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).     

A two-stage model for multiple time series data of counts

We propose a two-stage model for time series data of counts from multiple locations. This method fits first-stage model(s) using the technique of iteratively weighted filtered least squares (IWFLS) to obtain location-specific intercepts and slopes, with possible lagged effects via polynomial distributed lag modeling. These slopes and/or intercepts are then taken to a second-stage mixed-effects meta-regression model in order to stabilize results from various locations. The representation of the models from the stages into a combined mixed-effects model, issues of inference and choices of the parameters in modeling the lag structure are discussed. We illustrate this proposed model via detailed analysis on the effect of air pollution on school absenteeism based on data from the Southern California Children's Health Study.     

Time-varying coefficient models for the analysis of air pollution and health outcome data

In this article a time-varying coefficient model is developed to examine the relationship between adverse health and short-term (acute) exposure to air pollution. This model allows the relative risk to evolve over time, which may be due to an interaction with temperature, or from a change in the composition of pollutants, such as particulate matter, over time. The model produces a smooth estimate of these time-varying effects, which are not constrained to follow a fixed parametric form set by the investigator. Instead, the shape is estimated from the data using penalized natural cubic splines. Poisson regression models, using both quasi-likelihood and Bayesian techniques, are developed, with estimation performed using an iteratively re-weighted least squares procedure and Markov chain Monte Carlo simulation, respectively. The efficacy of the methods to estimate different types of time-varying effects are assessed via a simulation study, and the models are then applied to data from four cities that were part of the National Morbidity, Mortality, and Air Pollution Study.     

A Random Intercepts–Functional Slopes Model for Flexible Assessment of Susceptibility in Longitudinal Designs

Summary In many biomedical investigations, a primary goal is the identification of subjects who are susceptible to a given exposure or treatment of interest. We focus on methods for addressing this question in longitudinal studies when interest focuses on relating susceptibility to a subject's baseline or mean outcome level. In this context, we propose a random intercepts–functional slopes model that relaxes the assumption of linear association between random coefficients in existing mixed models and yields an estimate of the functional form of this relationship. We propose a penalized spline formulation for the nonparametric function that represents this relationship, and implement a fully Bayesian approach to model fitting. We investigate the frequentist performance of our method via simulation, and apply the model to data on the effects of particulate matter on coronary blood flow from an animal toxicology study. The general principles introduced here apply more broadly to settings in which interest focuses on the relationship between baseline and change over time.     

Bayesian Inference in Semiparametric Mixed Models for Longitudinal Data

Summary .  We consider Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. SPMMs are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariate effects, and parametric or nonparametric random effects to account for the within-subject correlation. We model the nonparametric function using a Bayesian formulation of a cubic smoothing spline, and the random effect distribution using a normal distribution and alternatively a nonparametric Dirichlet process (DP) prior. When the random effect distribution is assumed to be normal, we propose a uniform shrinkage prior (USP) for the variance components and the smoothing parameter. When the random effect distribution is modeled nonparametrically, we use a DP prior with a normal base measure and propose a USP for the hyperparameters of the DP base measure. We argue that the commonly assumed DP prior implies a nonzero mean of the random effect distribution, even when a base measure with mean zero is specified. This implies weak identifiability for the fixed effects, and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function. We propose an adjustment using a postprocessing technique. We show that under mild conditions the posterior is proper under the proposed USP, a flat prior for the fixed effect parameters, and an improper prior for the residual variance. We illustrate the proposed approach using a longitudinal hormone dataset, and carry out extensive simulation studies to compare its finite sample performance with existing methods.     

Modeling temperature effects on mortality: multiple segmented relationships with common break points

We present a model for estimation of temperature effects on mortality that is able to capture jointly the typical features of every temperature-death relationship, that is, nonlinearity and delayed effect of cold and heat over a few days. Using a segmented approximation along with a doubly penalized spline-based distributed lag parameterization, estimates and relevant standard errors of the cold- and heat-related risks and the heat tolerance are provided. The model is applied to data from Milano, Italy.     

