Bayesian analysis of measurement error models using integrated nested Laplace approximations

A joint Bayesian framework for missing data and measurement error using integrated nested Laplace approximations

Measurement error (ME) and missing values in covariates are often unavoidable in disciplines that deal with data, and both problems have separately received considerable attention during the past decades. However, while most researchers are familiar with methods for treating missing data, accounting for ME in covariates of regression models is less common. In addition, ME and missing data are typically treated as two separate problems, despite practical and theoretical similarities. Here, we exploit the fact that missing data in a continuous covariate is an extreme case of classical ME, allowing us to use existing methodology that accounts for ME via a Bayesian framework that employs integrated nested Laplace approximations (INLA) and thus to simultaneously account for both ME and missing data in the same covariate. As a useful by-product, we present an approach to handle missing data in INLA since this corresponds to the special case when no ME is present. In addition, we show how to account for Berkson ME in the same framework. In its broadest generality, the proposed joint Bayesian framework can thus account for Berkson ME, classical ME, and missing data, or any combination of these in the same or different continuous covariates of the family of regression models that are feasible with INLA. The approach is exemplified using both simulated and real data. We provide extensive and fully reproducible Supporting Information with thoroughly documented examples using R-INLA and inlabru.

Quantification of the pluriannual dynamics of grapevine growth responses to nitrogen supply using a Bayesian approach

The effect of nitrogen (N) nutrition on grapevine carbon (C) dynamics has been well studied at the annual scale, but poorly addressed at a pluriannual timescale. The aim of this study was to quantify, in an integrated conceptual framework, the effect of N nutrition on potted grapevine growth and storage over 2 consecutive years. The consequences of using destructive measurements were investigated using a hierarchical Bayesian model. The rate and duration of leaf growth were both positively impacted by the chlorophyll content of the leaves, but they were negatively impacted by the initial carbohydrate measurements, raising a distortion in the estimation of initial reserves. The C production per unit of global radiation depended on the leaf area dynamics. The allocation of dry matter mainly relied on the phenological stage. The present study highlights the importance of using appropriate statistical methods to overcome uncertainties due to destructive measurements. The genericity of the statistical approach presented may encourage its implementation in other agronomy studies. Based on our results, a simple conceptual framework of grapevine pluriannual growth under various N supplies was built. This provides a relevant basis for a future model of C and N balance and responses to N fertilization in grapevine.

A Bayesian approach for estimating the partial potential impact fraction with exposure measurement error under a main study/internal validation design

The partial potential impact fraction describes the proportion of disease cases that can be prevented if the distribution of modifiable continuous exposures is shifted in a population, while other risk factors are not modified. It is a useful quantity for evaluating the burden of disease in epidemiologic and public health studies. When exposures are measured with error, the partial potential impact fraction estimates may be biased, which necessitates methods to correct for the exposure measurement error. Motivated by the health professionals follow-up study, we develop a Bayesian approach to adjust for exposure measurement error when estimating the partial potential impact fraction under the main study/internal validation study design. We adopt the reclassification approach that leverages the strength of the main study/internal validation study design and clarifies transportability assumptions for valid inference. We assess the finite-sample performance of both the point and credible interval estimators via extensive simulations and apply the proposed approach in the health professionals follow-up study to estimate the partial potential impact fraction for colorectal cancer incidence under interventions exploring shifting the distributions of red meat, alcohol, and/or folate intake.

Substantial Reduction in Particulate Matter Air Pollution across Europe during 2006-2019: A Spatiotemporal Modeling Analysis

Air pollution poses the largest environmental health risk in Europe. Particulate matter (PM) concentrations are the most harmful pollutants representing the main air quality indicator in the Sustainable Development Goals (SDGs). The air quality surveillance in Europe is based on a monitoring network that is too coarse for a comprehensive evaluation of the air pollution burden. We link raw pollutant data with remotely sensed products using Bayesian geostatistical models and for the first time estimate pan-European near-surface concentrations of both fine (PM2.5) and coarse (PM10) particles at 1 km2 spatial resolution during 2006-2019. We evaluate the compliance with the air quality thresholds set by the World Health Organization (WHO) and the European Union (EU) and assess country-wise trends. The results show that during the last 14 years, PM10 and PM2.5 concentrations declined by 36.5% (95% credible interval: 30.3, 41.9%) and 39.1% (26.6, 50.5%), respectively. The number of people exposed to PM10 levels above the WHO thresholds decreased from 78.3% (52.6, 91.8%) in 2006 to 28.4% (16.2, 43.7%) in 2019; for PM2.5, the decrease was smaller: from 91.0% (61.3, 99.1%) exposed in 2006 to 53.6% (33.5, 76.3%) in 2019. Although there is a clear improvement in the overall picture, stricter measures are needed to ensure compliance with the WHO guidelines.

