Chronic airflow obstruction attributable to poverty in the multinational Burden of Obstructive Lung Disease (BOLD) study

Poverty is strongly associated with all-cause and chronic obstructive pulmonary disease (COPD) mortality. Less is known about the contribution of poverty to spirometrically defined chronic airflow obstruction (CAO)-a key characteristic of COPD. Using cross-sectional data from an asset-based questionnaire to define poverty in 21 sites of the Burden of Obstructive Lung Disease study, we estimated the risk of CAO attributable to poverty. Up to 6% of the population over 40 years had CAO attributable to poverty. Understanding the relationship between poverty and CAO might suggest ways to improve lung health, especially in low-income and middle-income countries.

BIMAM—a tool for imputing variables missing across datasets using a Bayesian imputation and analysis model

Motivation

Combination of multiple datasets is routine in modern epidemiology. However, studies may have measured different sets of variables; this is often inefficiently dealt with by excluding studies or dropping variables. Multilevel multiple imputation methods to impute these ‘systematically’ missing data (as opposed to ‘sporadically’ missing data within a study) are available, but problems may arise when many random effects are needed to allow for heterogeneity across studies. We show that the Bayesian IMputation and Analysis Model (BIMAM) implemented in our tool works well in this situation.

General features

BIMAM performs imputation and analysis simultaneously. It imputes both binary and continuous systematically and sporadically missing data, and analyses binary and continuous outcomes. BIMAM is a user-friendly, freely available tool that does not require knowledge of Bayesian methods. BIMAM is an R Shiny application. It is downloadable to a local machine and it automatically installs the required freely available packages (R packages, including R2MultiBUGS and MultiBUGS).

Availability

BIMAM is available at [www.alecstudy.org/bimam].

Prevalence and Population Attributable Risk for Chronic Airflow Obstruction in a Large Multinational Study

Rationale: The Global Burden of Disease programme identified smoking, and ambient and household air pollution as the main drivers of death and disability from Chronic Obstructive Pulmonary Disease (COPD). Objective: To estimate the attributable risk of chronic airflow obstruction (CAO), a quantifiable characteristic of COPD, due to several risk factors. Methods: The Burden of Obstructive Lung Disease study is a cross-sectional study of adults, aged≥40, in a globally distributed sample of 41 urban and rural sites. Based on data from 28,459 participants, we estimated the prevalence of CAO, defined as a post-bronchodilator one-second forced expiratory volume to forced vital capacity ratio < lower limit of normal, and the relative risks associated with different risk factors. Local RR were estimated using a Bayesian hierarchical model borrowing information from across sites. From these RR and the prevalence of risk factors, we estimated local Population Attributable Risks (PAR). Measurements and Main Results: Mean prevalence of CAO was 11.2% in men and 8.6% in women. Mean PAR for smoking was 5.1% in men and 2.2% in women. The next most influential risk factors were poor education levels, working in a dusty job for ≥10 years, low body mass index (BMI), and a history of tuberculosis. The risk of CAO attributable to the different risk factors varied across sites. Conclusions: While smoking remains the most important risk factor for CAO, in some areas poor education, low BMI and passive smoking are of greater importance. Dusty occupations and tuberculosis are important risk factors at some sites.

On point estimation of the abnormality of a Mahalanobis index

Mahalanobis distance may be used as a measure of the disparity between an individual’s profile of scores and the average profile of a population of controls. The degree to which the individual’s profile is unusual can then be equated to the proportion of the population who would have a larger Mahalanobis distance than the individual. Several estimators of this proportion are examined. These include plug-in maximum likelihood estimators, medians, the posterior mean from a Bayesian probability matching prior, an estimator derived from a Taylor expansion, and two forms of polynomial approximation, one based on Bernstein polynomial and one on a quadrature method. Simulations show that some estimators, including the commonly-used plug-in maximum likelihood estimators, can have substantial bias for small or moderate sample sizes. The polynomial approximations yield estimators that have low bias, with the quadrature method marginally to be preferred over Bernstein polynomials. However, the polynomial estimators sometimes yield infeasible estimates that are outside the 0–1 range. While none of the estimators are perfectly unbiased, the median estimators match their definition; in simulations their estimates of the proportion have a median error close to zero. The standard median estimator can give unrealistically small estimates (including 0) and an adjustment is proposed that ensures estimates are always credible. This latter estimator has much to recommend it when unbiasedness is not of paramount importance, while the quadrature method is recommended when bias is the dominant issue.

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We seek an estimate of the population proportion with extreme Mahalanobis index.

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Nine point estimates are examined in an extensive simulation study.

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Maximum likelihood estimates have substantial bias.

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Methods based on polynomial approximations give low bias, but can be out-of-range.

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An adapted median estimator that always gives sensible estimates is proposed.

Eliciting prior distributions for extra parameters in some generalized linear models

To elicit an informative prior distribution for a normal linear model or a gamma generalized linear model (GLM), expert opinion must be quantified about both the regression coefficients and the extra parameters of these models. The latter task has attracted comparatively little attention. In this article, we introduce two elicitation methods that aim to complete the prior structure of the normal and gamma GLMs. First, we develop a method of assessing a conjugate prior distribution for the error variance in normal linear models. The method quantifies an expert's opinions through assessments of a median and conditional medians. Second, we propose a novel method for eliciting a lognormal prior distribution for the scale parameter of gamma GLMs. Given the mean value of a gamma distributed response variable, the method is based on conditional quartile assessments. It can also be used to quantify an expert's opinion about the prior distribution for the shape parameter of any gamma random variable, if the mean of the distribution has been elicited or is assumed to be known. In the context of GLMs, the mean value is determined by the regression coefficients. Interactive graphics is the medium through which assessments for the two proposed methods are elicited. Examples illustrating use of the methods are given. Computer programs that implement both methods are available.