A flexible hierarchical framework for improving inference in area-referenced environmental health studies

Study designs where data have been aggregated by geographical areas are popular in environmental epidemiology. These studies are commonly based on administrative databases and, providing a complete spatial coverage, are particularly appealing to make inference on the entire population. However, the resulting estimates are often biased and difficult to interpret due to unmeasured confounders, which typically are not available from routinely collected data. We propose a framework to improve inference drawn from such studies exploiting information derived from individual-level survey data. The latter are summarized in an area-level scalar score by mimicking at ecological level the well-known propensity score methodology. The literature on propensity score for confounding adjustment is mainly based on individual-level studies and assumes a binary exposure variable. Here, we generalize its use to cope with area-referenced studies characterized by a continuous exposure. Our approach is based upon Bayesian hierarchical structures specified into a two-stage design: (i) geolocated individual-level data from survey samples are up-scaled at ecological level, then the latter are used to estimate a generalized ecological propensity score (EPS) in the in-sample areas; (ii) the generalized EPS is imputed in the out-of-sample areas under different assumptions about the missingness mechanisms, then it is included into the ecological regression, linking the exposure of interest to the health outcome. This delivers area-level risk estimates, which allow a fuller adjustment for confounding than traditional areal studies. The methodology is illustrated by using simulations and a case study investigating the risk of lung cancer mortality associated with nitrogen dioxide in England (UK).     

Role of Ecological Modeling in Risk Assessment

Ecological models are useful tools for evaluating the ecological significance of observed or predicted effects of toxic chemicals on individual organisms. Current risk estimation approaches using hazard quotients for individual-level endpoints have limited utility for assessing risks at the population, ecosystem, and landscape levels, which are the most relevant indicators for environmental management. In this paper, we define different types of ecological models, summarize their input and output variables, and present examples of the role of some recommended models in chemical risk assessments. A variety of population and ecosystem models have been applied successfully to evaluate ecological risks, including population viability of endangered species, habitat fragmentation, and toxic chemical issues. In particular, population models are widely available, and their value in predicting dynamics of natural populations has been demonstrated. Although data are often limited on vital rates and doseresponse functions needed for ecological modeling, accurate prediction of ecological effects may not be needed for all assessments. Often, a comparative assessment of risk (e.g., relative to baseline or reference) is of primary interest. Ecological modeling is currently a valuable approach for addressing many chemical risk assessment issues, including screening-level evaluations.     

Disease mapping and spatial regression with count data

In this paper, we provide critical reviews of methods suggested for the analysis of aggregate count data in the context of disease mapping and spatial regression. We introduce a new method for picking prior distributions, and propose a number of refinements of previously used models. We also consider ecological bias, mutual standardization, and choice of both spatial model and prior specification. We analyze male lip cancer incidence data collected in Scotland over the period 1975-1980, and outline a number of problems with previous analyses of these data. In disease mapping studies, hierarchical models can provide robust estimation of area-level risk parameters, though care is required in the choice of covariate model, and it is important to assess the sensitivity of estimates to the spatial model chosen, and to the prior specifications on the variance parameters. Spatial ecological regression is a far more hazardous enterprise for two reasons. First, there is always the possibility of ecological bias, and this can only be alleviated by the inclusion of individual-level data. For the Scottish data, we show that the previously used mean model has limited interpretation from an individual perspective. Second, when residual spatial dependence is modeled, and if the exposure has spatial structure, then estimates of exposure association parameters will change when compared with those obtained from the independence across space model, and the data alone cannot choose the form and extent of spatial correlation that is appropriate.     

A hierarchical bayesian approach to ecological count data: a flexible tool for ecologists

Many ecological studies use the analysis of count data to arrive at biologically meaningful inferences. Here, we introduce a hierarchical bayesian approach to count data. This approach has the advantage over traditional approaches in that it directly estimates the parameters of interest at both the individual-level and population-level, appropriately models uncertainty, and allows for comparisons among models, including those that exceed the complexity of many traditional approaches, such as ANOVA or non-parametric analogs. As an example, we apply this method to oviposition preference data for butterflies in the genus Lycaeides. Using this method, we estimate the parameters that describe preference for each population, compare the preference hierarchies among populations, and explore various models that group populations that share the same preference hierarchy.     