Dynamics of Covid-19 mortality and social determinants of health: a spatiotemporal analysis of exceedance probabilities

PURPOSE

To determine the association of social factors with Covid-19 mortality and identify high-risk clusters.

METHODS

Data on Covid-19 deaths across 3,108 contiguous U.S. counties from the Johns Hopkins University and social determinants of health (SDoH) data from the County Health Ranking and the Bureau of Labor Statistics were fitted to Bayesian semi-parametric spatiotemporal Negative Binomial models, and 95% credible intervals (CrI) of incidence rate ratios (IRR) were used to assess the associations. Exceedance probabilities were used for detecting clusters.

RESULTS

As of October 31, 2020, the median mortality rate was 40.05 per 100, 000. The monthly urban mortality rates increased with unemployment (IRRadjusted:1.41, 95% CrI: 1.24, 1.60), percent Black population (IRRadjusted:1.05, 95% CrI: 1.04, 1.07), and residential segregation (IRRadjusted:1.03, 95% CrI: 1.02, 1.04). The rural monthly mortality rates increased with percent female population (IRRadjusted: 1.17, 95% CrI: 1.11, 1.24) and percent Black population (IRRadjusted:1.07 95% CrI:1.06, 1.08). Higher college education rates were associated with decreased mortality rates in rural and urban counties. The dynamics of exceedance probabilities detected the shifts of high-risk clusters from the Northeast to Southern and Midwestern counties.

CONCLUSIONS

Spatiotemporal analyses enabled the inclusion of unobserved latent risk factors and aid in scientifically grounded decision-making at a granular level.

Dengue, Severity Paradox, and Socioeconomic Distribution Among Afro-Colombians

BACKGROUND

The clinical presentation of dengue ranges from self-limited mild illness to severe forms, including death. African ancestry is often described as protective against dengue severity. However, in the Latin American context, African ancestry has been associated with increased mortality. This "severity paradox" has been hypothesized as resulting from confounding or heterogeneity by socioeconomic status (SES). However, few systematic analyses have been conducted to investigate the presence and nature of the disparity paradox.

METHODS

We fit Bayesian hierarchical spatiotemporal models using individual-level surveillance data from Cali, Colombia (2012-2017), to assess the overall morbidity and severity burden of notified dengue. We fitted overall and ethnic-specific models to assess the presence of heterogeneity by SES across and within ethnic groups (Afro-Colombian vs. non-Afro-Colombians), conducting sensitivity analyses to account for potential underreporting.

RESULTS

Our study included 65,402 dengue cases and 13,732 (21%) hospitalizations. Overall notified dengue incidence rates did not vary across ethnic groups. Severity risk was higher among Afro-Colombians (risk ratio [RR] = 1.16; 95% Credible Interval [95% CrI] = 1.08, 1.24) but after accounting for underreporting by ethnicity this association was nearly null (RR = 1.02; 95% CrI = 0.97, 1.07). Subsidized health insurance and low-SES were associated with increased overall dengue rates and severity.

CONCLUSION

The paradoxically increased severity among Afro-Colombians can be attributed to differential health-seeking behaviors and reporting among Afro-Colombians. Such differential reporting can be understood as a type of intersectionality between SES, insurance scheme, and ethnicity that requires a quantitative assessment in future studies.

Measurement Uncertainty in Ecological and Environmental Models

In many applied cases of ecological and environmental modeling there is sizeable variation in the independent variables as a result of measurement and sampling errors. This uncertainty may lead to biased predictions. It is possible to avoid this problem by increased sampling and by modeling the errors using hierarchical modeling.