Air pollution and the lung: epidemiological approach

Epidemiological evidence has concurred with clinical and experimental evidence to correlate current levels of ambient air pollution, both indoors and outdoors, with respiratory effects. In this respect, the use of specific epidemiological methods has been crucial. Common outdoor pollutants are particulate matter, nitrogen dioxide, carbon monoxide, volatile organic compounds and ozone. Short-term effects of outdoor air pollution include changes in lung function, respiratory symptoms and mortality due to respiratory causes. Increase in the use of health care resources has also been associated with short-term effects of air pollution. Long-term effects of cumulated exposure to urban air pollution include lung growth impairment, chronic obstructive pulmonary disease (COPD), lung cancer, and probably the development of asthma and allergies. Lung cancer and COPD have been related to a shorter life expectancy. Common indoor pollutants are environmental tobacco smoke, particulate matter, nitrogen dioxide, carbon monoxide, volatile organic compounds and biological allergens. Concentrations of these pollutants can be many times higher indoors than outdoors. Indoor air pollution may increase the risk of irritation phenomena, allergic sensitisation, acute and chronic respiratory disorders and lung function impairment. Recent conservative estimates have shown that 1.5-2 million deaths per year worldwide could be attributed to indoor air pollution. Further epidemiological research is necessary to better evaluate the respiratory health effects of air pollution and to implement protective programmes for public health.     

A transformation approach for incorporating monotone or unimodal constraints

Samples of curves are collected in many applications, including studies of reproductive hormone levels in the menstrual cycle. Many approaches have been proposed for correlated functional data of this type, including smoothing spline methods and other flexible parametric modeling strategies. In many cases, the underlying biological processes involved restrict the curve to follow a particular shape. For example, progesterone levels in healthy women increase during the menstrual cycle to a peak achieved at random location with decreases thereafter. Reproductive epidemiologists are interested in studying the distribution of the peak and the trajectory for women in different groups. Motivated by this application, we propose a simple approach for restricting each woman's mean trajectory to follow an umbrella shape. An unconstrained hierarchical Bayesian model is used to characterize the data, and draws from the posterior distribution obtained using a Gibbs sampler are then mapped to the constrained space. Inferences are based on the resulting quasi-posterior distribution for the peak and individual woman trajectories. The methods are applied to a study comparing progesterone trajectories for conception and nonconception cycles.     

Using semiparametric‐mixed model and functional linear model to detect vulnerable prenatal window to carcinogenic polycyclic aromatic hydrocarbons on fetal growth

Prenatal exposure to carcinogenic polycyclic aromatic hydrocarbons (c‐PAHs) through maternal inhalation induces higher risk for a wide range of fetotoxic effects. However, the most health‐relevant dose function from chronic gestational exposure remains unclear. Whether there is a gestational window during which the human embryo/fetus is particularly vulnerable to PAHs has not been examined thoroughly. We consider a longitudinal semiparametric‐mixed effect model to characterize the individual prenatal PAH exposure trajectory, where a nonparametric cyclic smooth function plus a linear function are used to model the time effect and random effects are used to account for the within‐subject correlation. We propose a penalized least squares approach to estimate the parametric regression coefficients and the nonparametric function of time. The smoothing parameter and variance components are selected using the generalized cross‐validation (GCV) criteria. The estimated subject‐specific trajectory of prenatal exposure is linked to the birth outcomes through a set of functional linear models, where the coefficient of log PAH exposure is a fully nonparametric function of gestational age. This allows the effect of PAH exposure on each birth outcome to vary at different gestational ages, and the window associated with significant adverse effect is identified as a vulnerable prenatal window to PAHs on fetal growth. We minimize the penalized sum of squared errors using a spline‐based expansion of the nonparametric coefficient function to draw statistical inferences, and the smoothing parameter is chosen through GCV.     

On the equivalence of case-crossover and time series methods in environmental epidemiology

The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.     

An informative Bayesian structural equation model to assess source-specific health effects of air pollution

A primary objective of current air pollution research is the assessment of health effects related to specific sources of air particles or particulate matter (PM). Quantifying source-specific risk is a challenge because most PM health studies do not directly observe the contributions of the pollution sources themselves. Instead, given knowledge of the chemical characteristics of known sources, investigators infer pollution source contributions via a source apportionment or multivariate receptor analysis applied to a large number of observed elemental concentrations. Although source apportionment methods are well established for exposure assessment, little work has been done to evaluate the appropriateness of characterizing unobservable sources thus in health effects analyses. In this article, we propose a structural equation framework to assess source-specific health effects using speciated elemental data. This approach corresponds to fitting a receptor model and the health outcome model jointly, such that inferences on the health effects account for the fact that uncertainty is associated with the source contributions. Since the structural equation model (SEM) typically involves a large number of parameters, for small-sample settings, we propose a fully Bayesian estimation approach that leverages historical exposure data from previous related exposure studies. We compare via simulation the performance of our approach in estimating source-specific health effects to that of 2 existing approaches, a tracer approach and a 2-stage approach. Simulation results suggest that the proposed informative Bayesian SEM is effective in eliminating the bias incurred by the 2 existing approaches, even when the number of exposures is limited. We employ the proposed methods in the analysis of a concentrator study investigating the association between ST-segment, a cardiovascular outcome, and major sources of Boston PM and discuss the implications of our findings with respect to the design of future PM concentrator studies.     

