non-gamma frailty, and perhaps something oncompeting risks. I was disappointed also not to betold the true model when the authors used a smallsimulation study to illustrate use of scaled Schoen-feld residuals, to help judge their necessarilysubjective interpretation of plots. Even more mi-nor, the phrase &survivorship function' is awful} &survival' or &survivor' are both better.

The book is aimed at beginners in applied medi-cal survival analysis, especially those with ratherlittle statistical background. For more experienced

readers it forms a refresher in good practice, andalthough some of the descriptions might befound a little laborious, lots of topics are at leasttouched on, and an up-to-date reference list isprovided for advanced techniques.

ROBIN HENDERSON

Department of MathematicsUniversity of Lancaster

Lancaster LA1 4YL, U.K.

2. STATISTICS FOR THE ENVIRONMENT 4. STATIST-

ICAL ASPECTS OF HEALTH AND THE ENVIRONMENT.Vic Barnett, Alfred Stein and K. Feridun Turkman(eds),. Wiley, London, 1999. No. of pages: xv#404.Price: @95. IBSN 0-4719-7645-8

This volume is a collection of 20 papers from thefourth international SPRUCE (Statistics in PublicResources, Utilities and in Care of the Environ-ment) conference, held in September 1997, andedited by Vic Barnett, Alfred Stein and K. FeridunTurkman. The editors mention in their prefacethat the book includes all of the invited as well asselected contributed papers, organized into "vebroad categories. These are listed below togetherwith the titles of the articles in each section.

Part I: Small area studies and disease mapping1. Small-area studies of environment and

health2. Bayesian analysis of ecological data for

studying the association between insulin-de-pendent diabetes and malaria

3. On the analysis of spatial point process datawith inaccurately observed covariate in-formation

4. Geographical and statistical patterns ofcholera

Part II: Atmospheric pollution studies5. Quantifying the risks from residential radon6. Human health e!ects of environmental pol-

lution in the atmosphere7. Using spatial data in assessing the associ-

ation between air pollution episodes andrespiratory morbidity

8. Spatial models of pollution exposure froma road network: the e!ect on asthma

Part III: Disease and social e!ects9. Deriving safe exposure levels from animal

studies using statistical methods: recent de-velopments

10. What's the point? Exploring the spatial epi-demiology of motor neurone disease in partof north-west England

11. Decline of semen quality during the last 50years and possible links with environmentalchemicals

12. Quantitative risk assessment for develop-mental toxicants in non-homogeneouspopulations

13. An approach to intervention analysis inspatio-temporal modelling

Part IV: E!ects of radiation14. Stochastic models for estimation and pre-

diction of cancer risk15. Bayesian modelling of measurement error

problems with reference to the analysis ofatomic bomb survivor data

16. Piecewise linear Cox model for estimatingrelative risks adjusting for the heterogeneityof the sample

Part V: Agriculture and the food chain17. Environmental threshold values for agricul-

tural production systems varying in spaceand time

18. Linear and non-linear kriging methods:tools for monitoring soil pollution

19. Bayesian discrimination with uncertaincovariates for pesticide contamination

20. Assessing monitoring strategies by statist-ical methods } application to soil contami-nation studies

The "ve topics cover a broad spectrum of statist-ical applications to environmental data. Parts I, II,IV and to some extent V, covering geostatisticalmethods, are areas of specialization involving spe-ci"c kinds of data and statistical methods thathave been developed speci"cally for these applica-tions. For these Parts the initial article providesa good introduction to the topic, with the possibleexception of Part V, where the second article (18)"lls this role. In Part I, the introductory article (1)

1824 BOOK REVIEWS

Copyright ( 2000 John Wiley & Sons, Ltd. Statist. Med. 2000; 19:1823}1830

is an excellent introduction to small area studies,geographical studies of disease based on local vari-ation in disease rates and explonatory environ-mental factors. The article contains a wealth ofmaterial on epidemiological issues such as thesources and limitations of data on health out-comes, environmental exposure and confoundingvariables. There is also a useful sketch of recentlyproposed statistical models, with references to theliterature. The article concludes with discussionand illustration of four types of small area studies,point and line source exposures, disease mapping,geographical correlation and investigation of dis-ease clusters.

In Part II, article 5 provides a review of studiesof the health e!ects of exposure to residential ra-don gas. The dosimetry problems in this area ofresearch seem to be unusually di$cult. However,many, if not most, kinds of environmental expo-sures have longitudinal as well as geographicalcomponents, and problems with accurately recap-itulating complex exposure histories may not befully appreciated by some investigators. In Part IVthe article by S. H. Moolgavkar (14) provides aninteresting review of multi-stage models for car-cinogenesis. The discussion begins with a review ofthe original Armitage}Doll model, and proceedsto more recent developments. Su$cient detail isprovided to give the reader an overview of thestructure of these models, and references to theliterature are provided. An illustration is includedof model "tting using data from survivors of theatomic bomb attacks on Hiroshima and Nagasaki.Part III contains two papers on quantitative risk

assessment (9 and 12), a study of motor neuronedisease using point process methodology (also dis-cussed in article 3), and a study involving spatio-temporal modelling of a river system (13). Thearticle by Keiding (11) provides a window intowhat is apparently an intense debate that is stillongoing in the scienti"c community. The article isbrief but contains numerous references. Amongmany important issues Keiding criticizes the tend-ency to haggle about statistical models instead ofdealing with more di$cult questions of interpreta-tion involving the inherent epidemiological limita-tions of observational and particularly ecologicstudies.

These papers are written for the non-specialist,although technical ideas are discussed in generalterms. Many of these papers also include interest-ing background material on the medical and/orenvironmental aspects of the problem under study.An integrated index is included, and many of thereferences are to original methodological articles.In summary this volume is a useful collection foranyone wishing to get the #avour of modern en-vironmetrics, both in terms of sources of data, aswell as developing trends in statistical methodo-logy. The price is typical for books of this sort (@95,U.S. $180), but worth the investment for the inter-ested reader.

CHRISTOPHER COX

Department of BiostatisticsUniversity of Rochester

Box 630, Rochester,NY 14642, U.S.A.

3. THEORY OF SAMPLE SURVEYS. M. E. Thompson,Chapman & Hall, London, 1997. No. of pages:xiv#305. Price: @39.95. ISBN 0-412-31780-X

The theory of sample surveys has been developingvastly in the past 50 years. In addition to theclassical "nite population theory (design-basedtheory) the approaches more similar to othermathematical statistics have started to develop,often termed as model-based, model-design-based,model-assisted or prediction theory. The generalsampling theory today can be viewed as consistingof locally well-developed branches without system-atized joint treatment of these branches. This bookful"ls this task, and is therefore very much wel-comed. It has been written from a foundationalperspective on a solid mathematical basis. Results

are given with proofs or their outlines. Di!erentapproaches are justi"ed with connection pointsbetween them discussed. The material is presentedin a compressed but clear manner. It includesplenty of references to relevant sources and is illus-trated with many examples.

The material is presented in seven chapters. InChapters 1 and 2 the notions and the mathematicsof probability sampling designs are presented.Here the distributions considered are the design-based distributions. The estimation under classicalsampling designs is presented and the design-basedproperties of estimators explained. Some space isgiven to describe the implementation of unequalprobability sampling designs with "xed samplesize. Somewhat unusual in the sampling literatureis the section of "nite population cumulants.

BOOK REVIEWS 1825

Copyright ( 2000 John Wiley & Sons, Ltd. Statist. Med. 2000; 19:1823}1830