Accounting for measurement error to assess the effect of air pollution on omic signals

Studies on the effects of air pollution and more generally environmental exposures on health require measurements of pollutants, which are affected by measurement error. This is a cause of bias in the estimation of parameters relevant to the study and can lead to inaccurate conclusions when evaluating associations among pollutants, disease risk and biomarkers. Although the presence of measurement error in such studies has been recognized as a potential problem, it is rarely considered in applications and practical solutions are still lacking. In this work, we formulate Bayesian measurement error models and apply them to study the link between air pollution and omic signals. The data we use stem from the "Oxford Street II Study", a randomized crossover trial in which 60 volunteers walked for two hours in a traffic-free area (Hyde Park) and in a busy shopping street (Oxford Street) of London. Metabolomic measurements were made in each individual as well as air pollution measurements, in order to investigate the association between short-term exposure to traffic related air pollution and perturbation of metabolic pathways. We implemented error-corrected models in a classical framework and used the flexibility of Bayesian hierarchical models to account for dependencies among omic signals, as well as among different pollutants. Models were implemented using traditional Markov Chain Monte Carlo (MCMC) simulative methods as well as integrated Laplace approximation. The inclusion of a classical measurement error term resulted in variable estimates of the association between omic signals and traffic related air pollution measurements, where the direction of the bias was not predictable a priori. The models were successful in including and accounting for different correlation structures, both among omic signals and among different pollutant exposures. In general, more associations were identified when the correlation among omics and among pollutants were modeled, and their number increased when a measurement error term was additionally included in the multivariate models (particularly for the associations between metabolomics and NO2).

Bias in the detection of negative density dependence in plant communities

Regression dilution is a statistical inference bias that causes underestimation of the strength of dependency between two variables when the predictors are error-prone proxies (EPPs). EPPs are widely used in plant community studies focused on negative density-dependence (NDD) to quantify competitive interactions. Because of the nature of the bias, conspecific NDD is often overestimated in recruitment analyses, and in some cases, can be erroneously detected when absent. In contrast, for survival analyses, EPPs typically cause NDD to be underestimated, but underestimation is more severe for abundant species and for heterospecific effects, thereby generating spurious negative relationships between the strength of NDD and the abundances of con- and heterospecifics. This can explain why many studies observed rare species to suffer more severely from conspecific NDD, and heterospecific effects to be disproportionally smaller than conspecific effects. In general, such species-dependent bias is often related to traits associated with likely mechanisms of NDD, which creates false patterns and complicates the ecological interpretation of the analyses. Classic examples taken from literature and simulations demonstrate that this bias has been pervasive, which calls into question the emerging paradigm that intraspecific competition has been demonstrated by direct field measurements to be generally stronger than interspecific competition.

Inbreeding reduces long-term growth of Alpine ibex populations

Many studies document negative inbreeding effects on individuals, and conservation efforts to preserve rare species routinely employ strategies to reduce inbreeding. Despite this, there are few clear examples in nature of inbreeding decreasing the growth rates of populations, and the extent of population-level effects of inbreeding in the wild remains controversial. Here, we take advantage of a long-term dataset of 26 reintroduced Alpine ibex (Capra ibex ibex) populations spanning nearly 100 years to show that inbreeding substantially reduced per capita population growth rates, particularly for populations in harsher environments. Populations with high average inbreeding (F ≈ 0.2) had population growth rates reduced by 71% compared with populations with no inbreeding. Our results show that inbreeding can have long-term demographic consequences even when environmental variation is large and deleterious alleles may have been purged during bottlenecks. Thus, efforts to guard against inbreeding effects in populations of endangered species have not been misplaced.

Statistical Methodology in Studies of Prenatal Exposure to Mixtures of Endocrine-Disrupting Chemicals: A Review of Existing Approaches and New Alternatives

BACKGROUND

Prenatal exposures to endocrine-disrupting chemicals (EDCs) during critical developmental windows have been implicated in the etiologies of a wide array of adverse perinatal and pediatric outcomes. Epidemiological studies have concentrated on the health effects of individual chemicals, despite the understanding that EDCs act together via common mechanisms, that pregnant women are exposed to multiple EDCs simultaneously, and that substantial toxicological evidence of adverse developmental effects has been documented. There is a move toward multipollutant models in environmental epidemiology; however, there is no current consensus on appropriate statistical methods.