Bayesian regularization for flexible baseline hazard functions in Cox survival models

Fully Bayesian methods for Cox models specify a model for the baseline hazard function. Parametric approaches generally provide monotone estimations. Semi‐parametric choices allow for more flexible patterns but they can suffer from overfitting and instability. Regularization methods through prior distributions with correlated structures usually give reasonable answers to these types of situations. We discuss Bayesian regularization for Cox survival models defined via flexible baseline hazards specified by a mixture of piecewise constant functions and by a cubic B‐spline function. For those “semi‐parametric” proposals, different prior scenarios ranging from prior independence to particular correlated structures are discussed in a real study with microvirulence data and in an extensive simulation scenario that includes different data sample and time axis partition sizes in order to capture risk variations. The posterior distribution of the parameters was approximated using Markov chain Monte Carlo methods. Model selection was performed in accordance with the deviance information criteria and the log pseudo‐marginal likelihood. The results obtained reveal that, in general, Cox models present great robustness in covariate effects and survival estimates independent of the baseline hazard specification. In relation to the “semi‐parametric” baseline hazard specification, the B‐splines hazard function is less dependent on the regularization process than the piecewise specification because it demands a smaller time axis partition to estimate a similar behavior of the risk.     

A measurement error model for time-series studies of air pollution and mortality

One barrier to interpreting the observational evidence concerning the adverse health effects of air pollution for public policy purposes is the measurement error inherent in estimates of exposure based on ambient pollutant monitors. Exposure assessment studies have shown that data from monitors at central sites may not adequately represent personal exposure. Thus, the exposure error resulting from using centrally measured data as a surrogate for personal exposure can potentially lead to a bias in estimates of the health effects of air pollution. This paper develops a multi-stage Poisson regression model for evaluating the effects of exposure measurement error on estimates of effects of particulate air pollution on mortality in time-series studies. To implement the model, we have used five validation data sets on personal exposure to PM10. Our goal is to combine data on the associations between ambient concentrations of particulate matter and mortality for a specific location, with the validation data on the association between ambient and personal concentrations of particulate matter at the locations where data have been collected. We use these data in a model to estimate the relative risk of mortality associated with estimated personal-exposure concentrations and make a comparison with the risk of mortality estimated with measurements of ambient concentration alone. We apply this method to data comprising daily mortality counts, ambient concentrations of PM10measured at a central site, and temperature for Baltimore, Maryland from 1987 to 1994. We have selected our home city of Baltimore to illustrate the method; the measurement error correction model is general and can be applied to other appropriate locations.Our approach uses a combination of: (1) a generalized additive model with log link and Poisson error for the mortality-personal-exposure association; (2) a multi-stage linear model to estimate the variability across the five validation data sets in the personal-ambient-exposure association; (3) data augmentation methods to address the uncertainty resulting from the missing personal exposure time series in Baltimore. In the Poisson regression model, we account for smooth seasonal and annual trends in mortality using smoothing splines. Taking into account the heterogeneity across locations in the personal-ambient-exposure relationship, we quantify the degree to which the exposure measurement error biases the results toward the null hypothesis of no effect, and estimate the loss of precision in the estimated health effects due to indirectly estimating personal exposures from ambient measurements.     

Photosynthetic Development of Anaerobically Grown Rice (Oryza sativa) after Exposure to Air

During anaerobic germination, rice produces a coleoptile devoid of carotenoid and chlorophyll. Further development and greening of the shoot occur upon exposure of the seedlings to air. In this study, a comparison was made between anaerobically (N₂) germinated rice, greened upon exposure to air, and air/dark (A/D) germinated seedlings, greened upon exposure to light. After exposure to air, N₂-grown seedlings had a 76-hour lag before net oxygen evolution occurred compared to a 6-hour lag for A/D-grown seedlings. After 98 h of greening, N₂-grown seedlings reached a rate of oxygen evolution equivalent to that of A/D-grown seedlings after 24 hours. Chlorophyll and carotenoid content showed a similar lag, but did not reach the level found in A/D-grown seedlings even after 124 hours of exposure to air. RuBPcase activity also lagged in N₂-grown seedlings, ultimately reaching greater values than in the `greened' A/D-grown seedlings. Phosphoenolpyruvate carboxylase activity was constant and low in all treatments except for a transient increase after 24 hours of greening of the N₂-grown seedlings.     