Study design and parameter estimability for spatial and temporal ecological models

The statistical tools available to ecologists are becoming increasingly sophisticated, allowing more complex, mechanistic models to be fit to ecological data. Such models have the potential to provide new insights into the processes underlying ecological patterns, but the inferences made are limited by the information in the data. Statistical nonestimability of model parameters due to insufficient information in the data is a problem too‐often ignored by ecologists employing complex models. Here, we show how a new statistical computing method called data cloning can be used to inform study design by assessing the estimability of parameters under different spatial and temporal scales of sampling. A case study of parasite transmission from farmed to wild salmon highlights that assessing the estimability of ecologically relevant parameters should be a key step when designing studies in which fitting complex mechanistic models is the end goal.     

Measuring information-based complexity across scales using cluster analysis

Scaling of ecological data can present a challenge firstly because of the large amount of information contained in an ecological data set, and secondly because of the problem of fitting data to models that we want to use to capture structure. We present a measure of similarity between data collected at several scales using the same set of attributes. The measure is based on the concept of Kolmogorov complexity and implemented through minimal message length estimates of information content and cluster analysis (the models). The similarity represents common patterns across scales, within the model class. We thus provide a novel solution to the problem of simultaneously considering data structure, model fit and scale. The methods are illustrated in application to an ecological data set.     

Parameterizing Spatial Models of Infectious Disease Transmission that Incorporate Infection Time Uncertainty Using Sampling-Based Likelihood Approximations

A class of discrete-time models of infectious disease spread, referred to as individual-level models (ILMs), are typically fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. These models quantify probabilistic outcomes regarding the risk of infection of susceptible individuals due to various susceptibility and transmissibility factors, including their spatial distance from infectious individuals. The infectious pressure from infected individuals exerted on susceptible individuals is intrinsic to these ILMs. Unfortunately, quantifying this infectious pressure for data sets containing many individuals can be computationally burdensome, leading to a time-consuming likelihood calculation and, thus, computationally prohibitive MCMC-based analysis. This problem worsens when using data augmentation to allow for uncertainty in infection times. In this paper, we develop sampling methods that can be used to calculate a fast, approximate likelihood when fitting such disease models. A simple random sampling approach is initially considered followed by various spatially-stratified schemes. We test and compare the performance of our methods with both simulated data and data from the 2001 foot-and-mouth disease (FMD) epidemic in the U.K. Our results indicate that substantial computation savings can be obtained—albeit, of course, with some information loss—suggesting that such techniques may be of use in the analysis of very large epidemic data sets.     

Population growth rate as a basis for ecological risk assessment of toxic chemicals

Assessing the ecological risks of toxic chemicals is most often based on individual-level responses such as survival, reproduction or growth. Such an approach raises the following questions with regard to translating these measured effects into likely impacts on natural populations. (i) To what extent do individual-level variables underestimate or overestimate population-level responses? (ii) How do toxicant-caused changes in individual-level variables translate into changes in population dynamics for species with different life cycles? (iii) To what extent are these relationships complicated by population-density effects? These issues go to the heart of the ecological relevance of ecotoxicology and we have addressed them using the population growth rate as an integrating concept. Our analysis indicates that although the most sensitive individual-level variables are likely to be equally or more sensitive to increasing concentrations of toxic chemicals than population growth rate, they are difficult to identify a priori and, even if they could be identified, integrating impacts on key life-cycle variables via population growth rate analysis is nevertheless a more robust approach for assessing the ecological risks of chemicals. Populations living under density-dependent control may respond differently to toxic chemicals than exponentially growing populations, and greater care needs to be given to incorporating realistic density conditions (either experimentally or by simulation) into ecotoxicological test designs. It is impractical to expect full life-table studies, which record changes in survival, fecundity and development at defined intervals through the life cycle of organisms under specified conditions, for all relevant species, so we argue that population growth rate analysis should be used to provide guidance for a more pragmatic and ecologically sound approach to ecological risk assessment.     

Individual-scale variation, species-scale differences: inference needed to understand diversity

As ecological data are usually analysed at a scale different from the one at which the process of interest operates, interpretations can be confusing and controversial. For example, hypothesised differences between species do not operate at the species level, but concern individuals responding to environmental variation, including competition with neighbours. Aggregated data from many individuals subject to spatio-temporal variation are used to produce species-level averages, which marginalise away the relevant (process-level) scale. Paradoxically, the higher the dimensionality, the more ways there are to differ, yet the more species appear the same. The aggregate becomes increasingly irrelevant and misleading. Standard analyses can make species look the same, reverse species rankings along niche axes, make the surprising prediction that a species decreases in abundance when a competitor is removed from a model, or simply preclude parameter estimation. Aggregation explains why niche differences hidden at the species level become apparent upon disaggregation to the individual level, why models suggest that individual-level variation has a minor impact on diversity when disaggregation shows it to be important, and why literature-based synthesis can be unfruitful. We show how to identify when aggregation is the problem, where it has caused controversy, and propose three ways to address it.     