OBJECTIVES

We aimed to review the statistical methods used in these studies, to identify additional applicable methods, and to determine the strengths and weaknesses of each method for addressing the salient statistical and epidemiological challenges.

METHODS

We searched Embase, MEDLINE, and Web of Science for epidemiological studies of endocrine-sensitive outcomes in the children of mothers exposed to EDC mixtures during pregnancy and identified alternative statistical methods from the wider literature.

DISCUSSION

We identified 74 studies and analyzed the methods used to estimate mixture health effects, identify important mixture components, account for nonmonotonicity in exposure–response relationships, assess interactions, and identify windows of exposure susceptibility. We identified both frequentist and Bayesian methods that are robust to multicollinearity, performing shrinkage, variable selection, dimension reduction, statistical learning, or smoothing, including methods that were not used by the studies included in our review.

CONCLUSIONS

Compelling motivation exists for analyzing EDCs as mixtures, yet many studies make simplifying assumptions about EDC additivity, relative potency, and linearity, or overlook the potential for bias due to asymmetries in chemical persistence. We discuss the potential impacts of these choices and suggest alternative methods to improve analyses of prenatal exposure to EDC mixtures. https://doi.org/10.1289/EHP2207.

Warming seas increase cold-stunning events for Kemp's ridley sea turtles in the northwest Atlantic

Since the 1970s, the magnitude of turtle cold-stun strandings have increased dramatically within the northwestern Atlantic. Here, we examine oceanic, atmospheric, and biological factors that may affect the increasing trend of cold-stunned Kemp's ridleys in Cape Cod Bay, Massachusetts, United States of America. Using machine learning and Bayesian inference modeling techniques, we demonstrate higher cold-stunning years occur when the Gulf of Maine has warmer sea surface temperatures in late October through early November. Surprisingly, hatchling numbers in Mexico, a proxy for population abundance, was not identified as an important factor. Further, using our Bayesian count model and forecasted sea surface temperature projections, we predict more than 2,300 Kemp's ridley turtles may cold-stun annually by 2031 as sea surface temperatures continue to increase within the Gulf of Maine. We suggest warmer sea surface temperatures may have modified the northerly distribution of Kemp's ridleys and act as an ecological bridge between the Gulf Stream and nearshore waters. While cold-stunning may currently account for a minor proportion of juvenile mortality, we recommend continuing efforts to rehabilitate cold-stunned individuals to maintain population resiliency for this critically endangered species in the face of a changing climate and continuing anthropogenic threats.

Predicted Mercury Soil Concentrations from a Kriging Approach for Improved Human Health Risk Assessment

Health-risks from contaminated soils are assessed all over the world. An aspect that many risk assessments share is the heterogeneity in the distribution of contaminants. In a preceding study, we assessed potential health-risks for mothers and children living on mercury-contaminated soils in Switzerland using human biomonitoring-values (HBM) and soil samples. We assessed 64 mothers and 107 children who had resided in a defined area for at least 3 months. HBM-concentrations for mercury in urine and hair were measured, a detailed questionnaire was administered for each individual, and more than 4000 individual mercury soil values were obtained in 2015. In this study, we aimed at investigating possible associations of mercury soil- and HBM-values by re-analyzing our data, using predictions of the mercury concentrations at the exact location of the participant’s homes with a kriging approach. Although kriging proved to be a useful method to predict mercury soil concentrations, we did not detect an association between mercury soil- and HBM-values, in agreement with earlier findings. Benefits of geostatistical methods seem to be limited in the context of our study. Conclusions made in our preceding study about potential health risks for the residential population are robust and not altered by the current study.

