtures. We stress training for early career scientists as well as innovation in statistical methodology as an ongoing need. Ultimately, we direct efforts to the common goal of reducing harmful exposures to improve public health.

The developmental timing of exposures to toxic chemicals or combinations of chemicals may be as important as the dosage itself. This concept is called "critical windows of exposure." The time boundaries of such windows can be detected if exposure data are collected repeatedly in short time intervals. The development of tooth-matrix biomarkers which provide prenatal and postnatal exposure measures in repeated intervals can provide such data. Using teeth, we use reverse distributed lagged models (DLMs) to incorporate weekly prenatal and postnatal measures of exposures to estimate time-varying associations with developmental effects. The analysis of such data using lagged weighted quantile sum (WQS) regression as an extension to reverse DLMs for complex mixtures was first proposed by Bello et al. This prior algorithm was not operationally generalizable to large numbers of components (say, more than five or six). We propose a revised algorithm that may be useful for larger mixtures by combining time-specific WQS(t) indices in a reverse DLM. We demonstrate the new algorithm using tooth data in association with a neurodevelopmental score and in simulated data from 3 cases wherein different components of a mixture have time varying associations and in the case where none have associations. The new algorithm correctly detects the simulated associations when the number of samples within the time-specific analyses is moderate to large.

Exposure to mixtures of chemicals is an important and relevant environmental issue. Of particular interest is the detection and characterization of departure of biological effects from additivity. Met

Robust statistical methods are important to the evaluation of toxicological interactions (i.e., departures from additivity) among chemicals in a mixture. However, different concepts of joint toxic action as applied to the statistical analysis of chemical mixture toxicology data or as used in environmental risk assessment often appear to conflict with one another. A unifying approach for application of statistical methodology in chemical mixture toxicology research is based on consideration of change(s) in slope. If the slope of the dose-response curve of one chemical does not change in the presence of other chemicals, then there is no interaction between the first chemical and the others. Conversely, if the rate of change in the response with respect to dose of the first chemical changes in the presence of the other chemicals, then an interaction is said to exist. This concept of zero interaction is equivalent to the usual approach taken in additivity models in the statistical literature. In these additivity models, the rate of change in the response as a function of the i^th chemical does not change in the presence of other chemicals in a mixture. It is important to note that Berenbaum's (1985, J. Theor. Biol. 114, 413–431) general and fundamental definition of additivity does not require the chemicals in the mixture to have a common toxic mode of action nor to have similarly shaped dose response curves. We show an algebraic equivalence between these statistical additivity models and the definition of additivity given by Berenbaum.