Statistical Methods in Spatial Epidemiology

There is currently great interest in spatial epidemiology, as evidenced by the recent publication of two edited volumes devoted to this area.1,2 While it seems clear from a public health perspective that the spatial analysis of disease incidence can be of great benefit in reassuring population's concerns over local hazards, and in determining the success or otherwise of prevention programmes such as screening, the aetiological value of such studies is more controversial, for one extreme view see Rothman.3 Much of this caution stems from many epidemiologists' sceptical view of ecological studies in which data are available at the level of the group with these groups corresponding to areas in a spatial context. It is appealing to use ecological data, however, since it is often routinely available and can offer greater exposure contrasts than provided by individual studies. The interpretation of ecological studies requires great care, however. The analysis of both point and ecological data is considered in the book, in recent years there has been much statistical interest in methods for such data, including the contributions of the author of this volume. This book concentrates on statistical methods and is at a relatively high technical level, the author comments that, ‘… its target audience is largely confined to those with some statistical knowledge and is appropriate for third level degree and postgraduate students in statistics, or epidemiology with a strong statistical background’, and having read the book I find this an accurate assessment. Unfortunately, in places I found the book unnecessarily mathematical, for example, when defining a study window W on page 9, it is stated that, ‘The area of W is denoted by |W|, Lebesgue measure on RII’.2 The book is divided into five introductory chapters, six chapters in which specific topics are examined (disease clustering, putative sources of hazard, disease mapping, surveillance, ecological analyses, infectious disease modeling), and five appendices. A number of case studies are included to illustrate the methodology. The choice of material is quite idiosyncratic and strongly reflects the author's research interests. Consequently I would not recommend the text as a reference, but rather as a book for those with interests in methodological statistical research in spatial epidemiology. It is clear that the author has strong views on a number of issues and it is perhaps unfortunate that he does not indicate opposing opinions. For example, the author strongly disagrees with the use of risk models in relation to a point source of pollution that are simply monotonic in distance from the source, and not more complex allowing, for example, radial and orientation effects. This topic has been discussed in the literature and it is a shame that the exchange between Lawson4 and Diggle and Elliott5 was not included so that at least the interested reader could see a more balanced argument. The author describes statistically sophisticated approaches using a Poisson process formulation, with the use of a clustering model based on an unknown number of clusters. The author is one of the pioneers of this approach in spatial epidemiology. The implementation of such models is described from a Bayesian perspective based on reversible jump Markov chain Monte Carlo. Such methods are on the cutting edge of research in statistics but are far from being routinely applied due to the difficulties of implementation (including the assessment of convergence of the Markov chain) and the unknown robustness with respect to the prior specification. The last point is particularly relevant given the usual situation of sparse and messy data and the need to provide reliable inference. In general issues of data quality (for example errors in numerators and denominators) are not extensively covered in the volume. In my view the general statistical community has spent too much time on finessing methods for accommodating residual spatial dependence due to unmeasured risk factors while neglecting problems due to data inadequacy, the delineation of the role of ecological studies in epidemiology and issues of ecological bias. For a notable exception in which the latter was considered see Prentice and Sheppard6 who suggest an aggregate data approach in which ecological disease incidence may be combined with individual-level data on exposures and confounders. I found a number of errors in the text. For example, on page 178, the normalizing constant is missing from the expression on the left hand side of Bayes' theorem. There are also some non-standard definitions, for example, with respect to ecological analysis the author gives a definition which does not require grouping of data (so that individual level regression analyses in a spatial context are also judged to be ecological). This definition would seem inappropriate since in epidemiology ecological is always associated with grouping, for example, ‘An ecologic or aggregate study focuses on the comparison of groups, rather than individuals’.7 In summary, I found this book interesting and would recommend it to anyone in the author's target audience.