Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Disease map reconstruction

The analysis of the geographical distribution of disease incidence or prevalence is now of considerable importance for public health workers and epidemiologists alike. Important disease variations often have a spatial expression and so spatial analysis methods are an important additional tool in this connection. In this tutorial I have aimed to highlight the main issues relating to the analysis of disease where the goal is the reduction in noise in a disease map. This area is sometimes simply called disease mapping. A number of modelling approaches to disease mapping are considered and a case study highlighting the methods advocated is also included.

Cluster modelling of disease incidence via RJMCMC methods: a comparative evaluation. Reversible jump Markov chain Monte Carlo

The spatial modelling of small area health data has, for some time, included spatial autocorrelation as a random effect. This effect is non-specific and global and does not address the location of clusters of disease (a specific task). This paper addresses the need for specific and non-specific random effects within spatial epidemiology. In addition, individual frailty is also considered important and a computational algorithm based on reversible jump Markov chain Monte Carlo (RJMCMC) methods is described.

Controlling for socioeconomic confounding using regression methods

STUDY OBJECTIVE

To describe the advantages of using Poisson regression methods as an alternative to standardisation when computing expected numbers of disease occurrences adjusted for possible confounding factors. The problem of assessing the adequacy of model fit when the expectations are small is addressed by analytical calculations and by simulation. The method is illustrated with data from the national register of childhood tumours.

DESIGN

The tumour data are recorded in a national register.

SETTING

England, Scotland, and Wales.

SUBJECTS

The cases considered are all children registered with leukaemia or non-Hodgkin lymphoma under the age of 15 years between 1966-87.

MAIN RESULTS

The methods show a significant variation of leukaemia incidence in relation to the Register General's standard region and a negative association with socioeconomic deprivation, as measured by the Townsend index. After allowing for these variables, the incidence seems to be reasonably homogeneous throughout the population, in the sense that the residual deviance does not seem to be much larger than would be expected by chance.

CONCLUSIONS

The methods described have major advantages over standardisation in controlling for confounding, both in terms of flexibility of factor selection and assessment and also in the ability to determine whether there is residual variability of incidence after allowing for these factors.