Cookstove replacement trials have found mixed results on their impact on respiratory health. The limited range of concentrations and small sample sizes of individual studies are important factors that may be limiting their statistical power. We present a hierarchical approach to modeling exposure concentrations and pooling data from multiple studies in order to estimate a common exposure-response curve. The exposure concentration model accommodates temporally sparse, clustered longitudinal observations. The exposure-response curve model provides a flexible, semi-parametric estimate of the exposure-response relationship while accommodating heterogeneous clustered data. We apply this model to data from three studies of cookstoves and respiratory infections in children in Nepal, which represent three study types: crossover trial, parallel trial, and case-control study. We find evidence of increased odds of disease for particulate matter concentrations between 50 and 200 $μ$g/m$^3$ and a flattening of the exposure-response curve for higher exposure concentrations. The model we present can incorporate additional studies and be applied to other settings.
Numerous studies have examined the associations between long-term exposure to fine particulate matter (PM2.5) and adverse health outcomes. Recently, many of these studies have begun to employ high-resolution predicted PM2.5 concentrations, which are subject to measurement error. Previous approaches for exposure measurement error correction have either been applied in non-causal settings or have only considered a categorical exposure. Moreover, most procedures have failed to account for uncertainty induced by error correction when fitting an exposure-response function (ERF). To remedy these def…
Motivated by environmental policy questions, we address the challenges of estimation, change point detection, and uncertainty quantification of a causal exposure-response function (CERF). Under a potential outcome framework, the CERF describes the relationship between a continuously varying exposure (or treatment) and its causal effect on an outcome. We propose a new Bayesian approach that relies on a Gaussian process (GP) model to estimate the CERF nonparametrically. To achieve the desired separation of design and analysis phases, we parametrize the covariance (kernel) function of the GP to m…
In this paper we study the impact of exposure misclassification when cluster size is potentially informative (i.e., related to outcomes) and when misclassification is differential by cluster size. First, we show that misclassification in an exposure related to cluster size can induce informativeness when cluster size would otherwise be non-informative. Second, we show that misclassification that is differential by informative cluster size can not only attenuate estimates of exposure effects but even inflate or reverse the sign of estimates. To correct for bias in estimating marginal parameters…
This paper presents an approach to estimating the health effects of an environmental hazard. The approach is general in nature, but is applied here to the case of air pollution. It uses a computer model involving ambient pollution and temperature inputs, to simulate the exposures experienced by individuals in an urban area, whilst incorporating the mechanisms that determine exposures. The output from the model comprises a set of daily exposures for a sample of individuals from the population of interest. These daily exposures are approximated by parametric distributions, so that the predictive…
In estimating the causal effect of a continuous exposure or treatment, it is important to control for all confounding factors. However, most existing methods require parametric specification for how control variables influence the outcome or generalized propensity score, and inference on treatment effects is usually sensitive to this choice. Additionally, it is often the goal to estimate how the treatment effect varies across observed units. To address this gap, we propose a semiparametric model using Bayesian tree ensembles for estimating the causal effect of a continuous treatment of exposur…
Environmental epidemiologic studies routinely utilize aggregate health outcomes to estimate effects of short-term (e.g., daily) exposures that are available at increasingly fine spatial resolutions. However, areal averages are typically used to derive population-level exposure, which cannot capture the spatial variation and individual heterogeneity in exposures that may occur within the spatial and temporal unit of interest (e.g., within day or ZIP code). We propose a general modeling approach to incorporate within-unit exposure heterogeneity in health analyses via exposure quantile functions.…
The analysis of data arising from environmental health studies which collect a large number of measures of exposure can benefit from using latent variable models to summarize exposure information. However, difficulties with estimation of model parameters may arise since existing fitting procedures for linear latent variable models require correctly specified residual variance structures for unbiased estimation of regression parameters quantifying the association between (latent) exposure and health outcomes. We propose an estimating equations approach for latent exposure models with longitudin…
