Frank Tuyl

Global trends and projections for tobacco use, 1990–2025: an analysis of smoking indicators from the WHO Comprehensive Information Systems for Tobacco Control

BACKGROUND Countries have agreed on reduction targets for tobacco smoking stipulated in the WHO global monitoring framework, for achievement by 2025. In an analysis of data for tobacco smoking prevalence from nationally representative survey data, we aimed to provide comprehensive estimates of recent trends in tobacco smoking, projections for future tobacco smoking, and country-level estimates of probabilities of achieving tobacco smoking targets. METHODS We used a Bayesian hierarchical meta-regression modelling approach using data from the WHO Comprehensive Information Systems for Tobacco Control to assess trends from 1990 to 2010 and made projections up to 2025 for current tobacco smoking, daily tobacco smoking, current cigarette smoking, and daily cigarette smoking for 173 countries for men and 178 countries for women. Modelling was implemented in Python with DisMod-MR and PyMC. We estimated trends in country-specific prevalence of tobacco use, projections for future tobacco use, and probabilities for decreased tobacco use, increased tobacco use, and achievement of targets for tobacco control from posterior distributions. FINDINGS During the most recent decade (2000-10), the prevalence of tobacco smoking in men fell in 125 (72%) countries, and in women fell in 156 (88%) countries. If these trends continue, only 37 (21%) countries are on track to achieve their targets for men and 88 (49%) are on track for women, and there would be an estimated 1·1 billion current tobacco smokers (95% credible interval 700 million to 1·6 billion) in 2025. Rapid increases are predicted in Africa for men and in the eastern Mediterranean for both men and women, suggesting the need for enhanced measures for tobacco control in these regions. INTERPRETATION Our findings show that striking between-country disparities in tobacco use would persist in 2025, with many countries not on track to achieve tobacco control targets and several low-income and middle-income countries at risk of worsening tobacco epidemics if these trends remain unchanged. Immediate, effective, and sustained action is necessary to attain and maintain desirable trajectories for tobacco control and achieve global convergence towards elimination of tobacco use. FUNDING Ministry of Health, Labour and Welfare, Japan; Ministry of Education, Culture, Sports and Technology, Japan; Department of Health, Australia; Bloomberg Philanthropies.

A comparison of Bayes-Laplace, Jeffreys, and other priors: the case of zero events

Beta distributions with both parameters equal to 0, ½, or 1 are the usual choices for “noninformative” priors for Bayesian estimation of the binomial parameter. However, as illustrated by two examples from the Bayesian literature, care needs to be taken with parameter values below 1, both for noninformative and informative priors, as such priors concentrate their mass close to 0 and/or 1 and can suppress the importance of the observed data. These examples concern the case of no successes (or failures) and illustrate the informativeness of the Jeffreys prior usually recommended as the “consensus prior.” In particular, the second example suggests that when the binomial parameter is known to be very small, an informative prior from the beta (1, b) family (b > 1) seems appropriate, while a beta (a, b) with a < 1 can be too informative. It is thus argued that sensitivity analysis of an informative prior should be based on a consensus posterior corresponding to the Bayes–Laplace prior rather than the Jeffreys prior.

A Note on Priors for the Multinomial Model

Abstract An “overall objective” prior proposed for the multinomial model is shown to be inadequate in the presence of zero counts. An earlier proposed reference prior for when interest is in a particular category suffers from similar problems. It is argued that there is no need to deviate from the uniform prior proposed by Jeffreys, for which links with a non-Bayesian approach, when prediction is of interest, are shown.

A Method to Handle Zero Counts in the Multinomial Model

ABSTRACT In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.

New prior sampling methods for nested sampling - Development and testing

Nested Sampling is a powerful algorithm for fitting models to data in the Bayesian setting, introduced by Skilling [1]. The nested sampling algorithm proceeds by carrying out a series of compressive steps, involving successively nested iso-likelihood boundaries, starting with the full prior distribution of the problem parameters. The “central problem” of nested sampling is to draw at each step a sample from the prior distribution whose likelihood is greater than the current likelihood threshold, i.e., a sample falling inside the current likelihood-restricted region. For both flat and informative priors this ultimately requires uniform sampling restricted to the likelihood-restricted region. We present two new methods of carrying out this sampling step, and illustrate their use with the lighthouse problem [2], a bivariate likelihood used by Gregory [3] and a trivariate Gaussian mixture likelihood. All the algorithm development and testing reported here has been done with Mathematica® [4].

Simplifying Life Through Bayes: Hints for Practitioners New to Bayesian Inference

This paper explains why it is important to understand Bayesian techniques and how they are advantageous, even at a fundamental level, over the more traditionally taught classical, or frequentist-based, statistical techniques. The authors provide a brief introduction to the Bayesian approach and present an example of a scenario exhibiting some of the beneficial properties of Bayesian methods, including insights gained from their application in industry to overcome classical statistics-based problems. This example shows how Bayesian methods enable straightforward incorporation of constraints that result in sensible estimates, compared with ad hoc, and at times misleading or useless, classical approaches.

Consensus priors for multinomial and binomial ratios

Reference analysis is an objective Bayesian approach to finding non-informative prior distributions. For various models involving nuisance parameters the reference prior has been shown to be superior to the multiparameter Jeffreys prior. In this article, the performance of the reference prior is evaluated for models that are defined at the extremes of parameter ranges, in which case reference and Jeffreys priors are shown to be potentially informative. Two quantities of interest are analyzed: the ratio of two multinomial parameters and the ratio of two independent binomial parameters, where the latter is just one example of inference based on the common 2 × 2 contingency table. For these two specific examples, we show that reference and/or Jeffreys priors lead to overinformative inference in extreme data situations that would seem common in, for example, many medical contexts when interest is in rare events. It is recommended that in the context of noninformative priors and binary data with extreme observed data, practitioners adopt priors for which prior predictive distributions are uniform, as per Bayes’s original argument.

Equidistribution testing with Bayes factors and the ECT

John Skilling’ s Nested Sampling algorithm [9] is a numerical method for fitting models to data in the Bayesian setting, producing estimates of the Bayesian Evidence Z and Information ℋ as well as posterior samples. A central step in the process is the generation of a new random sample from the (typically uniform) prior distribution subject to the constraint that the new prior sample’s likelihood is greater than a current likelihood threshold. One way to test a generation method - the “outside in” approach - is to incorporate it in a Nested Sampling algorithm and compare the resulting model estimates with known cases. Another way - the “inside out” approach - is to validate the uniformity of prior samples produced by the new method before its incorporation in a Nested Sampling system. Using the “inside out” approach, we show that E T Jaynes’ Entropy Concentration Theorem (ECT) [5, 6] and a Bayes Factor test [7] of a particular type provide sensitive tests of uniformity in irregular 2D regions.