Distributed Lag Interaction Models with Two Pollutants

Dynamic Single-Index Scalar-On-Function Model

Environmental exposures often exhibit temporal variability, prompting extensive research to understand their dynamic impacts on human health. There has been a growing interest in studying time-dependent exposure mixtures beyond a single exposure. However, current analytic methods typically assess each exposure individually or assume an additive relationship. This paper aims to fill the gap in method development for evaluating the joint effects of multiple time-dependent exposures on a scalar outcome. We introduce a dynamic single-index scalar-on-function model to characterize the exposure mixture's time-varying effect through a non-parametric bivariate exposure-time-outcome surface function. Utilizing B-spline tensor product bases to approximate the surface function, we propose a profiling algorithm for model estimation and establish large-sample properties for the resulting single-index estimators. In addition, we introduce a non-parametric hypothesis testing procedure to determine whether the surface function varies over time at each fixed mixture level and a model averaging solution to circumvent the issue of knot selection for spline approximations. The performance of our proposed methods is examined through extensive simulations and further illustrated using real-world applications.

LOW-RANK LONGITUDINAL FACTOR REGRESSION WITH APPLICATION TO CHEMICAL MIXTURES

Developmental epidemiology commonly focuses on assessing the association between multiple early life exposures and childhood health. Statistical analyses of data from such studies focus on inferring the contributions of individual exposures, while also characterizing time-varying and interacting effects. Such inferences are made more challenging by correlations among exposures, nonlinearity, and the curse of dimensionality. Motivated by studying the effects of prenatal bisphenol A (BPA) and phthalate exposures on glucose metabolism in adolescence using data from the ELEMENT study, we propose a low-rank longitudinal factor regression (LowFR) model for tractable inference on flexible longitudinal exposure effects. LowFR handles highly-correlated exposures using a Bayesian dynamic factor model, which is fit jointly with a health outcome via a novel factor regression approach. The model collapses on simpler and intuitive submodels when appropriate, while expanding to allow considerable flexibility in time-varying and interaction effects when supported by the data. After demonstrating LowFR's effectiveness in simulations, we use it to analyze the ELEMENT data and find that diethyl and dibutyl phthalate metabolite levels in trimesters 1 and 2 are associated with altered glucose metabolism in adolescence.

The impact of air pollutants on emergency ambulance dispatches due to mental and behavioral disorders in Shenzhen, China

BACKGROUND

The relationships between air pollutants and mental and behavioral disorders (MBDs) remain unclear. We aimed to identify the primary pollutants affecting mental health and evaluate the short-term effects on emergency ambulance dispatches (EADs) due to MBDs.

METHODS

Time-stratified case-crossover study and conditional logistic regression model were adopted to explore the impact of air pollutants on EADs due to MBDs from 2013 to 2020 in Shenzhen, China. In order to clarify the influence of gender and age on association, subgroup analysis was carried out. We also applied binary response surface model and distributed lag interaction model to examine the interaction effects between pollutants and meteorological factors on EADs due to MBDs.

RESULTS

Nitrogen dioxide (NO2) was the primary pollutant in Shenzhen that affects the EADs due to mental and behavioral disorders, exhibiting significant immediate exposure effects and cumulative lag effects. As NO2 concentration increased, the risk of EADs due to mental and behavioral disorders showed a linear upward trend without a threshold. For each interquartile range (IQR) increase of NO2, the odds ratio (OR) associated with MBDs was highest at lag 2 in the single-day lag pattern (OR = 1.035, 95% CI: 1.012-1.060) and the effect of NO2 reached its maximum at lag 0-6 with OR of 1.078 (95% CI: 1.037-1.122). We did not observe significant associations between PM2.5, PM10, SO2, O3 and CO exposures and EADs due to MBDs. In addition, there was an interaction effect between NO2 and Humidity index (Humidex). Both high and low Humidex would aggravate the influence of pollutants on mental health.

CONCLUSIONS

Short exposure to NO2 was positively associated with acute onset of MBDs in Shenzhen, China. Health departments should take effective measures to raise public awareness of NO2 and Humidex, as well as their interaction effects.

