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regression structure may be the primary focus.The marginalized latent variable models allow a�exible choice between modelling the marginalmeans or the conditional means. The marginalizedtransition models separate the dependence on theexposure variables from the dependence on pre-vious response values. Orthogonality propertiesbetween the mean and the dependence parametersin a marginalized model secure robustness for themarginal means. Marginalized models further al-low for simple procedures to determine a suitabledependence model for the data.Chapter 12 on time-dependent covariates is also

new. The temporal order between key exposureand response events is emphasized and exogenousand endogenous covariates are formally de�ned.When covariates are endogenous, then meaning-ful targets for inference need to be formulated aswell as valid methods of estimation. A longitu-dinal study on maternal stress, child illness andmaternal employment illustrates concepts. Thescienti�c questions include (i) Is there an associ-ation between maternal employment and stress?(ii) Is there an association between maternalemployment and child illness? (iii) Do the dataprovide evidence that maternal stress causes childillness? Since stress may be in the causal path-way that leads from employment to illness noadjustment is made for the daily stress indicatorswhen evaluating the dependence of illness on em-ployment. Similarly no adjustment is made forillness in the analysis of employment and stress.Question (iii) raises issues such as ‘does illnessat day t depend on prior stress measured at day(t − k)’ and ‘does illness on day (t − k) pre-dict stress on day t’. A covariate which is botha predictor for the response and is predicted byearlier responses is endogenous. No standard re-gression methods are available to obtain causalstatements when dealing with endogenous covari-ates. Targets for inference are discussed in termsof counterfactual outcomes. Causal e�ects refer tointerventions in the entire population rather thanamong possibly select, observed subgroups. Focus

is on an average response after assignment of thecovariate value rather than the average responsein subgroups after simply observing the covariatestatus. The g-computation algorithm of Robins ispresented as well as estimation using inverse prob-ability of treatment weighting (IPTW).Chapter 13 discusses approaches to dealing

with incomplete data in longitudinal studies, withemphasis on random and informative missing datamechanism. Likelihood inference and generalizedestimating equations when data are missing at ran-dom are dealt with. Selection models and patternmixture models are presented for dropout pro-cesses and sensitivity analyses are recommendedwhen informative missing data is suspected.Chapter 14 discusses additional topics, includingnon-parametric modelling of the mean response,non-linear regression models, joint modelling oflongitudinal measurements and recurrent eventsand multivariate longitudinal data.Like its predecessor, the second edition of

‘Analysis of Longitudinal Data’ provides an ex-cellent bridge between novel concepts in theoret-ical statistics and their potential use in appliedresearch. In particular, I would recommend foranyone dealing with time varying covariates toread chapter 12 carefully. It can—and should—change the way in which data analysis is thoughtof and typically carried out. Some of the orig-inal papers on this topic are easily accessible,while others are more di�cult to penetrate. Thismakes the presentation in chapter 12 all the morevaluable and important.

JUNI PALMGRENDepartment of Mathematical Statistics

Stockholm University andDepartment of Medical Epidemiologyand Biostatistics, Karolinska Institutet

Nobels V�ag 12 A S-171 77 Karolinska InstitutetStockholm, Sweden

(DOI: 10.1002/sim.1701)

4. BAYESIAN DATA ANALYSIS (2nd edn). AndrewGel-man, John B. Carlin, Hal S. Stern and Donald B.Rubin (eds), Chapman & Hall/CRC, Boca Raton,2003. No. of pages: xxv + 668. Price: $59.95.ISBN 1-58488-388-X

The past 15 years have seen a remarkable increasein the use of Bayesian methods in real applica-

tions. This implies that increasing numbers ofstatisticians are learning Bayesian methods, teach-ing them to their students, and discussing themwith their collaborators. It is therefore importantthat good basic teaching materials be available,including textbooks for undergraduate and grad-uate students, as well as for researchers wishingto follow a course of self-study. The 1995 �rst

Copyright ? 2004 John Wiley & Sons, Ltd. Statist. Med. 2004; 23:3397–3403

3402 BOOK REVIEWS

edition of this very popular book proved to be anexcellent resource for all three of these audiences.The �rst editions’s success lay largely in the

choice of material to be included and excluded.While beginning with simple single parametermodels, the book quickly progresses to more real-istic multi-parameter and hierarchical models thatform the core of much Bayesian analysis today.As the title announces, the focus is squarely ondata analysis, with topics such as linear and non-linear models, missing data and model criticismat the forefront, and a wealth of solid practicaladvice sprinkled evenly throughout. Thus, unlikeBerger’s landmark book [1] of 10 years earlier,little space is given to philosophical comparisonsof the di�erent schools of statistical thought, andonly a single examples-oriented chapter is devo-ted to the decision theoretic approach to Bayesiananalysis. On the other hand, while there are dozensof detailed examples, the book does not go as faras the recent titles by Congdon [2; 3] in display-ing the range of complex models available to aBayesian analyst, although it does go much fur-ther than strictly introductory books on Bayesiananalysis [4; 5]. While it does not have the detailedchapter long examples of Berry and Stangl [6],many examples are to medicine. It is not as the-oretical as the o�erings by Bernardo and Smith[7] or O’Hagan [8], but elementary Bayesian the-ory is discussed where needed. Overall, by takingthe middle path, it is simply the best all roundmodern book focussed on data analysis currentlyavailable.One drawback to the �rst edition was that only