Generalized additive distributed lag models: quantifying mortality displacement

There are a number of applied settings where a response is measured repeatedly over time, and the impact of a stimulus at one time is distributed over several subsequent response measures. In the motivating application the stimulus is an air pollutant such as airborne particulate matter and the response is mortality. However, several other variables (e.g. daily temperature) impact the response in a possibly non-linear fashion. To quantify the effect of the stimulus in the presence of covariate data we combine two established regression techniques: generalized additive models and distributed lag models. Generalized additive models extend multiple linear regression by allowing for continuous covariates to be modeled as smooth, but otherwise unspecified, functions. Distributed lag models aim to relate the outcome variable to lagged values of a time-dependent predictor in a parsimonious fashion. The resultant, which we call generalized additive distributed lag models, are seen to effectively quantify the so-called 'mortality displacement effect' in environmental epidemiology, as illustrated through air pollution/mortality data from Milan, Italy.     

Perspectives in chronobiology of air pollution

In a series of experiments, male and female Sprague Dawley rats, kept in light (L) from 06(00) to 18(00) alternating with darkness (LD 12:12) inhaled different concentrations of carbon monoxide (50-1,700 ppm) at each of two test times, 12 h apart. A decrease in flow of CO2 (VCO2) resulting from CO inhalation was greater in the active dark (D) than resting light (L) span. Experimental hypoxic mortality of male and female mice also shows circadian variations, being greater in the D than in the L span. Moreover, a difference of mortality was observed betwen hypoxic exposures performed at 12(00) (in LD or DL) and hypoxic exposures performed at 00(00) (in LD or DL). Such results await tests of any extent to which they model responses of human beings to air pollution. In human beings any external environmental circadian, circaseptan and circannual variations in air pollution as such may serve to variable extent as socioeconomic synchronizers of innate rhythms with a corresponding frequency, rather than as solely generators of time patterns in any physiopathologic response to air pollution.     

Ambient particulate matter exposure and cardiovascular diseases: a focus on progenitor and stem cells

Air pollution is a major challenge to public health. Ambient fine particulate matter (PM) is the key component for air pollution, and associated with significant mortality. The majority of the mortality following PM exposure is related to cardiovascular diseases. However, the mechanisms for the adverse effects of PM exposure on cardiovascular system remain largely unknown and under active investigation. Endothelial dysfunction or injury is considered one of the major factors that contribute to the development of cardiovascular diseases such as atherosclerosis and coronary heart disease. Endothelial progenitor cells (EPCs) play a critical role in maintaining the structural and functional integrity of vasculature. Particulate matter exposure significantly suppressed the number and function of EPCs in animals and humans. However, the mechanisms for the detrimental effects of PM on EPCs remain to be fully defined. One of the important mechanisms might be related to increased level of reactive oxygen species (ROS) and inflammation. Bone marrow (BM) is a major source of EPCs. Thus, the number and function of EPCs could be intimately associated with the population and functional status of stem cells (SCs) in the BM. Bone marrow stem cells and other SCs have the potential for cardiovascular regeneration and repair. The present review is focused on summarizing the detrimental effects of PM exposure on EPCs and SCs, and potential mechanisms including ROS formation as well as clinical implications.     

