Methodological problems in health-environment ecological studies

Different approaches are used to study the effects of the environment on health. We restrict our discussion to observational studies at the aggregated level, the so-called ecological studies. We discuss several sources of bias for group-level studies and consider questions relating to the link between individual-level and group-level dose-effect relationship, the difference between group exposure and environmental exposure, and the influence of measurement error and variability in the exposure. Taking into consideration confounding factors in the analyses is another important item that is discussed. A final item concerns the necessity of studying the temporal direction of the effect, as well as assessing the existence of a potential threshold in the effect. As a broad conclusion, we can say that realistic quantification of uncertainty in dose-effect relationships is a delicate task that requires the systematic consideration of all sources of variability, as well as a transparent sensitivity analysis of the choices and hypotheses made during the statistical analysis.     

Inference of Cross-Level Interaction between Genes and Contextual Factors in a Matched Case-Control Metabolic Syndrome Study: A Bayesian Approach

Genes, environment, and the interaction between them are each known to play an important role in the risk for developing complex diseases such as metabolic syndrome. For environmental factors, most studies focused on the measurements observed at the individual level, and therefore can only consider the gene-environment interaction at the same individual scale. Indeed the group-level (called contextual) environmental variables, such as community factors and the degree of local area development, may modify the genetic effect as well. To examine such cross-level interaction between genes and contextual factors, a flexible statistical model quantifying the variability of the genetic effects across different categories of the contextual variable is in need. With a Bayesian generalized linear mixed-effects model with an unconditional likelihood, we investigate whether the individual genetic effect is modified by the group-level residential environment factor in a matched case-control metabolic syndrome study. Such cross-level interaction is evaluated by examining the heterogeneity in allelic effects under various contextual categories, based on posterior samples from Markov chain Monte Carlo methods. The Bayesian analysis indicates that the effect of rs1801282 on metabolic syndrome development is modified by the contextual environmental factor. That is, even among individuals with the same genetic component of PPARG_Pro12Ala, living in a residential area with low availability of exercise facilities may result in higher risk. The modification of the group-level environment factors on the individual genetic attributes can be essential, and this Bayesian model is able to provide a quantitative assessment for such cross-level interaction. The Bayesian inference based on the full likelihood is flexible with any phenotype, and easy to implement computationally. This model has a wide applicability and may help unravel the complexity in development of complex diseases.     

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).     

The compliance score as a regressor in randomized trials

The compliance score in randomized trials is a measure of the effect of randomization on treatment received. It is in principle a group-level pretreatment variable and so can be used where individual-level measures of treatment received can produce misleading inferences. The interpretation of models with the compliance score as a regressor of interest depends on the link function. Using the identity link can lead to valid inference about the effects of treatment received even in the presence of nonrandom noncompliance; such inference is more problematic for nonlinear links. We illustrate these points with data from two randomized trials.     

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.     

Evaluation of community-intervention trials via generalized linear mixed models

In community-intervention trials, communities, rather than individuals, are randomized to experimental arms. Generalized linear mixed models offer a flexible parametric framework for the evaluation of community-intervention trials, incorporating both systematic and random variations at the community and individual levels. We propose here a simple two-stage inference method for generalized linear mixed models, specifically tailored to the analysis of community-intervention trials. In the first stage, community-specific random effects are estimated from individual-level data, adjusting for the effects of individual-level covariates. This reduces the model approximately to a linear mixed model with the unit of analysis being community. Because the number of communities is typically small in community-intervention studies, we apply the small-sample inference method of Kenward and Roger (1997, Biometrics53, 983-997) to the linear mixed model of second stage. We show by simulation that, under typical settings of community-intervention studies, the proposed approach improves the inference on the intervention-effect parameter uniformly over both the linearized mixed-effect approach and the adaptive Gaussian quadrature approach for generalized linear mixed models. This work is motivated by a series of large randomized trials that test community interventions for promoting cancer preventive lifestyles and behaviors.     

