Background Global and regional projections of mortality and burden of disease by cause for the years 2000, 2010, and 2030 were published by Murray and Lopez in 1996 as part of the Global Burden of Disease project. These projections, which are based on 1990 data, continue to be widely quoted, although they are substantially outdated; in particular, they substantially underestimated the spread of HIV/AIDS. To address the widespread demand for information on likely future trends in global health, and thereby to support international health policy and priority setting, we have prepared new projections of mortality and burden of disease to 2030 starting from World Health Organization estimates of mortality and burden of disease for 2002. This paper describes the methods, assumptions, input data, and results. Methods and Findings Relatively simple models were used to project future health trends under three scenarios—baseline, optimistic, and pessimistic—based largely on projections of economic and social development, and using the historically observed relationships of these with cause-specific mortality rates. Data inputs have been updated to take account of the greater availability of death registration data and the latest available projections for HIV/AIDS, income, human capital, tobacco smoking, body mass index, and other inputs. In all three scenarios there is a dramatic shift in the distribution of deaths from younger to older ages and from communicable, maternal, perinatal, and nutritional causes to noncommunicable disease causes. The risk of death for children younger than 5 y is projected to fall by nearly 50% in the baseline scenario between 2002 and 2030. The proportion of deaths due to noncommunicable disease is projected to rise from 59% in 2002 to 69% in 2030. Global HIV/AIDS deaths are projected to rise from 2.8 million in 2002 to 6.5 million in 2030 under the baseline scenario, which assumes coverage with antiretroviral drugs reaches 80% by 2012. Under the optimistic scenario, which also assumes increased prevention activity, HIV/AIDS deaths are projected to drop to 3.7 million in 2030. Total tobacco-attributable deaths are projected to rise from 5.4 million in 2005 to 6.4 million in 2015 and 8.3 million in 2030 under our baseline scenario. Tobacco is projected to kill 50% more people in 2015 than HIV/AIDS, and to be responsible for 10% of all deaths globally. The three leading causes of burden of disease in 2030 are projected to include HIV/AIDS, unipolar depressive disorders, and ischaemic heart disease in the baseline and pessimistic scenarios. Road traffic accidents are the fourth leading cause in the baseline scenario, and the third leading cause ahead of ischaemic heart disease in the optimistic scenario. Under the baseline scenario, HIV/AIDS becomes the leading cause of burden of disease in middle- and low-income countries by 2015. Conclusions These projections represent a set of three visions of the future for population health, based on certain explicit assumptions. Despite the wide uncertainty ranges around future projections, they enable us to appreciate better the implications for health and health policy of currently observed trends, and the likely impact of fairly certain future trends, such as the ageing of the population, the continued spread of HIV/AIDS in many regions, and the continuation of the epidemiological transition in developing countries. The results depend strongly on the assumption that future mortality trends in poor countries will have a relationship to economic and social development similar to those that have occurred in the higher-income countries.

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Projections of Global Mortality and Burden of Disease from 2002 to 2030

Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

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Modern Applied Statistics With S

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionF if he or she issues the probabilistic forecast F, rather than G ≠ F. It is strictly proper if the maximum is unique. In prediction problems, proper scoring rules encourage the forecaster to make careful assessments and to be honest. In estimation problems, strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand. This article reviews and develops the theory of proper scoring rules on general probability spaces, and proposes and discusses examples thereof. Proper scoring rules derive from convex functions and relate to information measures, entropy functions, and Bregman divergences. In the case of categorical variables, we prove a rigorous version of the ...

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Strictly Proper Scoring Rules, Prediction, and Estimation

One important component of model selection using generalized linear models (GLM) is the choice of a link function. We propose using approximate Bayes factors to assess the improvement in fit over a GLM with canonical link when a parametric link family is used. The approximate Bayes factors are calculated using the Laplace approximations given in [32], together with a reference set of prior distributions. This methodology can be used to differentiate between different parametric link families, as well as allowing one to jointly select the link family and the independent variables. This involves comparing nonnested models and so standard significance tests cannot be used. The approach also accounts explicitly for uncertainty about the link function. The methods are illustrated using parametric link families studied in [12] for two data sets involving binomial responses.

/pdf/choosing-the-link-function-and-accounting-for-link-3wv9f8ha6r.pdf

Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors

In this paper we introduce an exponential continuous time GARCH(p, q) process. It is defined in such a way that it is a continuous time extension of the discrete time EGARCH(p, q) process. We investigate stationarity and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous time GARCH(p, p) model.

An Exponential Continuous-Time GARCH Process

In insurance applications yearly claim totals of different coverage fields are often dependent. In many cases there are numerous claim totals which are zero. A marginal claim distribution will have an additional point mass at zero, hence this probability function (pf) will not be continuous at zero and the cumulative distribution functions will not be uniform. Therefore using a copula approach to model dependency is not straightforward. We will illustrate how to express the joint pf by copulas with discrete and continuous margins. A pair-copula construction will be used for the fit of the continuous copula allowing to choose appropriate copulas for each pair of margins.

Modeling dependent yearly claim totals including zero claims in private health insurance

http://www.stochastik.math.uni-goettingen.de/preprints/sdarticle.pdf

A nonparametric test for similarity of marginals—With applications to the assessment of population bioequivalence

In the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models, several approaches to nonparametric estimation of vine copulas have been proposed. In this article, we extend these approaches and compare them in an extensive simulation study and a real data application. We identify several factors driving the relative performance of the estimators. The most important one is the strength of dependence. No method was found to be uniformly better than all others. Overall, the kernel estimators performed best, but do worse than penalized B-spline estimators when there is weak dependence and no tail dependence.

/pdf/nonparametric-estimation-of-simplified-vine-copula-models-2zzux1oq8p.pdf

Claudia Czado

Papers

Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors

An Exponential Continuous-Time GARCH Process

Modeling dependent yearly claim totals including zero claims in private health insurance

A nonparametric test for similarity of marginals—With applications to the assessment of population bioequivalence

Nonparametric estimation of simplified vine copula models: comparison of methods