Background: Humans are exposed to mixtures of chemicals across their lifetimes, a concept sometimes called the “exposome.” Mixtures likely have temporal “critical windows” of susceptibility like single agents and measuring them repeatedly might help to define such windows. Common approaches to evaluate the effects of chemical mixtures have focused on their effects at a single time point. Our goal is to expand upon these previous techniques and examine the time-varying critical windows for metal mixtures on subsequent neurobehavior in children. Methods: We propose two methods, joint weighted quantile sum regression (JWQS) and meta-weighted quantile sum regression (MWQS), to estimate the effects of chemical mixtures measured across multiple time points, while providing data on their critical windows of exposure. We compare the performance of both methods using simulations. We also applied both techniques to assess second and third trimester metal mixture effects in predicting performance in the Rapid Visual Processing (RVP) task from the Cambridge Neuropsychological Test Automated Battery (CANTAB) assessed at 6–9 years in children who are part of the PROGRESS (Programming Research in Obesity, GRowth, Environment and Social Stressors) longitudinal cohort study. The metals, arsenic, cadmium (Cd), cesium, chromium, lead (Pb) and antimony (Sb) were selected based on their toxicological profile. Results: In simulations, JWQS and MWQS had over 80% accuracy in classifying exposures as either strongly or weakly contributing to an association. In real data, both JWQS and MWQS consistently found that Pb and Cd exposure jointly predicted longer latency in the RVP and that second trimester exposure better predicted the results than the third trimester. Additionally, both JWQS and MWQS highlighted the strong association Cd and Sb had with lower accuracy in the RVP and that third trimester exposure was a better predictor than second trimester exposure. Conclusions: Our results indicate that metal mixtures effects vary across time, have distinct critical windows and that both JWQS and MWQS can determine longitudinal mixture effects including the cumulative contribution of each exposure and critical windows of effect.

Every day humans are exposed to mixtures of chemicals, such as lead (Pb) and manganese (Mn). An underappreciated aspect of studying the health effects of mixtures is the role that the exposure biomarker media (blood, hair, etc.) may play in estimating the effects of the mixture. Different biomarker media represent different aspects of each chemical's toxicokinetics, thus no single medium can fully capture the toxicokinetic profile for all the chemicals in a mixture. A potential solution to this problem is to combine exposure data across different media to derive integrated estimates of each chemical's internal concentration. This concept, formalized as a multi-media biomarker (MMB) has proven effective for estimating the health impacts of Pb exposure, but may also be useful to estimate mixture effects, such as the joint effects of metals like Pb and Mn, while factoring in how the association changes based upon the biomarker media. Levels of Pb and Mn were quantified in five media: blood, hair, nails, urine, and saliva in the Public Health Impact of Metals Exposure (PHIME) project, a study of Italian adolescents aged 10-14 years. MMBs were derived for both metals using weighted quantile sum (WQS) regression across the five media. Age-adjusted Wechsler Intelligence Scale for Children (WISC) IQ scores, measured at the same time as the exposure measures, were the primary outcome and models were adjusted for sex and socioeconomic status. The levels Pb and Mn were relatively low, with median blood Pb of 1.27 (IQR: 0.84) μg/dL and median blood Mn of 1.09 (IQR: 0.45) μg/dL. Quartile increases in a Pb-Mn combination predicted decreased Full Scale IQ of 1.9 points (95% CI: 0.3, 3.5) when Pb and Mn exposure levels were estimated using MMBs, while individual regressions for each metal were not associated with Full Scale IQ. Additionally, a quartile increase in the WQS index of Pb and Mn, measured using MMBs, were associated with reductions in Verbal IQ by 2.8 points (1.0, 4.5). Weights that determine the contributions of the metals to the joint effect highlighted that the contribution of the Pb-Mn was 72-28% for Full Scale IQ and 42-58% for Verbal IQ. We found that the joint effects of Pb and Mn are strongly affected by the medium used to measure exposure and that the joint effects of the Pb and Mn MMBs on cognition were the stronger than any individual biomarker. Thus, increase power and accuracy for measuring mixture effects compared to individual biomarkers. As the number of chemicals in mixtures increases, appropriate biomarker selection will become increasingly important and MMBs are a natural way to reduce bias in such analyses.

The extraction of information from multiple sets of data is a problem inherent to many disciplines. This is possible by either analyzing the data sets jointly as in data fusion or separately and then combining as in data integration. However, selecting the optimal method to combine and analyze multiset data is an ever-present challenge. The primary reason for this is the difficulty in determining the optimal contribution of each data set to an analysis as well as the amount of potentially exploitable complementary information among data sets. In this paper, we propose a novel classification rate-based technique to unambiguously quantify the contribution of each data set to a fusion result as well as facilitate direct comparisons of fusion methods on real data and apply a new method, independent vector analysis (IVA), to multiset fusion. This classification rate-based technique is used on functional magnetic resonance imaging data collected from 121 patients with schizophrenia and 150 healthy controls during the performance of three tasks. Through this application, we find that though optimal performance is achieved by exploiting all tasks, each task does not contribute equally to the result and this framework enables effective quantification of the value added by each task. Our results also demonstrate that data fusion methods are more powerful than data integration methods, with the former achieving a classification rate of 73.5 % and the latter achieving one of 70.9 %, a difference which we show is significant when all three tasks are analyzed together. Finally, we show that IVA, due to its flexibility, has equivalent or superior performance compared with the popular data fusion method, joint independent component analysis.

The widespread use of data-driven methods, such as independent component analysis (ICA), for the analysis of functional magnetic resonance imaging data (fMRI) has enabled deeper understanding of neural function. However, most popular ICA algorithms for fMRI analysis make several simplifying assumptions, thus ignoring sources of statistical information, types of "diversity," and limiting their performance. We propose the use of complex entropy rate bound minimization (CERBM) for the analysis of actual fMRI data in its native, complex, domain. Though CERBM achieves enhanced performance through the exploitation of the three types of diversity inherent to complex fMRI data: noncircularity, non-Gaussianity, and sample-to-sample dependence, CERBM produces results that are more variable than simpler methods. This motivates the development of a minimum spanning tree (MST)-based stability analysis that mitigates the variability of CERBM. In order to validate our method, we compare the performance of CERBM with the popular CInfomax as well as complex entropy bound minimization (CEBM). We show that by leveraging CERBM and the MST-based stability analysis, we are able to consistently produce components that have a greater number of activated voxels in physically meaningful regions and can more accurately classify patients with schizophrenia than components generated using simpler models. Our results demonstrate the advantages of using ICA algorithms that can exploit all inherent types of diversity for the analysis of fMRI data when coupled with appropriate stability analyses.