A hierarchical aggregate data model with spatially correlated disease rates

The aggregate data study design (Prentice and Sheppard, 1995, Biometrika 82, 113-125) estimates individual-level exposure effects by regressing population-based disease rates on covariate data from survey samples in each population group. In this work, we further develop the aggregate data model to allow for residual spatial correlation among disease rates across populations. Geographical variation that is not explained by model predictors and has a spatial component often arises in studies of rare chronic diseases, such as breast cancer. We combine the aggregate and Bayesian disease-mapping models to provide an intuitive approach to the modeling of spatial effects while drawing correct inference regarding the exposure effect. Based on the results of simulation studies, we suggest guidelines for use of the proposed model.     

Bias and Sensitivity Analysis When Estimating Treatment Effects from the Cox Model with Omitted Covariates

Summary

Omission of relevant covariates can lead to bias when estimating treatment or exposure effects from survival data in both randomized controlled trials and observational studies. This paper presents a general approach to assessing bias when covariates are omitted from the Cox model. The proposed method is applicable to both randomized and non‐randomized studies. We distinguish between the effects of three possible sources of bias: omission of a balanced covariate, data censoring and unmeasured confounding. Asymptotic formulae for determining the bias are derived from the large sample properties of the maximum likelihood estimator. A simulation study is used to demonstrate the validity of the bias formulae and to characterize the influence of the different sources of bias. It is shown that the bias converges to fixed limits as the effect of the omitted covariate increases, irrespective of the degree of confounding. The bias formulae are used as the basis for developing a new method of sensitivity analysis to assess the impact of omitted covariates on estimates of treatment or exposure effects. In simulation studies, the proposed method gave unbiased treatment estimates and confidence intervals with good coverage when the true sensitivity parameters were known. We describe application of the method to a randomized controlled trial and a non‐randomized study.     

Polydesigns and causal inference

In an increasingly common class of studies, the goal is to evaluate causal effects of treatments that are only partially controlled by the investigator. In such studies there are two conflicting features: (1) a model on the full cohort design and data can identify the causal effects of interest, but can be sensitive to extreme regions of that design's data, where model specification can have more impact; and (2) models on a reduced design (i.e., a subset of the full data), for example, conditional likelihood on matched subsets of data, can avoid such sensitivity, but do not generally identify the causal effects. We propose a framework to assess how inference is sensitive to designs by exploring combinations of both the full and reduced designs. We show that using such a "polydesign" framework generates a rich class of methods that can identify causal effects and that can also be more robust to model specification than methods using only the full design. We discuss implementation of polydesign methods, and provide an illustration in the evaluation of a needle exchange program.     

Robustness of self-organised systems to changes in behaviour: an example from real and simulated self-organised snail aggregations

Group or population level self-organised systems comprise many individuals displaying group-level emergent properties. Current theory indicates that individual-level behaviours have an effect on the final group-level behaviour; that is, self-organised systems are sensitive to small changes in individual behaviour. Here we examine a self-organised behaviour in relation to environmentally-driven individual-level changes in behaviour, using both natural systems and computer simulations. We demonstrate that aggregations of intertidal snails slightly decrease in size when, owing to hotter and more desiccating conditions, individuals forage for shorter periods--a seemingly non-adaptive behaviour for the snails since aggregation reduces desiccation stress. This decrease, however, only occurs in simple experimental systems (and simulations of these systems). When studied in their natural and more complex environment, and simulations of such an environment, using the same reduced foraging time, no difference in aggregation behaviour was found between hot and cool days. These results give an indication of how robust self-organised systems are to changes in individual-level behaviour. The complexity of the natural environment and the interactions of individuals with this environment, therefore, can result in self-organised systems being more resilient to individual-level changes than previously assumed.     