Addressing complex structures of measurement error arising in the exposure assessment in occupational epidemiology using a Bayesian hierarchical approach
In observational studies for the interaction between exposures on dichotomous outcome of a population, one usually uses one parameter of a regression model to describe the interaction, leading to one measure of the interaction. In this article, we use the conditional risk of outcome given exposures and covariates to describe the interaction and obtain five different measures for the interaction in observational studies, i.e. difference between the marginal risk differences, ratio of the marginal risk ratios, ratio of the marginal odds ratios, ratio of the conditional risk ratios, and ratio of …
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 sub-populations 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 parame…
Environmental health studies are increasingly measuring multiple pollutants to characterize the joint health effects attributable to exposure mixtures. However, the underlying dose-response relationship between toxicants and health outcomes of interest may be highly nonlinear, with possible nonlinear interaction effects. Existing penalized regression methods that account for exposure interactions either cannot accommodate nonlinear interactions while maintaining strong heredity or are computationally unstable in applications with limited sample size. In this paper, we propose a general shrinka…
Statistical methods for identifying harmful chemicals in a correlated mixture often assume linearity in exposure-response relationships. Non-monotonic relationships are increasingly recognised (e.g., for endocrine-disrupting chemicals); however, the impact of non-monotonicity on exposure selection has not been evaluated. In a simulation study, we assessed the performance of Bayesian kernel machine regression (BKMR), Bayesian additive regression trees (BART), Bayesian structured additive regression with spike-slab priors (BSTARSS), and lasso penalised regression. We used data on exposure to 12 …
Distributed lag models are useful in environmental epidemiology as they allow the user to investigate critical windows of exposure, defined as the time period during which exposure to a pollutant adversely affects health outcomes. Recent studies have focused on estimating the health effects of a large number of environmental exposures, or an environmental mixture, on health outcomes. In such settings, it is important to understand which environmental exposures affect a particular outcome, while acknowledging the possibility that different exposures have different critical windows. Further, in …
In epidemiology, identifying the effect of exposure variables in relation to a time-to-event outcome is a classical research area of practical importance. Incorporating propensity score in the Cox regression model, as a measure to control for confounding, has certain advantages when outcome is rare. However, in situations involving exposure measured with moderate to substantial error, identifying the exposure effect using propensity score in Cox models remains a challenging yet unresolved problem. In this paper, we propose an estimating equation method to correct for the exposure misclassifica…
We propose a hierarchical Bayesian model to estimate the proportional contribution of source populations to a newly founded colony. Samples are derived from the first generation offspring in the colony, but mating may occur preferentially among migrants from the same source population. Genotypes of the newly founded colony and source populations are used to estimate the mixture proportions, and the mixture proportions are related to environmental and demographic factors that might affect the colonizing process. We estimate an assortative mating coefficient, mixture proportions, and regression …
As the global HIV pandemic enters its fourth decade, increasing numbers of surveillance sites have been established which allows countries to look into the epidemics at a finer scale, e.g. at sub-national level. However, the epidemic models have been applied independently to the sub-national areas within countries. An important technical barrier is that the availability and quality of the data vary widely from area to area, and many areas lack data for deriving stable and reliable results. To improve the accuracy of the results in areas with little data, we propose a hierarchical model that ut…
Air pollution is a major risk factor for global health, with both ambient and household air pollution contributing substantial components of the overall global disease burden. One of the key drivers of adverse health effects is fine particulate matter ambient pollution (PM$_{2.5}$) to which an estimated 3 million deaths can be attributed annually. The primary source of information for estimating exposures has been measurements from ground monitoring networks but, although coverage is increasing, there remain regions in which monitoring is limited. Ground monitoring data therefore needs to be s…
In 2017 an estimated 3 billion people used polluting fuels and technologies as their primary cooking solution, with 3.8 million deaths annually attributed to household exposure to the resulting fine particulate matter air pollution. Currently, health burdens are calculated using aggregations of fuel types, e.g. solid fuels, as country-level estimates of the use of specific fuel types, e.g. wood and charcoal, are unavailable. To expand the knowledge base about impacts of household air pollution on health, we develop and implement a Bayesian hierarchical model, based on Generalized Dirichlet Mul…