Deep learning and differential equations for modeling changes in individual-level latent dynamics between observation periods

When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction and differential equations for dynamic modeling of individual-level trajectories. However, such approaches so far assume that parameters of individual-level dynamics are constant throughout the observation period. Motivated by an application from psychological resilience research, we propose an extension where different sets of differential equation parameters are allowed for observation subperiods. Still, estimation for intra-individual subperiods is coupled for being able to fit the model also with a relatively small dataset. We subsequently derive prediction targets from individual dynamic models of resilience in the application. These serve as outcomes for predicting resilience from characteristics of individuals, measured at baseline and a follow-up time point, and selecting a small set of important predictors. Our approach is seen to successfully identify individual-level parameters of dynamic models that allow to stably select predictors, that is, resilience factors. Furthermore, we can identify those characteristics of individuals that are the most promising for updates at follow-up, which might inform future study design. This underlines the usefulness of our proposed deep dynamic modeling approach with changes in parameters between observation subperiods.     

Generalized additive models for cancer mapping with incomplete covariates

Maps depicting cancer incidence rates have become useful tools in public health research, giving valuable information about the spatial variation in rates of disease. Typically, these maps are generated using count data aggregated over areas such as counties or census blocks. However, with the proliferation of geographic information systems and related databases, it is becoming easier to obtain exact spatial locations for the cancer cases and suitable control subjects. The use of such point data allows us to adjust for individual-level covariates, such as age and smoking status, when estimating the spatial variation in disease risk. Unfortunately, such covariate information is often subject to missingness. We propose a method for mapping cancer risk when covariates are not completely observed. We model these data using a logistic generalized additive model. Estimates of the linear and non-linear effects are obtained using a mixed effects model representation. We develop an EM algorithm to account for missing data and the random effects. Since the expectation step involves an intractable integral, we estimate the E-step with a Laplace approximation. This framework provides a general method for handling missing covariate values when fitting generalized additive models. We illustrate our method through an analysis of cancer incidence data from Cape Cod, Massachusetts. These analyses demonstrate that standard complete-case methods can yield biased estimates of the spatial variation of cancer risk.     

Unravelling the dynamics of organisms in a changing world using ecological modelling

Understanding and predicting the dynamics of organisms is a central objective in ecology and conservation biology, and modelling provides a solution to tackling this problem. However, the complex nature of ecological systems means that for a thorough understanding of ecological dynamics at hierarchical scales, a set of modeling approaches need to be adopted. This review illustrates how modelling approaches can be used to understand the dynamics of organisms in applied ecological problems, focussing on mechanistic models at a local scale and statistical models at a broad scale. Mechanistic models incorporate ecological processes explicitly and thus are likely to be robust under novel conditions. Models based on behavioural decisions by individuals represent a typical example of the successful application of mechanistic models to applied problems. Considering the data-hungry nature of such mechanistic models, model complexity and parameterisation need to be explored further for a quick and widespread implementation of this model type. For broad-scale phenomena, statistical models play an important role in dealing with problems that are often inherent in data. Examples include models for quantifying population trends from long-term, large-scale data and those for comparative methods of extinction risk. Novel statistical approaches also allow mechanistic models to be parameterised using readily obtained data at a macro scale. In conclusion, the complementary use and improvement of multiple model types, the increased use of novel model parameterisation, the examination of model transferability and the achievement of wider biodiversity information availability are key challenges for the effective use of modelling in applied ecological problems.     

Application of wavelet analysis to ecological data

Ecological data are difficult to analyze due to complexity residing in the ecological systems with the variables varying in non-linear fashion. Efficient methods are required to properly extract information out of the complex data. Wavelets have good time–frequency (time-scale) localization, can represent data parsimoniously, and can be implemented with very fast algorithms. Brief backgrounds and computational aspects of wavelets were outlined for implementation to ecological data analysis. Wavelets are well suited for building mathematical models of ecological data and the statistical analysis of combined effects of complex factors in ecological network. Wavelet based analysis and synthesis may lead researchers in ecological studies to new insights and novel theories for understanding complex ecological and environmental phenomena.     