Bayesian Inference for Correlations in the Presence of Measurement Error and Estimation Uncertainty

Whenever parameter estimates are uncertain or observations are contaminated by measurement error, the Pearson correlation coefficient can severely underestimate the true strength of an association. Various approaches exist for inferring the correlation in the presence of estimation uncertainty and measurement error, but none are routinely applied in psychological research. Here we focus on a Bayesian hierarchical model proposed by Behseta, Berdyyeva, Olson, and Kass (2009) that allows researchers to infer the underlying correlation between error-contaminated observations. We show that this approach may be also applied to obtain the underlying correlation between uncertain parameter estimates as well as the correlation between uncertain parameter estimates and noisy observations. We illustrate the Bayesian modeling of correlations with two empirical data sets; in each data set, we first infer the posterior distribution of the underlying correlation and then compute Bayes factors to quantify the evidence that the data provide for the presence of an association.

Principles of Experimental Design for Big Data Analysis

Big Datasets are endemic, but are often notoriously difficult to analyse because of their size, heterogeneity and quality. The purpose of this paper is to open a discourse on the potential for modern decision theoretic optimal experimental design methods, which by their very nature have traditionally been applied prospectively, to improve the analysis of Big Data through retrospective designed sampling in order to answer particular questions of interest. By appealing to a range of examples, it is suggested that this perspective on Big Data modelling and analysis has the potential for wide generality and advantageous inferential and computational properties. We highlight current hurdles and open research questions surrounding efficient computational optimisation in using retrospective designs, and in part this paper is a call to the optimisation and experimental design communities to work together in the field of Big Data analysis.

Bias away from the null due to miscounted outcomes? A case study on the TORCH trial

Count outcomes occur in virtually all disciplines, such as medicine, epidemiology or biology, but they often contain error. Recently, it has been shown that self-reported numbers of exacerbations of Chronic Obstructive Pulmonary Disease patients can be considerably miscounted. Motivated by this result, we reanalysed data from the Towards a Revolution in Chronic Obstructive Pulmonary Disease Health trial, a large randomized controlled trial with the self-reported number of exacerbations of Chronic Obstructive Pulmonary Disease patients as outcome. To adjust for miscounting error in the response of Poisson and (zero-inflated) negative binomial models, we introduce novel, general methodology. The key idea is to formulate a zero-inflated negative binomial model to capture the error mechanism. This parametric approach automatically circumvents drawbacks of previously suggested methodology that treats miscounted outcomes in the misclassification framework. Prior information for the response error model parameters was elicited from validation data of an external study and adaptively weighted to account for potential prior-data conflict. The results of the Bayesian hierarchical modelling approach indicated that the treatment effect has been overestimated in the original study. However, closer inspection revealed that this unexpected result was an artefact of an unaccounted time dependency of the treatment effect.

Meiotic recombination shapes precision of pedigree- and marker-based estimates of inbreeding

The proportion of an individual's genome that is identical by descent (GWIBD) can be estimated from pedigrees (inbreeding coefficient 'Pedigree F') or molecular markers ('Marker F'), but both estimators come with error. Assuming unrelated pedigree founders, Pedigree F is the expected proportion of GWIBD given a specific inbreeding constellation. Meiotic recombination introduces variation around that expectation (Mendelian noise) and related pedigree founders systematically bias Pedigree F downward. Marker F is an estimate of the actual proportion of GWIBD but it suffers from the sampling error of markers plus the error that occurs when a marker is homozygous without reflecting common ancestry (identical by state). We here show via simulation of a zebra finch and a human linkage map that three aspects of meiotic recombination (independent assortment of chromosomes, number of crossovers and their distribution along chromosomes) contribute to variation in GWIBD and thus the precision of Pedigree and Marker F. In zebra finches, where the genome contains large blocks that are rarely broken up by recombination, the Mendelian noise was large (nearly twofold larger s.d. values compared with humans) and Pedigree F thus less precise than in humans, where crossovers are distributed more uniformly along chromosomes. Effects of meiotic recombination on Marker F were reversed, such that the same number of molecular markers yielded more precise estimates of GWIBD in zebra finches than in humans. As a consequence, in species inheriting large blocks that rarely recombine, even small numbers of microsatellite markers will often be more informative about inbreeding and fitness than large pedigrees.