Air pollution combustion emissions: characterization of causative agents and mechanisms associated with cancer, reproductive, and cardiovascular effects

Combustion emissions account for over half of the fine particle (PM(2.5)) air pollution and most of the primary particulate organic matter. Human exposure to combustion emissions including the associated airborne fine particles and mutagenic and carcinogenic constituents (e.g., polycyclic aromatic compounds (PAC), nitro-PAC) have been studied in populations in Europe, America, Asia, and increasingly in third-world counties. Bioassay-directed fractionation studies of particulate organic air pollution have identified mutagenic and carcinogenic polycyclic aromatic hydrocarbons (PAH), nitrated PAH, nitro-lactones, and lower molecular weight compounds from cooking. A number of these components are significant sources of human exposure to mutagenic and carcinogenic chemicals that may also cause oxidative and DNA damage that can lead to reproductive and cardiovascular effects. Chemical and physical tracers have been used to apportion outdoor and indoor and personal exposures to airborne particles between various combustion emissions and other sources. These sources include vehicles (e.g., diesel and gasoline vehicles), heating and power sources (e.g., including coal, oil, and biomass), indoor sources (e.g., cooking, heating, and tobacco smoke), as well as secondary organic aerosols and pollutants derived from long-range transport. Biomarkers of exposure, dose and susceptibility have been measured in populations exposed to air pollution combustion emissions. Biomarkers have included metabolic genotype, DNA adducts, PAH metabolites, and urinary mutagenic activity. A number of studies have shown a significant correlation of exposure to PM(2.5) with these biomarkers. In addition, stratification by genotype increased this correlation. New multivariate receptor models, recently used to determine the sources of ambient particles, are now being explored in the analysis of human exposure and biomarker data. Human studies of both short- and long-term exposures to combustion emissions and ambient fine particulate air pollution have been associated with measures of genetic damage. Long-term epidemiologic studies have reported an increased risk of all causes of mortality, cardiopulmonary mortality, and lung cancer mortality associated with increasing exposures to air pollution. Adverse reproductive effects (e.g., risk for low birth weight) have also recently been reported in Eastern Europe and North America. Although there is substantial evidence that PAH or substituted PAH may be causative agents in cancer and reproductive effects, an increasing number of studies investigating cardiopulmonary and cardiovascular effects are investigating these and other potential causative agents from air pollution combustion sources.     

The lag-effect pattern in the relationship of particulate air pollution to daily mortality in Seoul,Korea

To assess differences in the lag-effect pattern in the relationship between particulate matter less than 10 microm in aerodynamic diameter (PM(10)) and cause-specific mortality in Seoul, Korea, from January 1995 to December 1999, we performed a time-series analysis. We used a generalized additive Poisson regression model to control for time trends, temperature, humidity, air pressure, and the day of the week. The PM(10) effect was estimated on the basis of the time-series models using the 24-h means and the quadratic distributed-lag models using a cumulative 6-day effect. One interquartile range increase in the 6-day cumulative mean of PM(10) (43.12 microg/m(3)) was associated with an increase in non-accidental deaths [3.7%, 95% confidence interval (CI): 2.1, 5.4], respiratory disease (13.9%, 95% CI: 6.8, 21.5), cardiovascular disease (4.4%, 95% CI: -1.0, 9.0), and cerebrovascular disease (6.3%, 95% CI: 2.3, 10.5). We found the following patterns in the disease-specific lag-effect window: respiratory mortality was more affected by air pollution level on the day of death, whereas cardiovascular deaths were more affected by the previous day's air pollution level. Cerebrovascular deaths were simultaneously associated with the air pollution levels of the same day and the previous day. The patterns in the lag effect from the distributed-lag models were similar to those of a series of time-series models with 24-h means. These results contribute to our understanding of how exposure to air pollution causes adverse health effects.     

Deforestation and infant mortality: Evidence from Indonesia

Factors expected to change concurrently with forest loss—such as economic activity and air pollution—shape human health in different ways, making it difficult to ex ante predict the net impact of deforestation. This paper investigates the infant mortality effects of prenatal exposure to high biomass forest loss in Indonesia, a country with rich forest reserves increasingly being subjected to high levels of deforestation. Indonesia officially bans clearing in areas with high biomass natural forests (referred to henceforth as ‘protected forests’), yet these forests face illegal logging. The analysis uses a fixed effects approach, essentially tracking how mortality responds to protected forest cover changes over time within districts. Results suggest that protected forest loss favors survival among all infants. However, there is variation in the protected forest loss-infant mortality relationship by pregnancy order or gravidity—while children born from women’s higher order pregnancies are less likely to die when exposed to deforestation, children born from first pregnancies experience an increase in their risk of death. Potential mechanisms such as overall air pollution, economic activity and perinatal health care do not appear to explain the gravidity-specific effects of deforestation in protected areas. However, the observed pattern of results suggests that effects are being channeled through malaria—the disease, which is likely to increase with forest loss, tends to disproportionately infect women during their first pregnancy, thus causing greater harm to the children born from these pregnancies.