生物多样性遥感研究方法浅议

概括了遥感在生物多样性研究方面的的优势及在各种尺度为生物多样性评价提供信息的能力;讨论了生物多样性信息系统应具备的功能和应包含的内容;分析了生物多样性遥感研究中数学模型与地理信息系统的耦合问题。     

From mixed effects modeling to spike and slab variable selection: A Bayesian regression model for group testing data

Due to reductions in both time and cost, group testing is a popular alternative to individual-level testing for disease screening. These reductions are obtained by testing pooled biospecimens (eg, blood, urine, swabs, etc.) for the presence of an infectious agent. However, these reductions come at the expense of data complexity, making the task of conducting disease surveillance more tenuous when compared to using individual-level data. This is because an individual's disease status may be obscured by a group testing protocol and the effect of imperfect testing. Furthermore, unlike individual-level testing, a given participant could be involved in multiple testing outcomes and/or may never be tested individually. To circumvent these complexities and to incorporate all available information, we propose a Bayesian generalized linear mixed model that accommodates data arising from any group testing protocol, estimates unknown assay accuracy probabilities and accounts for potential heterogeneity in the covariate effects across population subgroups (eg, clinic sites, etc.); this latter feature is of key interest to practitioners tasked with conducting disease surveillance. To achieve model selection, our proposal uses spike and slab priors for both fixed and random effects. The methodology is illustrated through numerical studies and is applied to chlamydia surveillance data collected in Iowa.     

Exploring the Complex Pattern of Information Spreading in Online Blog Communities

Information spreading in online social communities has attracted tremendous attention due to its utmost practical values in applications. Despite that several individual-level diffusion data have been investigated, we still lack the detailed understanding of the spreading pattern of information. Here, by comparing information flows and social links in a blog community, we find that the diffusion processes are induced by three different spreading mechanisms: social spreading, self-promotion and broadcast. Although numerous previous studies have employed epidemic spreading models to simulate information diffusion, we observe that such models fail to reproduce the realistic diffusion pattern. In respect to users behaviors, strikingly, we find that most users would stick to one specific diffusion mechanism. Moreover, our observations indicate that the social spreading is not only crucial for the structure of diffusion trees, but also capable of inducing more subsequent individuals to acquire the information. Our findings suggest new directions for modeling of information diffusion in social systems, and could inform design of efficient propagation strategies based on users behaviors.     

Carrying capacity and demographic stochasticity: scaling behavior of the stochastic logistic model

The stochastic logistic model is the simplest model that combines individual-level demography with density dependence. It explicitly or implicitly underlies many models of biodiversity of competing species, as well as non-spatial or metapopulation models of persistence of individual species. The model has also been used to study persistence in simple disease models. The stochastic logistic model has direct relevance for questions of limiting similarity in ecological systems. This paper uses a biased random walk heuristic to derive a scaling relationship for the persistence of a population under this model, and discusses its implications for models of biodiversity and persistence. Time to extinction of a species under the stochastic logistic model is approximated by the exponential of the scaling quantity U=(R-1)(2) N/R(R+1), where N is the habitat size and R is the basic reproductive number.     

Insights on bias and information in group-level studies

Ecological and aggregate data studies are examples of group-level studies. Even though the link between the predictors and outcomes is not preserved in these studies, inference about individual-level exposure effects is often a goal. The disconnection between the level of inference and the level of analysis expands the array of potential biases that can invalidate the inference from group-level studies. While several sources of bias, specifically due to measurement error and confounding, may be more complex in group-level studies, two sources of bias, cross-level and model specification bias, are a direct consequence of the disconnection. With the goal of aligning inference from individual versus group-level studies, I discuss the interplay between exposure and study design. I specify the additional assumptions necessary for valid inference, specifically that the between- and within-group exposure effects are equal. Then cross-level inference is possible. However, all the information in the group-level analysis comes from between-group comparisons. Models where the group-level analysis provides even a small percentage of information about the within-group exposure effect are most susceptible to model specification bias. Model specification bias can be even more serious when the group-level model isn't derived from an individual-level model.     

Bias correction of bounded location error in binary data

Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons. The COS accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice.     

ModEco: an integrated software package for ecological niche modeling

ModEco is a software package for ecological niche modeling. It integrates a range of niche modeling methods within a geographical information system. ModEco provides a user friendly platform that enables users to explore, analyze, and model species distribution data with relative ease. ModEco has several unique features: 1) it deals with different types of ecological observation data, such as presence and absence data, presence‐only data, and abundance data; 2) it provides a range of models when dealing with presence‐only data, such as presence‐only models, pseudo‐absence models, background vs presence data models, and ensemble models; and 3) it includes relatively comprehensive tools for data visualization, feature selection, and accuracy assessment.