Improving inference for aerial surveys of bears: The importance of assumptions and the cost of unnecessary complexity

Obtaining useful estimates of wildlife abundance or density requires thoughtful attention to potential sources of bias and precision, and it is widely understood that addressing incomplete detection is critical to appropriate inference. When the underlying assumptions of sampling approaches are violated, both increased bias and reduced precision of the population estimator may result. Bear (Ursus spp.) populations can be difficult to sample and are often monitored using mark‐recapture distance sampling (MRDS) methods, although obtaining adequate sample sizes can be cost prohibitive. With the goal of improving inference, we examined the underlying methodological assumptions and estimator efficiency of three datasets collected under an MRDS protocol designed specifically for bears. We analyzed these data using MRDS, conventional distance sampling (CDS), and open‐distance sampling approaches to evaluate the apparent bias‐precision tradeoff relative to the assumptions inherent under each approach. We also evaluated the incorporation of informative priors on detection parameters within a Bayesian context. We found that the CDS estimator had low apparent bias and was more efficient than the more complex MRDS estimator. When combined with informative priors on the detection process, precision was increased by >50% compared to the MRDS approach with little apparent bias. In addition, open‐distance sampling models revealed a serious violation of the assumption that all bears were available to be sampled. Inference is directly related to the underlying assumptions of the survey design and the analytical tools employed. We show that for aerial surveys of bears, avoidance of unnecessary model complexity, use of prior information, and the application of open population models can be used to greatly improve estimator performance and simplify field protocols. Although we focused on distance sampling‐based aerial surveys for bears, the general concepts we addressed apply to a variety of wildlife survey contexts.     

A hybrid model for reducing ecological bias

A major drawback of epidemiological ecological studies, in which the association between area-level summaries of risk and exposure is used to make inference about individual risk, is the difficulty in characterizing within-area variability in exposure and confounder variables. To avoid ecological bias, samples of individual exposure/confounder data within each area are required. Unfortunately, these may be difficult or expensive to obtain, particularly if large samples are required. In this paper, we propose a new approach suitable for use with small samples. We combine a Bayesian nonparametric Dirichlet process prior with an estimating functions' approach and show that this model gives a compromise between 2 previously described methods. The method is investigated using simulated data, and a practical illustration is provided through an analysis of lung cancer mortality and residential radon exposure in counties of Minnesota. We conclude that we require good quality prior information about the exposure/confounder distributions and a large between- to within-area variability ratio for an ecological study to be feasible using only small samples of individual data.     

Random-Effects,Fixed-Effects and the within-between Specification for Clustered Data in Observational Health Studies: A Simulation Study

Background

When unaccounted-for group-level characteristics affect an outcome variable, traditional linear regression is inefficient and can be biased. The random- and fixed-effects estimators (RE and FE, respectively) are two competing methods that address these problems. While each estimator controls for otherwise unaccounted-for effects, the two estimators require different assumptions. Health researchers tend to favor RE estimation, while researchers from some other disciplines tend to favor FE estimation. In addition to RE and FE, an alternative method called within-between (WB) was suggested by Mundlak in 1978, although is utilized infrequently.

Methods

We conduct a simulation study to compare RE, FE, and WB estimation across 16,200 scenarios. The scenarios vary in the number of groups, the size of the groups, within-group variation, goodness-of-fit of the model, and the degree to which the model is correctly specified. Estimator preference is determined by lowest mean squared error of the estimated marginal effect and root mean squared error of fitted values.

Results

Although there are scenarios when each estimator is most appropriate, the cases in which traditional RE estimation is preferred are less common. In finite samples, the WB approach outperforms both traditional estimators. The Hausman test guides the practitioner to the estimator with the smallest absolute error only 61% of the time, and in many sample sizes simply applying the WB approach produces smaller absolute errors than following the suggestion of the test.

Conclusions

Specification and estimation should be carefully considered and ultimately guided by the objective of the analysis and characteristics of the data. The WB approach has been underutilized, particularly for inference on marginal effects in small samples. Blindly applying any estimator can lead to bias, inefficiency, and flawed inference.     

