Quantifying statistical uncertainty in the attribution of human influence on severe weather

Event attribution in the context of climate change seeks to understand the role of anthropogenic greenhouse gas emissions on extreme weather events, either specific events or classes of events. A common approach to event attribution uses climate model output under factual (real-world) and counterfactual (world that might have been without anthropogenic greenhouse gas emissions) scenarios to estimate the probabilities of the event of interest under the two scenarios. Event attribution is then quantified by the ratio of the two probabilities. While this approach has been applied many times in the last 15 years, the statistical techniques used to estimate the risk ratio based on climate model ensembles have not drawn on the full set of methods available in the statistical literature and have in some cases used and interpreted the bootstrap method in non-standard ways. We present a precise frequentist statistical framework for quantifying the effect of sampling uncertainty on estimation of the risk ratio, propose the use of statistical methods that are new to event attribution, and evaluate a variety of methods using statistical simulations. We conclude that existing statistical methods not yet in use for event attribution have several advantages over the widely-used bootstrap, including better statistical performance in repeated samples and robustness to small estimated probabilities. Software for using the methods is available through the climextRemes package available for R or Python. While we focus on frequentist statistical methods, Bayesian methods are likely to be particularly useful when considering sources of uncertainty beyond sampling uncertainty.Comment: 41 pages, 11 figures, 1 tabl

Semiparametric Bayesian Density Estimation with Disparate Data Sources: A Meta-Analysis of Global Childhood Undernutrition

Undernutrition, resulting in restricted growth, and quantified here using height-for-age z-scores, is an important contributor to childhood morbidity and mortality. Since all levels of mild, moderate and severe undernutrition are of clinical and public health importance, it is of interest to estimate the shape of the z-scores' distributions. We present a finite normal mixture model that uses data on 4.3 million children to make annual country-specific estimates of these distributions for under-5-year-old children in the world's 141 low- and middle-income countries between 1985 and 2011. We incorporate both individual-level data when available, as well as aggregated summary statistics from studies whose individual-level data could not be obtained. We place a hierarchical Bayesian probit stick-breaking model on the mixture weights. The model allows for nonlinear changes in time, and it borrows strength in time, in covariates, and within and across regional country clusters to make estimates where data are uncertain, sparse, or missing. This work addresses three important problems that often arise in the fields of public health surveillance and global health monitoring. First, data are always incomplete. Second, different data sources commonly use different reporting metrics. Last, distributions, and especially their tails, are often of substantive interest.Comment: 41 total pages, 6 figures, 1 tabl

Quantifying the effect of interannual ocean variability on the attribution of extreme climate events to human influence

In recent years, the climate change research community has become highly interested in describing the anthropogenic influence on extreme weather events, commonly termed "event attribution." Limitations in the observational record and in computational resources motivate the use of uncoupled, atmosphere/land-only climate models with prescribed ocean conditions run over a short period, leading up to and including an event of interest. In this approach, large ensembles of high-resolution simulations can be generated under factual observed conditions and counterfactual conditions that might have been observed in the absence of human interference; these can be used to estimate the change in probability of the given event due to anthropogenic influence. However, using a prescribed ocean state ignores the possibility that estimates of attributable risk might be a function of the ocean state. Thus, the uncertainty in attributable risk is likely underestimated, implying an over-confidence in anthropogenic influence. In this work, we estimate the year-to-year variability in calculations of the anthropogenic contribution to extreme weather based on large ensembles of atmospheric model simulations. Our results both quantify the magnitude of year-to-year variability and categorize the degree to which conclusions of attributable risk are qualitatively affected. The methodology is illustrated by exploring extreme temperature and precipitation events for the northwest coast of South America and northern-central Siberia; we also provides results for regions around the globe. While it remains preferable to perform a full multi-year analysis, the results presented here can serve as an indication of where and when attribution researchers should be concerned about the use of atmosphere-only simulations

Measurement error caused by spatial misalignment in environmental epidemiology

Copyright @ 2009 Gryparis et al - Published by Oxford University Press.In many environmental epidemiology studies, the locations and/or times of exposure measurements and health assessments do not match. In such settings, health effects analyses often use the predictions from an exposure model as a covariate in a regression model. Such exposure predictions contain some measurement error as the predicted values do not equal the true exposures. We provide a framework for spatial measurement error modeling, showing that smoothing induces a Berkson-type measurement error with nondiagonal error structure. From this viewpoint, we review the existing approaches to estimation in a linear regression health model, including direct use of the spatial predictions and exposure simulation, and explore some modified approaches, including Bayesian models and out-of-sample regression calibration, motivated by measurement error principles. We then extend this work to the generalized linear model framework for health outcomes. Based on analytical considerations and simulation results, we compare the performance of all these approaches under several spatial models for exposure. Our comparisons underscore several important points. First, exposure simulation can perform very poorly under certain realistic scenarios. Second, the relative performance of the different methods depends on the nature of the underlying exposure surface. Third, traditional measurement error concepts can help to explain the relative practical performance of the different methods. We apply the methods to data on the association between levels of particulate matter and birth weight in the greater Boston area.This research was supported by NIEHS grants ES012044 (AG, BAC), ES009825 (JS, BAC), ES007142 (CJP), and ES000002 (CJP), and EPA grant R-832416 (JS, BAC)

Children’s height and weight in rural and urban populations in low-income and middle-income countries: a systematic analysis of population-representative data

Background Urban living aff ects children’s nutrition and growth, which are determinants of their survival, cognitive development, and lifelong health. Little is known about urban–rural diff erences in children’s height and weight, and how these diff erences have changed over time. We aimed to investigate trends in children’s height and weight in rural and urban settings in low-income and middle-income countries, and to assess changes in the urban–rural diff erentials in height and weight over time. Methods We used comprehensive population-based data and a Bayesian hierarchical mixture model to estimate trends in children’s height-for-age and weight-for-age Z scores by rural and urban place of residence, and changes in urban–rural diff erentials in height and weight Z scores, for 141 low-income and middle-income countries between 1985 and 2011. We also estimated the contribution of changes in rural and urban height and weight, and that of urbanisation, to the regional trends in these outcomes. Findings Urban children are taller and heavier than their rural counterparts in almost all low-income and middleincome countries. The urban–rural diff erential is largest in Andean and central Latin America (eg, Peru, Honduras, Bolivia, and Guatemala); in some African countries such as Niger, Burundi, and Burkina Faso; and in Vietnam and China. It is smallest in southern and tropical Latin America (eg, Chile and Brazil). Urban children in China, Chile, and Jamaica are the tallest in low-income and middle-income countries, and children in rural areas of Burundi, Guatemala, and Niger the shortest, with the tallest and shortest more than 10 cm apart at age 5 years. The heaviest children live in cities in Georgia, Chile, and China, and the most underweight in rural areas of Timor-Leste, India, Niger, and Bangladesh. Between 1985 and 2011, the urban advantage in height fell in southern and tropical Latin America and south Asia, but changed little or not at all in most other regions. The urban–rural weight diff erential also decreased in southern and tropical Latin America, but increased in east and southeast Asia and worldwide, because weight gain of urban children outpaced that of rural children.Interpretation Further improvement of child nutrition will require improved access to a stable and aff ordable food supply and health care for both rural and urban children, and closing of the the urban–rural gap in nutritional status