a relatively short chapter on computation includ-ing Markov chain Monte Carlo (MCMC) wasincluded, despite the key role played by thesetechniques in the rise of Bayesian analysis inpractice. Thus, naive readers were perhaps led tobelieve that these techniques played a more minorrole than was in fact the case. Readers were alsoleft somewhat on their own when it came to thedetails of computation, as no software or genericalgorithms were presented. Therefore, one neededto consult other books on computation [9; 10]and software [11] to analyse data beyond theexamples in the book. This criticism is partiallyaddressed in the second edition, with an entirenew chapter and several additional sections oncomputation, including recent MCMC techniques,and an appendix brie�y discussing programmingin R and BUGS. The second edition also addsuseful discussions of non-linear models and deci-sion analysis, and a new chapter on the analysisof survey data. There is enough important addi-

tional material here that those with the �rst editionshould seriously consider updating to the newversion.The 22 book chapters are structured into four

main sections: Part I introduces the fundamentalsof Bayesian analysis, including motivation andbackground, simple single and multi-parametermodels, and large sample asymptotic inferences.Part II begins with an introduction to hierarchicalmodels, before going on to chapters on modelchecking and improvement, accounting for thesampling design, and a short chapter on Bayesianinterpretations of frequentist methods. The sec-tion concludes with a nice chapter titled ‘GeneralAdvice’, which could only have been written bya group of statisticians with years of practicalexperience. Part III is on computation, includ-ing both numerical and analytic approximations.Simple and more advanced MCMC methods arediscussed. Part IV is entitled ‘Regression Models’,but in fact goes much further, as long with chapterson linear, generalized, non-linear and hierarchicalregression, there are chapters on robust inference,mixture models, multivariate models includingtime series, missing data, and decision analysis.There are also four appendices, which provide

useful tables of standard families of distributionswith their main properties, some proofs of asymp-totic theorems, and computation.Among the many examples are applications

to medicine, including simple genetics, can-cer mapping, bioassays, pharmacokinetics, non-compliance and radon measurements. There arealso many illustrations in other �elds (rangingfrom politics to chess), but similar models canbe applied to clinical or epidemiological data, sothat they remain relevant to biostatisticians. Theexamples of course do not cover everything a bio-statistician will encounter, for example, survivalanalysis is not mentioned, but there are specialtybooks that �ll in these gaps [6; 12].Conclusion: This review has mentioned a num-

ber of books now available for learning aboutBayesian statistics. Many others are also avail-able, with new titles seeming to appear in everincreasing numbers each month. It is not reason-able to ask that any single volume be the onlysource needed to take a reader from no knowledgeof Bayesian statistics to being an expert in allaspects, including philosophy, theory, modelling,and practical aspects of data analysis includingcomputation. However, when students or col-leagues ask me which book they need to start within order to take them as far as possible down theroad towards analysing their own data, Gelman

Copyright ? 2004 John Wiley & Sons, Ltd. Statist. Med. 2004; 23:3397–3403

BOOK REVIEWS 3403

et al. has been my answer since 1995. The secondedition makes this an even more robust choice.

LAWRENCE JOSEPHDivision of Clinical Epidemiology

Department of MedicineMontreal General Hospital

1650 Cedar AvenueMontreal; Que. Canada H3G 1A4

Department of Epidemiology and BiostatisticsMcGill University

1020 Pine Avenue WestMontreal; Que. Canada H3A 1A2

REFERENCES

1. Berger J. Statistical Decision Theory and BayesianAnalysis. Springer: New York, 1985.

2. Congdon P. Bayesian Statistical Modelling. Wiley:New York, 2001.

3. Congdon P. Applied Bayesian Modelling. Wiley:New York, 2003.

4. Lee P. Bayesian Statistics (2nd edn). OxfordUniversity Press: Oxford, 1997.

5. Berry D. Statistics: A Bayesian Perspective.Duxbury: London, 1996.

6. Berry D, Stangl D. Bayesian Biostatistics. MarcelDekker, New York, 1996.

7. Bernardo J, Smith A. Bayesian Theory. Wiley: NewYork, 1994.

8. O’Hagan A. Kendall’s Advanced Theory ofStatistics: Bayesian Inference, vol. 2B. OxfordUniversity Press: Oxford, 1994.

9. Chen M, Shao Q, Ibrahim J.Monte Carlo Methodsin Bayesian Computation. Springer: New York,2000.

10. Evans M, Swartz T. Approximating Integrals viaMonte Carlo and Deterministic Methods. OxfordUniversity Press: Oxford, 2000.

11. Gilks W, Richardson S, Spiegelhalter D. MarkovChain Monte Carlo Methods in Practice. Chapman& Hall: New York, 1996.

12. Ibrahim J, Chen M, Sinha D. Bayesian SurvivalAnalysis. Springer: New York, 2001.

(DOI: 10.1002/sim.1856)

Copyright ? 2004 John Wiley & Sons, Ltd. Statist. Med. 2004; 23:3397–3403