Bayesian Modelling of Inseparable Space-Time Variation in Disease Risk

This paper proposes a unified framework for a Bayesian analysis of incidence or mortality data in space and time. We introduce four different types of prior distributions for space $\times$ time interaction in extension of a model with only main effects. Each type implies a certain degree of prior dependence for the interaction parameters, and corresponds to the product of one of the two spatial with one of the two temporal main effects. The methodology is illustrated by an analysis of Ohio lung cancer data 1968-88 via Markov chain Monte Carlo simulation. We compare the fit and the complexity of several models with different types of interaction by means of quantities related to the posterior deviance. Our results confirm an epidemiological hypothesis about the temporal development of the association between urbanization and risk factors for cancer

Bayesian Estimation of the Size of a Population

We consider the following problem: estimate the size of a population marked with serial numbers after only a sample of the serial numbers has been observed. Its simplicity in formulation and the inviting possibilities of application make this estimation well suited for an undergraduate level probability course. Our contribution consists in a Bayesian treatment of the problem. For an improper uniform prior distribution, we show that the posterior mean and variance have nice closed form expressions and we demonstrate how to compute highest posterior density intervals. Maple and R code is provided on the authors’ web-page to allow students to verify the theoretical results and experiment with data

A Bayesian geoadditive relative survival analysis of registry data on breast cancer mortality

In this paper we develop a so called relative survival analysis, that is used to model the excess risk of a certain subpopulation relative to the natural mortality risk, i.e. the base risk that is present in the whole population. Such models are typically used in the area of clinical studies, that aim at identifying prognostic factors for disease specific mortality with data on specific causes of death being not available. Our work has been motivated by continuous-time spatially referenced survival data on breast cancer where causes of death are not known. This paper forms an extension of the analyses presented in Sauleau et al. (2007), where those data are analysed via a geoadditive, semiparametric approach, however without allowance to incorporate natural mortality. The usefulness of this relative survival approach is supported by means of a simulated data set

Prognosis of Lung Cancer Mortality in West Germany: A Case Study in Bayesian Prediction. (REVISED, January 2000)

We apply a generalized Bayesian age-period-cohort (APC) model to a dataset on lung cancer mortality in West Germany, 1952-1996. Our goal is to predict future deaths rates until the year 2010, separately for males and females. Since age and period is not measured on the same grid, we propose a generalized APC-model where consecutive cohort parameters represent strongly overlapping birth cohorts. This approach results in a rather large number of parameters, where standard algorithms for statistical inference by Markov chain Monte Carlo (MCMC) methods turn out to be computationally intensive. We propose a more efficient implementation based on ideas of block sampling from the time series literature. We entertain two different formulations, penalizing either first or second differences of age, period and cohort parameters. To assess the predictive quality of both formulations, we first forecast the rates for the period 1987-1996 based on data until 1986. A comparison with the actual observed rates is made based on quantities related to the predictive deviance. Predictions of lung cancer mortality until 2010 both for males and females are finally reported

Hyper-g Priors for Generalized Linear Models

We develop an extension of the classical Zellner's g-prior to generalized linear models. The prior on the hyperparameter g is handled in a flexible way, so that any continuous proper hyperprior f(g) can be used, giving rise to a large class of hyper-g priors. Connections with the literature are described in detail. A fast and accurate integrated Laplace approximation of the marginal likelihood makes inference in large model spaces feasible. For posterior parameter estimation we propose an efficient and tuning-free Metropolis-Hastings sampler. The methodology is illustrated with variable selection and automatic covariate transformation in the Pima Indians diabetes data set.Comment: 30 pages, 12 figures, poster contribution at ISBA 201

Statistical approaches to the surveillance of infectious diseases for veterinary public health

This technical report covers the aspect of using statistical methodology for the monitoring of routinely collected surveillance data in veterinary public health. An account of the Farrington algorithm and Poisson cumulative sum schemes for the detection of aberrations is given with special attention devoted to the occurrence of seasonality and spatial aggregation of the time series. Modelling approaches for retrospective analysis of surveillance counts are described. To illustrate the applicability of the methodology in veterinary public health, data from the surveillance of rabies among fox in Hesse, Germany, are analysed

A stochastic model for multivariate surveillance of infectious diseases

We describe a stochastic model based on a branching process for analyzing surveillance data of infectious diseases that allows to make forecasts of the future development of the epidemic. The model is based on a Poisson branching process with immigration with additional adjustment for possible overdispersion. An extension to a space-time model for the multivariate case is described. The model is estimated in a Bayesian context using Markov Chain Monte Carlo (MCMC) techniques. We illustrate the applicability of the model through analyses of simulated and real data