Statistical Methods in Medical Research

Inserm has developed, since 1984, an information system based on a computer network of physicians in France. It allows for constitution of large databases on diseases, with individual description of cases, and to explore some aspects of the mathematical theory of communicable diseases. We developed user-friendly interfaces for remote data entry and GIS tools providing real-time atlas of the epidemiologic situation in any location. The continuous and ongoing surveillance network is constituted of about 1200 sentinel voluntary and unpaid investigators. We studied their motivation, reasons for either withdrawal or compliance using survival analyses. We implemented early warning systems for outbreak detection and for time-space forecasting. We conducted epidemiological surveys for investigating outbreaks. Large available time and space series allowed us to calibrate and explore synchronism of influenza epidemics, to test the assumption of panmixing in susceptibles-infectious-removed type models and to study the role of closing school in influenza morbidity and mortality in elderly. More than 250 000 cases of influenza, 150 000 cases of acute diarrheas, 35 000 patients for whom HIV tests have been prescribed by general practitioners and 25 000 cases of chickenpox have been collected. Detection of regional influenza or acute diarrhea outbreaks and forecasting of epidemic trends three weeks ahead are currently broadcasted to the French media and published on Sentiweb© on a weekly basis. Age-cohort-period models assessed field effectiveness of mass immunization strategies against measles and influenza in the country. Case-control studies with more than 1200 sets of cases of acute diarrheas and their matched controls showed the role of calicivirus and rotavirus as probable major causes of gastroenteritis during recurrent widespread outbreaks in winter in France. An age-specific model for chickenpox showed the probable role of children in disease transmission to their susceptible parents or grandparents. High level of synchronism between influenza epidemics has been demonstrated, either at a regional level (in France) or between France and the USA. The designation of our lab as a WHO collaborating center for electronic disease surveillance stimulates the development of global monitoring of diseases. We developed operational systems that are now available for the global monitoring of influenza (FluNet©), and human and animal rabies (RABNET©). Extension of electronic syndromic surveillance is needed in the world for improving surveillance capacities and real-time response against emerging diseases.

Online surveillance of disease has become an important issue in public health. In particular, the space-time monitoring of disease plays an important part in any syndromic system. However, methodology for these systems is generally lacking. One approach to space-time monitoring of health data is to consider the space-time model parameters as the focus and to monitor their changes as multivariate time series (Lawson AB. Some considerations in spatial-temporal analysis of public health surveillance data. In Brookmeyer R, Stroup DF eds. Monitoring the Health of Populations. Oxford University Press, 2004; Vidal Rodeiro CL, Lawson AB. Monitoring changes in spatio-temporal maps of disease. Biometrical Journal 2006; to appear). However with complex space-time models, this becomes very time consuming. Some simplifications may be necessary and these can be made in a number of ways. In this article, the focus is on particle filters that can be used to resample the history of the process and thereby reduce computation time. This article describes a particular case of particle filters, the resample-move algorithm, proposed by Gilks and Berzuini (Gilks WR, Berzuini C. Following a moving target - Monte Carlo inference for dynamic Bayesian models. Journal of the Royal Statistical Society, Series B 2001; 63: 127-46), in the context of disease map surveillance. This is followed by an application to a real data set in which a comparison between the use of Markov chain Monte Carlo methods and the resample-move algorithm is carried out.

Monitoring ongoing processes of illness to detect sudden changes is an important aspect of practical epidemiology and medicine more generally. Most commonly, the monitoring has been restricted to a unidimensional stream of data over time. In such situations, analytic results from the industrial process monitoring have suggested optimal approaches to monitor the data streams. Data streams including spatial location as well as temporal sequence are becoming available. Monitoring methods that incorporate spatial data may prove superior to those that ignore it. However, analytically, optimal methods for spatial surveil-lance data may not exist. In the present article, we introduce and discuss evaluation metrics that can be used to compare the performance of statistical methods of surveillance. Our general approach is to generalize receiver operating characteristic (ROC) curves to incorporate the time of detection in addition to the usual test characteristics of sensitivity and specificity. In addition to weighting ordinary ROC curves by two measures of timeliness, we describe three three-dimensional generalizations of ROC curves that result in timeliness-ROC surfaces. Working in the context of surveillance of cases of disease to detect a sudden outbreak, we demonstrate these in an artificial example and in a previously described simulation context and show how the metrics differ. We also discuss the differences and under which circumstances one might prefer a given method.