Testing major evolutionary hypotheses about religion with a random sample

Theories of religion that are supported with selected examples can be criticized for selection bias. This paper evaluates major evolutionary hypotheses about religion with a random sample of 35 religions drawn from a 16-volume encyclopedia of world religions. The results are supportive of the group-level adaptation hypothesis developed in Darwin’s Cathedral: Evolution, Religion, and the Nature of Society (Wilson 2002). Most religions in the sample have what Durkheim called secular utility. Their otherworldly elements can be largely understood as proximate mechanisms that motivate adaptive behaviors. Jainism, the religion in the sample that initially appeared most challenging to the group-level adaptation hypothesis, is highly supportive upon close examination. The results of the survey are preliminary and should be built upon by a multidisciplinary community as part of a field of evolutionary religious studies. This research was supported by a grant from the Institute for Research on Unlimited Love. David Sloan Wilson is an evolutionary biologist interested in a broad range of issues relevant to human behavior. He has published in psychology, anthropology, and philosophy journals in addition to his mainstream biological research. He is co-author with the philosopher Elliott Sober of Unto Others: The Evolution and Psychology of Unselfish Behavior (Harvard University Press, 1998).     

Phylogenomic Subsampling and the Search for Phylogenetically Reliable Loci

Phylogenomic subsampling is a procedure by which small sets of loci are selected from large genome-scale data sets and used for phylogenetic inference. This step is often motivated by either computational limitations associated with the use of complex inference methods or as a means of testing the robustness of phylogenetic results by discarding loci that are deemed potentially misleading. Although many alternative methods of phylogenomic subsampling have been proposed, little effort has gone into comparing their behavior across different data sets. Here, I calculate multiple gene properties for a range of phylogenomic data sets spanning animal, fungal, and plant clades, uncovering a remarkable predictability in their patterns of covariance. I also show how these patterns provide a means for ordering loci by both their rate of evolution and their relative phylogenetic usefulness. This method of retrieving phylogenetically useful loci is found to be among the top performing when compared with alternative subsampling protocols. Relatively common approaches such as minimizing potential sources of systematic bias or increasing the clock-likeness of the data are found to fare worse than selecting loci at random. Likewise, the general utility of rate-based subsampling is found to be limited: loci evolving at both low and high rates are among the least effective, and even those evolving at optimal rates can still widely differ in usefulness. This study shows that many common subsampling approaches introduce unintended effects in off-target gene properties and proposes an alternative multivariate method that simultaneously optimizes phylogenetic signal while controlling for known sources of bias.     

Inter-observer reliability of animal-based welfare indicators included in the Animal Welfare Indicators welfare assessment protocol for dairy goats

This study was conducted within the context of the Animal Welfare Indicators (AWIN) project and the underlying scientific motivation for the development of the study was the scarcity of data regarding inter-observer reliability (IOR) of welfare indicators, particularly given the importance of reliability as a further step for developing on-farm welfare assessment protocols. The objective of this study is therefore to evaluate IOR of animal-based indicators (at group and individual-level) of the AWIN welfare assessment protocol (prototype) for dairy goats. In the design of the study, two pairs of observers, one in Portugal and another in Italy, visited 10 farms each and applied the AWIN prototype protocol. Farms in both countries were visited between January and March 2014, and all the observers received the same training before the farm visits were initiated. Data collected during farm visits, and analysed in this study, include group-level and individual-level observations. The results of our study allow us to conclude that most of the group-level indicators presented the highest IOR level (‘substantial’, 0.85 to 0.99) in both field studies, pointing to a usable set of animal-based welfare indicators that were therefore included in the first level of the final AWIN welfare assessment protocol for dairy goats. Inter-observer reliability of individual-level indicators was lower, but the majority of them still reached ‘fair to good’ (0.41 to 0.75) and ‘excellent’ (0.76 to 1) levels. In the paper we explore reasons for the differences found in IOR between the group and individual-level indicators, including how the number of individual-level indicators to be assessed on each animal and the restraining method may have affected the results. Furthermore, we discuss the differences found in the IOR of individual-level indicators in both countries: the Portuguese pair of observers reached a higher level of IOR, when compared with the Italian observers. We argue how the reasons behind these differences may stem from the restraining method applied, or the different background and experience of the observers. Finally, the discussion of the results emphasizes the importance of considering that reliability is not an absolute attribute of an indicator, but derives from an interaction between the indicators, the observers and the situation in which the assessment is taking place. This highlights the importance of further considering the indicators’ reliability while developing welfare assessment protocols.     