Civil registration vital statistics (CRVS) data are used to produce national estimates of maternal mortality, but are often subject to substantial reporting errors due to misclassification of maternal deaths. The accuracy of CRVS systems can be assessed by comparing CRVS-based counts of maternal and non-maternal deaths to those obtained from specialized studies, which are rigorous assessments of maternal mortality for a given country-period. We developed a Bayesian bivariate random walk model to estimate sensitivity and specificity of the reporting on maternal mortality in CRVS data, and assoc…
Reducing the global burden of stillbirths is important to improving child and maternal health. Of interest is understanding patterns in the timing of stillbirths -- that is, whether they occur in the intra- or antepartum period -- because stillbirths that occur intrapartum are largely preventable. However, data availability on the timing of stillbirths is highly variable across the world, with low- and middle-income countries generally having few reliable observations. In this paper we develop a Bayesian penalized splines regression framework to estimate the proportion of stillbirths that are …
This paper discusses the fundamental principles of causal inference - the area of statistics that estimates the effect of specific occurrences, treatments, interventions, and exposures on a given outcome from experimental and observational data. We explain the key assumptions required to identify causal effects, and highlight the challenges associated with the use of observational data. We emphasize that experimental thinking is crucial in causal inference. The quality of the data (not necessarily the quantity), the study design, the degree to which the assumptions are met, and the rigor of th…
The Greenland Sea is an important breeding ground for harp and hooded seals. Estimates of the annual seal pup production are critical factors in the abundance estimation needed for management of the species. These estimates are usually based on counts from aerial photographic surveys. However, only a minor part of the whelping region can be photographed, due to its large extent. To estimate the total seal pup production, we propose a Bayesian hierarchical modeling approach motivated by viewing the seal pup appearances as a realization of a log-Gaussian Cox process using covariate information f…
Indirect information on population size, like pellet counts or volunteer counts, is the main source of information in most ecological studies and applied population management situations. Often, such observations are treaded as if they were actual measurements of population size. This assumption results in incorrect conclusions about a population's size and its dynamics. We propose a model with a temporal varying link, denoted countability, between indirect observations and actual population size. We show that, when indirect measurement has high precision (for instance many observation hours) …
The effective reproduction number is a key figure to monitor the course of the COVID-19 pandemic. In this study we consider a retrospective modelling approach for estimating the effective reproduction number based on death counts during the first year of the pandemic in Germany. The proposed Bayesian hierarchical model incorporates splines to estimate reproduction numbers flexibly over time while adjusting for varying effective infection fatality rates. The approach also provides estimates of dark figures regarding undetected infections over time. Results for Germany illustrate that estimated …
We consider Bayesian high-dimensional mediation analysis to identify among a large set of correlated potential mediators the active ones that mediate the effect from an exposure variable to an outcome of interest. Correlations among mediators are commonly observed in modern data analysis; examples include the activated voxels within connected regions in brain image data, regulatory signals driven by gene networks in genome data and correlated exposure data from the same source. When correlations are present among active mediators, mediation analysis that fails to account for such correlation c…
In this report we fit a semi-mechanistic Bayesian hierarchical model to describe the Mexican COVID-19 epidemic. We obtain two epidemiological measures: the number of infections and the reproduction number. Estimations are based on death data. Hence, we expect our estimates to be more accurate than the attack rates estimated from the reported number of cases.
To combat the HIV/AIDS pandemic effectively, targeted interventions among certain key populations play a critical role. Examples of such key populations include sex workers, people who inject drugs, and men who have sex with men. While having accurate estimates for the size of these key populations is important, any attempt to directly contact or count members of these populations is difficult. As a result, indirect methods are used to produce size estimates. Multiple approaches for estimating the size of such populations have been suggested but often give conflicting results. It is therefore …
