A hierarchical model for space–time surveillance data on meningococcal disease incidence

Summary. We describe a model-based approach to analyse space–time surveillance data on meningococcal disease. Such data typically comprise a number of time series of disease counts, each representing a specific geographical area. We propose a hierarchical formulation, where latent parameters capture temporal, seasonal and spatial trends in disease incidence. We then add—for each area—a hidden Markov model to describe potential additional (autoregressive) effects of the number of cases at the previous time point. Different specifications for the functional form of this autoregressive term are compared which involve the number of cases in the same or in neighbouring areas. The two states of the Markov chain can be interpreted as representing an 'endemic' and a 'hyperendemic' state. The methodology is applied to a data set of monthly counts of the incidence of meningococcal disease in the 94 départements of France from 1985 to 1997. Inference is carried out by using Markov chain Monte Carlo simulation techniques in a fully Bayesian framework. We emphasize that a central feature of our model is the possibility of calculating—for each region and each time point—the posterior probability of being in a hyperendemic state, adjusted for global spatial and temporal trends, which we believe is of particular public health interest.     

A Bayesian approach to sequential analysis in post‐licensure vaccine safety surveillance

With rapid development of computing technology, Bayesian statistics have increasingly gained more attention in various areas of public health. However, the full potential of Bayesian sequential methods applied to vaccine safety surveillance has not yet been realized, despite acknowledged practical benefits and philosophical advantages of Bayesian statistics. In this paper, we describe how sequential analysis can be performed in a Bayesian paradigm in the field of vaccine safety. We compared the performance of the frequentist sequential method, specifically, Maximized Sequential Probability Ratio Test (MaxSPRT), and a Bayesian sequential method using simulations and a real world vaccine safety example. The performance is evaluated using three metrics: false positive rate, false negative rate, and average earliest time to signal. Depending on the background rate of adverse events, the Bayesian sequential method could significantly improve the false negative rate and decrease the earliest time to signal. We consider the proposed Bayesian sequential approach to be a promising alternative for vaccine safety surveillance.     

On the use and evaluation of prospective scan methods for health-related surveillance

Summary.  We review some prospective scan-based methods that are used in health-related applications to detect increased rates of mortality or morbidity and to detect bioterrorism or active clusters of disease. We relate these methods to the use of the moving average chart in industrial applications. Issues that are related to the performance evaluation of spatiotemporal scan-based methods are discussed. In particular we clarify the definition of a recurrence interval and demonstrate that this measure does not reflect some important aspects of the statistical performance of scan-based, and other, surveillance methods. Some research needs in this area are given.     

Using the Cuscore technique in the surveillance of rare health events

An adaptation from Cuscore control charts for normal distributions to the problem of monitoring the rate of occurrence of a rare event is considered. The presented scheme defines an alarm in terms of the sum of ‘scored distances' between successive events of interest. A procedure is given for using this scheme in an ‘optimal’ manner which minimizes the out of control expected delay for a given rate of false alarms. Comparisons over a number of examples, after matching the rate of false alarms, show that the present technique is more efficient than those of Shewhart and Sets, and also than Cusum under conditions of practical relevance.     

Bayesian factor analysis for spatially correlated data: application to cancer incidence data in Scotland

A hierarchical Bayesian factor model for multivariate spatially correlated data is proposed. Multiple cancer incidence data in Scotland are jointly analyzed, looking for common components, able to detect etiological factors of diseases hidden behind the data. The proposed method searches factor scores incorporating a dependence within observations due to a geographical structure. The great flexibility of the Bayesian approach allows the inclusion of prior opinions about adjacent regions having highly correlated observable and latent variables. The proposed model is an extension of a model proposed by Rowe (2003a) and starts from the introduction of separable covariance matrix for the observations. A Gibbs sampling algorithm is implemented to sample from the posterior distributions.     

A statistical signalling model for use in surveillance of adverse drug reaction data

SUMMARY This paper presents a statistically superior lag-adjusted model for detecting increased frequency of reports of adverse drug event (ADE) rates. The effect of a significant lag time between ADE occurrence and report dates is studied. The approach in this paper to analyzing ADE data of this nature involves proposing a statistical model that utilizes a lag density function. The statistical method proposed was the development of an 'exact' procedure to monitor drugs that have a low incidence of ADEs. The approach determines statistically whether a change in the frequency of a specific ADE exists between two predetermined time intervals. There exist immense public health implications associated with the early detection of serious ADEs. The reduced risk of unfavorable outcomes associated with medication therapy is the goal of all involved. Simulated illustrations and discussion are provided, along with a detailed FORTRAN program used to implement the newly suggested lag-adjusted procedure.     

GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar–Fisz transform

Summary.  We consider the stochastic mechanisms behind the data that were collected by the solar X-ray sensor (XRS) on board the GOES-8 satellite. We discover and justify a non-trivial mean–variance relationship within the XRS data. Transforming such data so that their variance is stable and its distribution is taken closer to the Gaussian distribution is the aim of many techniques (e.g. Anscombe and Box–Cox). Recently, new techniques based on the Haar–Fisz transform have been introduced that use a multiscale method to transform and stabilize data with a known mean–variance relationship. In many practical cases, such as the XRS data, the variance of the data can be assumed to increase with the mean, but other characteristics of the distribution are unknown. We introduce a method, the data-driven Haar–Fisz transform, which uses the Haar–Fisz transform but also estimates the mean–variance relationship. For known noise distributions, the data-driven Haar–Fisz transform is shown to be competitive with the fixed Haar–Fisz methods. We show how our data-driven Haar–Fisz transform method denoises the XRS series where other existing methods fail.     

A computational algorithm for the loss probability in the M/G/1+PH queue

This article develops a computational algorithm for the loss probability in the stationary M/G/1 queue with impatient customers whose impatience times follow a phase-type distribution (M/G/1+PH). The algorithm outputs the loss probability, along with an upper-bound of its numerical error due to truncation, and it is readily applicable to the M/D/1+PH, M/PH/1+PH, and M/Pareto/1+PH queues.     

On the Use of the Importance Measure for Multi-State Repairable k-out-of-n: G Systems

Importance measures in reliability systems are used to identify weak components in contributing to proper functioning of the system. Traditional importance measures mainly concern the change of the system reliability as the change of the reliability of one component and seldom consider the expected number of repairs of the objective component in unit time. This paper proposes an improvement potential rate importance (IPR) to verify the effectiveness of the improvement in system reliability for multi-state repairable k-out-of-n: G systems. Then the comparisons between IPR and Birnbaum importance are discussed. Finally, a case study is given to demonstrate the proposed IPR.     

Bayesian estimation for the M/G/1 queue using a phase-type approximation

This article deals with Bayesian inference and prediction for M/G/1 queueing systems. The general service time density is approximated with a class of Erlang mixtures which are phase-type distributions. Given this phase-type approximation, an explicit evaluation of measures such as the stationary queue size, waiting time and busy period distributions can be obtained. Given arrival and service data, a Bayesian procedure based on reversible jump Markov Chain Monte Carlo methods is proposed to estimate system parameters and predictive distributions.     

Outliers and Model Selection: Discussion of the Paper by Søren Johansen and Bent Nielsen

It is argued that model selection and robust estimation should be handled jointly. Impulse indicator saturation makes that possible, but leads to the situation where there are more variables than observations. This is illustrated by revisiting the analysis of Tobin's food data.     

Aspects on the control of false alarms in statistical surveillance and the impact on the return of financial decision systems

In systems for online detection of regime shifts, a process is continually observed. Based on the data available an alarm is given when there is enough evidence of a change. There is a risk of a false alarm and here two different ways of controlling the false alarms are compared: a fixed average run length until the first false alarm and a fixed probability of any false alarm (fixed size). The two approaches are evaluated in terms of the timeliness of alarms. A system with a fixed size is found to have a drawback: the ability to detect a change deteriorates with the time of the change. Consequently, the probability of successful detection will tend to zero and the expected delay of a motivated alarm tends to infinity. This drawback is present even when the size is set to be very large (close to one). Utility measures expressing the costs for a false or a too late alarm are used in the comparison. How the choice of the best approach can be guided by the parameters of the process and the different costs of alarms is demonstrated. The technique is illustrated by financial transactions of the Hang Seng Index.     

Estimating the variance for heterogeneity in arm‐based network meta‐analysis

Network meta‐analysis can be implemented by using arm‐based or contrast‐based models. Here we focus on arm‐based models and fit them using generalized linear mixed model procedures. Full maximum likelihood (ML) estimation leads to biased trial‐by‐treatment interaction variance estimates for heterogeneity. Thus, our objective is to investigate alternative approaches to variance estimation that reduce bias compared with full ML. Specifically, we use penalized quasi‐likelihood/pseudo‐likelihood and hierarchical (h) likelihood approaches. In addition, we consider a novel model modification that yields estimators akin to the residual maximum likelihood estimator for linear mixed models. The proposed methods are compared by simulation, and 2 real datasets are used for illustration. Simulations show that penalized quasi‐likelihood/pseudo‐likelihood and h‐likelihood reduce bias and yield satisfactory coverage rates. Sum‐to‐zero restriction and baseline contrasts for random trial‐by‐treatment interaction effects, as well as a residual ML‐like adjustment, also reduce bias compared with an unconstrained model when ML is used, but coverage rates are not quite as good. Penalized quasi‐likelihood/pseudo‐likelihood and h‐likelihood are therefore recommended.     

Gaining acceptability for the Bayesian decision‐theoretic approach in dose‐escalation studies

There has recently been increasing demand for better designs to conduct first‐into‐man dose‐escalation studies more efficiently, more accurately and more quickly. The authors look into the Bayesian decision‐theoretic approach and use simulation as a tool to investigate the impact of compromises with conventional practice that might make the procedures more acceptable for implementation. Copyright © 2005 John Wiley & Sons, Ltd.     

Goodness‐of‐fit tests for the hyperbolic distribution

The authors give tests of fit for the hyperbolic distribution, based on the Cramér‐von Mises statistic W². They consider the general case with four parameters unknown, and some specific cases where one or two parameters are fixed. They give two examples using stock price data.