WHY DOES A METHOD THAT FAILS CONTINUE TO BE USED?

As a critical framework for addressing a diversity of evolutionary and ecological questions, any method that provides accurate and detailed phylogeographic inference would be embraced. What is difficult to understand is the continued use of a method that not only fails, but also has never been shown to work--nested clade analysis is applied widely even though the conditions under which the method will provide reliable results have not yet been demonstrated. This contradiction between performance and popularity is even more perplexing given the recent methodological and computational advances for making historical inferences, which include estimating population genetic parameters and testing different biogeographic scenarios. Here I briefly review the history of criticisms and rebuttals that focus specifically on the high rate of incorrect phylogeographic inference of nested-clade analysis, with the goal of understanding what drives its unfettered popularity. In this case, the appeal of what nested-clade analysis claims to do--not what the method actually achieves--appears to explain its paradoxical status as a favorite method that fails. What a method promises, as opposed to how it performs, must be considered separately when evaluating whether the method represents a valuable tool for historical inference.     

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.     

Self-organized fish schools: an examination of emergent properties

Heterogeneous, "aggregated" patterns in the spatial distributions of individuals are almost universal across living organisms, from bacteria to higher vertebrates. Whereas specific features of aggregations are often visually striking to human eyes, a heuristic analysis based on human vision is usually not sufficient to answer fundamental questions about how and why organisms aggregate. What are the individual-level behavioral traits that give rise to these features? When qualitatively similar spatial patterns arise from purely physical mechanisms, are these patterns in organisms biologically significant, or are they simply epiphenomena that are likely characteristics of any set of interacting autonomous individuals? If specific features of spatial aggregations do confer advantages or disadvantages in the fitness of group members, how has evolution operated to shape individual behavior in balancing costs and benefits at the individual and group levels? Mathematical models of social behaviors such as schooling in fishes provide a promising avenue to address some of these questions. However, the literature on schooling models has lacked a common framework to objectively and quantitatively characterize relationships between individual-level behaviors and group-level patterns. In this paper, we briefly survey similarities and differences in behavioral algorithms and aggregation statistics among existing schooling models. We present preliminary results of our efforts to develop a modeling framework that synthesizes much of this previous work, and to identify relationships between behavioral parameters and group-level statistics.     

A reanalysis of thyroid neoplasms in the Israeli tinea capitis study accounting for dose uncertainties

In the 1940s and 1950s, children in Israel were treated for tinea capitis by irradiation to the scalp to induce epilation. Follow-up studies of these patients and of other radiation- exposed populations show an increased risk of malignant and benign thyroid tumors. Those analyses, however, assume that thyroid dose for individuals is estimated precisely without error. Failure to account for uncertainties in dosimetry may affect standard errors and bias dose-response estimates. For the Israeli tinea capitis study, we discuss sources of uncertainties and adjust dosimetry for uncertainties in the prediction of true dose from X-ray treatment parameters. We also account for missing ages at exposure for patients with multiple X-ray treatments, since only ages at first treatment are known, and for missing data on treatment center, which investigators use to define exposure. Our reanalysis of the dose response for thyroid cancer and benign thyroid tumors indicates that uncertainties in dosimetry have minimal effects on dose-response estimation and for inference on the modifying effects of age at first exposure, time since exposure, and other factors. Since the components of the dose uncertainties we describe are likely to be present in other epidemiological studies of patients treated with radiation, our analysis may provide a model for considering the potential role of these uncertainties.