CD4/CD8 ratio and CD8 counts predict CD4 response in HIV-1-infected drug naive and in patients on cART

Plasma HIV viral load is related to declining CD4 lymphocytes. The extent to which CD8 cells, in addition to RNA viral load, predict the depletion of CD4 cells is not well characterized so far. We examine if CD8 cell count is a prognostic factor for CD4 cell counts during an HIV infection.A longitudinal analysis is conducted using data from the Swiss HIV cohort study collected between January 2000 and October 2014. Linear mixed regression models were applied to observations from HIV-1-infected treatment naive patients (NAIVE) and cART-treated patients to predict the short-term evolution of CD4 cell counts. For each subgroup, it was quantified to which extent CD8 cell counts or CD4/CD8 ratios are prognostic factors for disease progression.In both subgroups, 2500 NAIVE and 8902 cART patients, past CD4 cells are positively (P < 0.0001) and past viral load is negatively (P < 0.0001) associated with the outcome. Including additionally past CD8 cell counts improves the fit significantly (P < 0.0001) and increases the marginal explained variation 31.7% to 40.7% for the NAIVE and from 44.1% to 50.7% for the cART group. The past CD4/CD8 ratio (instead of the past CD8 level) is positively associated with the outcome, increasing the explained variation further to 41.8% for NAIVE and 51.9% for cART.

Evaluating vegetation effects on animal demographics: the role of plant phenology and sampling bias

Plant phenological processes produce temporal variation in the height and cover of vegetation. Key aspects of animal life cycles, such as reproduction, often coincide with the growing season and therefore may inherently covary with plant growth. When evaluating the influence of vegetation variables on demographic rates, the decision about when to measure vegetation relative to the timing of demographic events is important to avoid confounding between the demographic rate of interest and vegetation covariates. Such confounding could bias estimated effect sizes or produce results that are entirely spurious. We investigated how the timing of vegetation sampling affected the modeled relationship between vegetation structure and nest survival of greater sage-grouse (Centrocercus urophasianus), using both simulated and observational data. We used the height of live grasses surrounding nests as an explanatory covariate, and analyzed its effect on daily nest survival. We compared results between models that included grass height measured at the time of nest fate (hatch or failure) with models where grass height was measured on a standardized date - that of predicted hatch date. Parameters linking grass height to nest survival based on measurements at nest fate produced more competitive models, but slope coefficients of grass height effects were biased high relative to truth in simulated scenarios. In contrast, measurements taken at predicted hatch date accurately predicted the influence of grass height on nest survival. Observational data produced similar results. Our results demonstrate the importance of properly considering confounding between demographic traits and plant phenology. Not doing so can produce results that are plausible, but ultimately inaccurate.

Two-stage Bayesian model to evaluate the effect of air pollution on chronic respiratory diseases using drug prescriptions

Exposure to high levels of air pollutant concentration is known to be associated with respiratory problems which can translate into higher morbidity and mortality rates. The link between air pollution and population health has mainly been assessed considering air quality and hospitalisation or mortality data. However, this approach limits the analysis to individuals characterised by severe conditions. In this paper we evaluate the link between air pollution and respiratory diseases using general practice drug prescriptions for chronic respiratory diseases, which allow to draw conclusions based on the general population. We propose a two-stage statistical approach: in the first stage we specify a space-time model to estimate the monthly NO2 concentration integrating several data sources characterised by different spatio-temporal resolution; in the second stage we link the concentration to the β2-agonists prescribed monthly by general practices in England and we model the prescription rates through a small area approach.

Network meta-analysis with integrated nested Laplace approximations

Analyzing the collected evidence of a systematic review in form of a network meta-analysis (NMA) enjoys increasing popularity and provides a valuable instrument for decision making. Bayesian inference of NMA models is often propagated, especially if correlated random effects for multiarm trials are included. The standard choice for Bayesian inference is Markov chain Monte Carlo (MCMC) sampling, which is computationally intensive. An alternative to MCMC sampling is the recently suggested approximate Bayesian method of integrated nested Laplace approximations (INLA) that dramatically saves computation time without any substantial loss in accuracy. We show how INLA apply to NMA models for summary level as well as trial-arm level data. Specifically, we outline the modeling of multiarm trials and inference for functional contrasts with INLA. We demonstrate how INLA facilitate the assessment of network inconsistency with node-splitting. Three applications illustrate the use of INLA for a NMA.