A major obstacle in the spatial analysis of infectious disease surveillance data is the problem of under-reporting. This article investigates the possibility of inferring reporting rates through joint statistical modelling of several infectious diseases with different aetiologies. Once variation in under-reporting can be estimated, geographic risk patterns for infections associated with specific food vehicles may be discerned. We adopt the shared component model, proposed by Knorr-Held and Best for two chronic diseases and further extended by (Held L, Natario I, Fenton S, Rue H, Becker N. Towards joint disease mapping. Statistical Methods in Medical Research 2005b; 14: 61-82) for more than two chronic diseases to the infectious disease setting. Our goal is to estimate a shared component, common to all diseases, which may be interpreted as representing the spatial variation in reporting rates. Additional components are introduced to describe the real spatial variation of the different diseases. Of course, this interpretation is only allowed under specific assumptions, in particular, the geographical variation in under-reporting should be similar for the diseases considered. In addition, it is vital that the data do not contain large local outbreaks, so adjustment based on a time series method recently proposed by (Held L, Höhle M, Hofmann M. A statistical framework for the analysis of multivariate infectious disease surveillance data. Statistical Modelling 2005a; 5: 187-99) is made at a preliminary stage. We will illustrate our approach through the analysis of gastrointestinal diseases notification data obtained from the German infectious disease surveillance system, administered by the Robert Koch Institute in Berlin.

This paper is concerned with stochastic models for the spread of an epidemic among a community of households, in which individuals mix uniformly within households and, in addition, uniformly at a much lower rate within the population at large. This two-level mixing structure has important implications for the threshold behaviour of the epidemic and, consequently, for both the effectiveness of vaccination strategies for controlling an outbreak and the form of optimal vaccination schemes. A brief introduction to optimal vaccination schemes in this setting is provided by presenting a unified treatment of the simplest and most-studied case, viz. the single-type SIR (susceptible → infective → removed) epidemic.

A reproduction number R _*, which determines whether a trace of initial infection can give rise to a major epidemic, is derived and the effect of a vaccination scheme on R _* is studied using a general model for vaccine action. In particular, optimal vaccination schemes which reduce R _* to its threshold value of one with minimum vaccination coverage are considered. The theory is illustrated by application to data on a variola minor outbreak in São Paulo, which, together with other examples, is used to highlight key issues related to vaccination schemes.

There is increasing evidence, mainly from daily time series studies, linking air pollution and stroke. Small area level geographical correlation studies offer another means of examining the air pollution-stroke association. Populations within small areas may be more homogeneous than those within larger areal units, and census-based socioeconomic information may be available to adjust for confounding effects. Data on smoking from health surveys may be incorporated in spatial analyses to adjust for potential confounding effects but may be sparse at the small area level. Smoothing, using data from neighbouring areas, may be used to increase the precision of smoking prevalence estimates for small areas. We examined the effect of modelled outdoor NOx levels on stroke mortality using a Bayesian hierarchical spatial model to incorporate random effects, in order to allow for unmeasured confounders and to acknowledge sampling error in the estimation of smoking prevalence. We observed an association between NOx and stroke mortality after taking into account random effects at the small area level. We found no association between smoking prevalence and stroke mortality at the small area level after modelling took into account imprecision in estimating smoking prevalence. The approach we used to incorporate smoking as a covariate in a single large model is conceptually sound, though it made little difference to the substantive results.