Adverse effects of temperature on perinatal and pregnancy outcomes: methodological challenges and knowledge gaps

Evidence linking temperature with adverse perinatal and pregnancy outcomes is emerging. We searched for literature published until 30 January 2023 in PubMed, Web of Science, and reference lists of articles focusing on the outcomes that were most studied like preterm birth, low birth weight, stillbirth, and hypertensive disorders of pregnancy. A review of the literature reveals important gaps in knowledge and several methodological challenges. One important gap is the lack of knowledge of how core body temperature modulates under extreme ambient temperature exposure during pregnancy. We do not know the magnitude of non-modulation of body temperature during pregnancy that is clinically significant, i.e., when the body starts triggering physiologic counterbalances. Furthermore, few studies are conducted in places where extreme temperature conditions are more frequently encountered, such as in South Asia and sub-Saharan Africa. Little is also known about specific cost-effective interventions that can be implemented in vulnerable communities to reduce adverse outcomes. As the threat of global warming looms large, effective interventions are critically necessary to mitigate its effects.

Semiparametric distributed lag quantile regression for modeling time-dependent exposure mixtures

Studying time-dependent exposure mixtures has gained increasing attentions in environmental health research. When a scalar outcome is of interest, distributed lag (DL) models have been employed to characterize the exposures effects distributed over time on the mean of final outcome. However, there is a methodological gap on investigating time-dependent exposure mixtures with different quantiles of outcome. In this paper, we introduce semiparametric partial-linear single-index (PLSI) DL quantile regression, which can describe the DL effects of time-dependent exposure mixtures on different quantiles of outcome and identify susceptible periods of exposures. We consider two time-dependent exposure settings: discrete and functional, when exposures are measured in a small number of time points and at dense time grids, respectively. Spline techniques are used to approximate the nonparametric DL function and single-index link function, and a profile estimation algorithm is proposed. Through extensive simulations, we demonstrate the performance and value of our proposed models and inference procedures. We further apply the proposed methods to study the effects of maternal exposures to ambient air pollutants of fine particulate and nitrogen dioxide on birth weight in New York University Children's Health and Environment Study (NYU CHES).

Estimating perinatal critical windows of susceptibility to environmental mixtures via structured Bayesian regression tree pairs

Maternal exposure to environmental chemicals during pregnancy can alter birth and children's health outcomes. Research seeks to identify critical windows, time periods when exposures can change future health outcomes, and estimate the exposure-response relationship. Existing statistical approaches focus on estimation of the association between maternal exposure to a single environmental chemical observed at high temporal resolution (e.g., weekly throughout pregnancy) and children's health outcomes. Extending to multiple chemicals observed at high temporal resolution poses a dimensionality problem and statistical methods are lacking. We propose a regression tree-based model for mixtures of exposures observed at high temporal resolution. The proposed approach uses an additive ensemble of tree pairs that defines structured main effects and interactions between time-resolved predictors and performs variable selection to select out of the model predictors not correlated with the outcome. In simulation, we show that the tree-based approach performs better than existing methods for a single exposure and can accurately estimate critical windows in the exposure-response relation for mixtures. We apply our method to estimate the relationship between five exposures measured weekly throughout pregnancy and birth weight in a Denver, Colorado, birth cohort. We identified critical windows during which fine particulate matter, sulfur dioxide, and temperature are negatively associated with birth weight and an interaction between fine particulate matter and temperature. Software is made available in the R package dlmtree.

CRITICAL WINDOW VARIABLE SELECTION FOR MIXTURES: ESTIMATING THE IMPACT OF MULTIPLE AIR POLLUTANTS ON STILLBIRTH

Understanding the role of time-varying pollution mixtures on human health is critical as people are simultaneously exposed to multiple pollutants during their lives. For vulnerable subpopulations who have well-defined exposure periods (e.g., pregnant women), questions regarding critical windows of exposure to these mixtures are important for mitigating harm. We extend critical window variable selection (CWVS) to the multipollutant setting by introducing CWVS for mixtures (CWVSmix), a hierarchical Bayesian method that combines smoothed variable selection and temporally correlated weight parameters to: (i) identify critical windows of exposure to mixtures of time-varying pollutants, (ii) estimate the time-varying relative importance of each individual pollutant and their first order interactions within the mixture, and (iii) quantify the impact of the mixtures on health. Through simulation we show that CWVSmix offers the best balance of performance in each of these categories in comparison to competing methods. Using these approaches, we investigate the impact of exposure to multiple ambient air pollutants on the risk of stillbirth in New Jersey, 2005-2014. We find consistent elevated risk in gestational weeks 2, 16-17, and 20 for non-Hispanic Black mothers, with pollution mixtures dominated by ammonium (weeks 2, 17, 20), nitrate (weeks 2, 17), nitrogen oxides (weeks 2, 16), PM2.5 (week 2), and sulfate (week 20). The method is available in the R package CWVSmix.

