A Bayesian information criterion for singular models

We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher-information matrices may fail to be invertible along other competing submodels. Such singular models do not obey the regularity conditions underlying the derivation of Schwarz's Bayesian information criterion (BIC) and the penalty structure in BIC generally does not reflect the frequentist large-sample behavior of their marginal likelihood. While large-sample theory for the marginal likelihood of singular models has been developed recently, the resulting approximations depend on the true parameter value and lead to a paradox of circular reasoning. Guided by examples such as determining the number of components of mixture models, the number of factors in latent factor models or the rank in reduced-rank regression, we propose a resolution to this paradox and give a practical extension of BIC for singular model selection problems

Lexis: An R Class for Epidemiological Studies with Long-Term Follow-Up

The Lexis class in the R package Epi provides an object-based framework for managing follow-up time on multiple time scales, which is an important feature of prospective epidemiological studies with long duration. Follow-up time may be split either into fixed time bands, or on individual event times and the split data may be used in Poisson regression models that account for the evolution of disease risk on multiple time scales. The summary and plot methods for Lexis objects allow inspection of the follow-up times.

Using Lexis Objects for Multi-State Models in R

The Lexis class in the R package Epi provides tools for creation, manipulation and display of data from multi-state models. Transitions between states are described by rates (intensities); Lexis objects represent this kind of data and provide tools to show states and transitions annotated by relevant summary numbers. Data can be transformed to a form that allows modelling of several transition rates with common parameters.

Lexis: An R Class for Epidemiological Studies with Long-Term Follow-Up

The Lexis class in the R package Epi provides an object-based framework for managing follow-up time on multiple time scales, which is an important feature of prospective epidemiological studies with long duration. Follow-up time may be split either into fixed time bands, or on individual event times and the split data may be used in Poisson regression models that account for the evolution of disease risk on multiple time scales. The summary and plot methods for Lexis objects allow inspection of the follow-up times

Using Lexis Objects for Multi-State Models in R

The Lexis class in the R package Epi provides tools for creation, manipulation and display of data from multi-state models. Transitions between states are described by rates (intensities); Lexis objects represent this kind of data and provide tools to show states and transitions annotated by relevant summary numbers. Data can be transformed to a form that allows modelling of several transition rates with common parameters

A Note on Bayesian Modeling Specification of Censored Data in JAGS

Just Another Gibbs Sampling (JAGS) is a convenient tool to draw posterior samples using Markov Chain Monte Carlo for Bayesian modeling. However, the built-in function dinterval() to model censored data misspecifies the computation of deviance function, which may limit its usage to perform likelihood based model comparison. To establish an automatic approach to specify the correct deviance function in JAGS, we propose a simple alternative modeling strategy to implement Bayesian model selection for analysis of censored outcomes. The proposed approach is applicable to a broad spectrum of data types, which include survival data and many other right-, left- and interval-censored Bayesian model structures

Correction: On Bayesian modeling of censored data in JAGS

Following the publication of the original article [1], the authors identified errors in the model specifications 1 and 2. The correct models are given below

How vague is vague? How informative is informative? Reference analysis for Bayesian meta‐analysis

Meta-analysis provides important insights for evidence-based medicine by synthesizing evidence from multiple studies which address the same research question. Within the Bayesian framework, meta-analysis is frequently expressed by a Bayesian normal-normal hierarchical model (NNHM). Recently, several publications have discussed the choice of the prior distribution for the between-study heterogeneity in the Bayesian NNHM and used several “vague” priors. However, no approach exists to quantify the informativeness of such priors, and thus, we develop a principled reference analysis framework for the Bayesian NNHM acting at the posterior level. The posterior reference analysis (post-RA) is based on two posterior benchmarks: one induced by the improper reference prior, which is minimally informative for the data, and the other induced by a highly anticonservative proper prior. This approach applies the Hellinger distance to quantify the informativeness of a heterogeneity prior of interest by comparing the corresponding marginal posteriors with both posterior benchmarks. The post-RA is implemented in the freely accessible R package ra4bayesmeta and is applied to two medical case studies. Our findings show that anticonservative heterogeneity priors produce platykurtic posteriors compared with the reference posterior, and they produce shorter 95% credible intervals (CrI) and optimistic inference compared with the reference prior. Conservative heterogeneity priors produce leptokurtic posteriors, longer 95% CrI and cautious inference. The novel post-RA framework could support numerous Bayesian meta-analyses in many research fields, as it determines how informative a heterogeneity prior is for the actual data as compared with the minimally informative reference prior

Global burden of cancers attributable to infections in 2012:a synthetic analysis

Background Infections with certain viruses, bacteria, and parasites are strong risk factors for specifi c cancers. As new cancer statistics and epidemiological fi ndings have accumulated in the past 5 years, we aimed to assess the causal involvement of the main carcinogenic agents in diff erent cancer types for the year 2012. Methods We considered ten infectious agents classifi ed as carcinogenic to human beings by the International Agency for Research on Cancer. We calculated the number of new cancer cases in 2012 attributable to infections by country, by combining cancer incidence estimates (from GLOBOCAN 2012) with estimates of attributable fraction (AF) for the infectious agents. AF estimates were calculated from the prevalence of infection in cancer cases and the relative risk for the infection (for some sites). Estimates of infection prevalence, relative risk, and corresponding 95% CIs for AF were obtained from systematic reviews and pooled analyses. Findings Of 14 million new cancer cases in 2012, 2·2 million (15·4%) were attributable to carcinogenic infections. The most important infectious agents worldwide were Helicobacter pylori (770 000 cases), human papillomavirus (640 000), hepatitis B virus (420 000), hepatitis C virus (170 000), and Epstein-Barr virus (120 000). Kaposi’s sarcoma was the second largest contributor to the cancer burden in sub-Saharan Africa. The AFs for infection varied by country and development status—from less than 5% in the USA, Canada, Australia, New Zealand, and some countries in western and northern Europe to more than 50% in some countries in sub-Saharan Africa. Interpretation A large potential exists for reducing the burden of cancer caused by infections. Socioeconomic development is associated with a decrease in infection-associated cancers; however, to reduce the incidence of these cancers without delay, population-based vaccination and screen-and-treat programmes should be made accessible and available