KERNEL MACHINE AND DISTRIBUTED LAG MODELS FOR ASSESSING WINDOWS OF SUSCEPTIBILITY TO ENVIRONMENTAL MIXTURES IN CHILDREN'S HEALTH STUDIES

Exposures to environmental chemicals during gestation can alter health status later in life. Most studies of maternal exposure to chemicals during pregnancy have focused on a single chemical exposure observed at high temporal resolution. Recent research has turned to focus on exposure to mixtures of multiple chemicals, generally observed at a single time point. We consider statistical methods for analyzing data on chemical mixtures that are observed at a high temporal resolution. As motivation, we analyze the association between exposure to four ambient air pollutants observed weekly throughout gestation and birth weight in a Boston-area prospective birth cohort. To explore patterns in the data, we first apply methods for analyzing data on (1) a single chemical observed at high temporal resolution, and (2) a mixture measured at a single point in time. We highlight the shortcomings of these approaches for temporally-resolved data on exposure to chemical mixtures. Second, we propose a novel method, a Bayesian kernel machine regression distributed lag model (BKMR-DLM), that simultaneously accounts for nonlinear associations and interactions among time-varying measures of exposure to mixtures. BKMR-DLM uses a functional weight for each exposure that parameterizes the window of susceptibility corresponding to that exposure within a kernel machine framework that captures non-linear and interaction effects of the multivariate exposure on the outcome. In a simulation study, we show that the proposed method can better estimate the exposure-response function and, in high signal settings, can identify critical windows in time during which exposure has an increased association with the outcome. Applying the proposed method to the Boston birth cohort data, we find evidence of a negative association between organic carbon and birth weight and that nitrate modifies the organic carbon, elemental carbon, and sulfate exposure-response functions.

A spatially varying distributed lag model with application to an air pollution and term low birth weight study

Distributed lag models have been used to identify critical pregnancy periods of exposure (i.e. critical exposure windows) to air pollution in studies of pregnancy outcomes. However, much of the previous work in this area has ignored the possibility of spatial variability in the lagged health effect parameters that may result from exposure characteristics and/or residual confounding. We develop a spatially varying Gaussian process model for critical windows called 'SpGPCW' and use it to investigate geographic variability in the association between term low birth weight and average weekly concentrations of ozone and PM_2:5 during pregnancy by using birth records from North Carolina. SpGPCW is designed to accommodate areal level spatial correlation between lagged health effect parameters and temporal smoothness in risk estimation across pregnancy. Through simulation and a real data application, we show that the consequences of ignoring spatial variability in the lagged health effect parameters include less reliable inference for the parameters and diminished ability to identify true critical window sets, and we investigate the use of existing Bayesian model comparison techniques as tools for determining the presence of spatial variability. We find that exposure to PM_2:5 is associated with elevated term low birth weight risk in selected weeks and counties and that ignoring spatial variability results in null associations during these periods. An R package (SpGPCW) has been developed to implement the new method.

Selection of nonlinear interactions by a forward stepwise algorithm: Application to identifying environmental chemical mixtures affecting health outcomes

In this paper, we propose a stepwise forward selection algorithm for detecting the effects of a set of correlated exposures and their interactions on a health outcome of interest when the underlying relationship could potentially be nonlinear. Though the proposed method is very general, our application in this paper remains to be on analysis of multiple pollutants and their interactions. Simultaneous exposure to multiple environmental pollutants could affect human health in a multitude of complex ways. For understanding the health effects of multiple environmental exposures, it is often important to identify and estimate complex interactions among exposures. However, this issue becomes analytically challenging in the presence of potential nonlinearity in the outcome-exposure response surface and a set of correlated exposures. Through simulation studies and analyses of test datasets that were simulated as a part of a data challenge in multipollutant modeling organized by the National Institute of Environmental Health Sciences (http://www.niehs.nih.gov/about/events/pastmtg/2015/statistical/), we illustrate the advantages of our proposed method in comparison with existing alternative approaches. A particular strength of our method is that it demonstrates very low false positives across empirical studies. Our method is also used to analyze a dataset that was released from the Health Outcomes and Measurement of the Environment Study as a benchmark beta-tester dataset as a part of the same workshop.