Elementary Bayesian Biostatistics Lemuel Moye (2008) ISBN: 9781584887249; 400 pages; $79.95, £42.99...
2
Elementary Bayesian Biostatistics Lemuel Moye (2008) ISBN: 9781584887249; 400 pages;$79.95, £42.99 Chapman & Hall/CRC; http://www.crcpress.com The book starts with an introductory Prologue describing the historical development of Bayesian statistics alongside the frequentist approach from the time of the publication of the Bayes’ Theorem in 1763 until the present. Chapter 1 presents some of the basic principles of probability, including independence, union and complement, illustrated with helpful Venn dia- grams. The basic principles are used to define the Law of Total Probability and then derive Bayes’ Theorem. In Chapter 2, compounding is intro- duced. This is described as finding the marginal distribution P(X 5 x) by manipulating a condi- tional distribution P(X 5 x|Y 5 y) and another marginal P(y). Chapter 3 extends the use of compounding and gives worked examples using the binomial with the exponential, the Poisson with the gamma, the gamma with the negative binomial and the normal with the normal. The heavily mathematical proofs required for com- pounding are presented in Appendices. Finally, Chapter 4 completes the development of Bayes’ Theorem by showing how the compounding technique, developed in Chapters 2 and 3, is used to calculate P[y|x] from P[x|y]. Worked examples are given with both discrete and continuous distributions, which show how changes in the prior distribution affect the resulting posterior distribution. As in Chapter 2, problems are presented at the end of the chapter for self-test but no answers are provided. Chapter 5 discusses the different approaches of Bayesian and frequentists to a clinical trial in an imagined three way discussions between a clin- ician, a Bayesian and a frequentist. The result is long winded and would have been more succinctly summarised with a table or a list of points for and against. Methods for developing priors are given in Chapter 6. Most of the chapter is devoted to worked examples. Some of these illustrate occa- sions when the prior belief of the efficacy of a treatment was subsequently shown to be inaccu- rate or even incorrect, a lesson for both Bayesians and frequentists. The ideas of loss and risk quantifying the penalty incurred for incorrect decisions and incorporating them into the process of decision making are developed in Chapter 7. Clear examples of both discrete and continuous loss functions are presented but the figures illustrating the probability of different risks are rather confusing. Chapter 8 gives two examples using techniques developed in the previous chapters. The first derives the probability of the time between a patient having a stroke and the first injection of an anti-clotting agent from the length of stay in hospital. The second estimates the probability of adverse events. The derivations are not straight- forward and use the same advanced calculus required in earlier chapters. Chapter 9 introduces Bayesian sample size. One chapter cannot hope to cover the variety of sample size calculations that are needed in clinical research, for example, two-stage designs in Phase II studies. However, it was disappointing not to find Machin and Campbell’s Sample size tables for clinical studies in the references at the end of the chapter particularly in view of the 14 page appendix that ‘provides an introductory review’ of frequentist sample size calculations. Adaptive Bayes procedures and predictive power methods are presented in Chapter 10. These methods are used, for example, to adjust patient recruitment and end a research project. Chapter 11 uses the problem of predicting the day of ovulation as an example of using Bayesian methods. The prior has been mysteriously acquired from pre- vious months of temperature readings. This would have been a good opportunity to compare a frequentist estimate against a Bayesian one but the reader has to accept that the Bayesian’s posterior is superior. Chapter 12 provides a summary and conclusion by the author but no new Bayesian techniques are given. The mathematical proofs required in the main text are given in the appendices. The mathematics is advanced, which belies the ‘Elementary’ of the title, requiring a good knowledge of probability Copyright r 2009 John Wiley & Sons, Ltd. Pharmaceut. Statist. 2009; 8: 255–258 DOI: 10.1002/pst Book Reviews 257
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Transcript of Elementary Bayesian Biostatistics Lemuel Moye (2008) ISBN: 9781584887249; 400 pages; $79.95, £42.99...
Elementary Bayesian Biostatistics
Lemuel Moye (2008)ISBN: 9781584887249; 400 pages; $79.95, £42.99Chapman & Hall/CRC; http://www.crcpress.com
The book starts with an introductory Prologuedescribing the historical development of Bayesianstatistics alongside the frequentist approach fromthe time of the publication of the Bayes’ Theoremin 1763 until the present.
Chapter 1 presents some of the basic principlesof probability, including independence, union andcomplement, illustrated with helpful Venn dia-grams. The basic principles are used to define theLaw of Total Probability and then derive Bayes’Theorem. In Chapter 2, compounding is intro-duced. This is described as finding the marginaldistribution P(X5 x) by manipulating a condi-tional distribution P(X5 x|Y5 y) and anothermarginal P(y). Chapter 3 extends the use ofcompounding and gives worked examples usingthe binomial with the exponential, the Poissonwith the gamma, the gamma with the negativebinomial and the normal with the normal. Theheavily mathematical proofs required for com-pounding are presented in Appendices. Finally,Chapter 4 completes the development of Bayes’Theorem by showing how the compoundingtechnique, developed in Chapters 2 and 3, is usedto calculate P[y|x] from P[x|y]. Worked examplesare given with both discrete and continuousdistributions, which show how changes in theprior distribution affect the resulting posteriordistribution. As in Chapter 2, problems arepresented at the end of the chapter for self-testbut no answers are provided.
Chapter 5 discusses the different approaches ofBayesian and frequentists to a clinical trial in animagined three way discussions between a clin-ician, a Bayesian and a frequentist. The result islong winded and would have been more succinctlysummarised with a table or a list of points for andagainst. Methods for developing priors are givenin Chapter 6. Most of the chapter is devoted toworked examples. Some of these illustrate occa-sions when the prior belief of the efficacy of a
treatment was subsequently shown to be inaccu-rate or even incorrect, a lesson for both Bayesiansand frequentists. The ideas of loss and riskquantifying the penalty incurred for incorrectdecisions and incorporating them into the processof decision making are developed in Chapter 7.Clear examples of both discrete and continuousloss functions are presented but the figuresillustrating the probability of different risks arerather confusing.
Chapter 8 gives two examples using techniquesdeveloped in the previous chapters. The firstderives the probability of the time between apatient having a stroke and the first injection of ananti-clotting agent from the length of stay inhospital. The second estimates the probability ofadverse events. The derivations are not straight-forward and use the same advanced calculusrequired in earlier chapters.
Chapter 9 introduces Bayesian sample size. Onechapter cannot hope to cover the variety of samplesize calculations that are needed in clinicalresearch, for example, two-stage designs in PhaseII studies. However, it was disappointing not tofind Machin and Campbell’s Sample size tables forclinical studies in the references at the end of thechapter particularly in view of the 14 pageappendix that ‘provides an introductory review’of frequentist sample size calculations.
Adaptive Bayes procedures and predictivepower methods are presented in Chapter 10. Thesemethods are used, for example, to adjust patientrecruitment and end a research project. Chapter 11uses the problem of predicting the day of ovulationas an example of using Bayesian methods. Theprior has been mysteriously acquired from pre-vious months of temperature readings. This wouldhave been a good opportunity to compare afrequentist estimate against a Bayesian one butthe reader has to accept that the Bayesian’sposterior is superior. Chapter 12 provides asummary and conclusion by the author but nonew Bayesian techniques are given.
The mathematical proofs required in the maintext are given in the appendices. The mathematicsis advanced, which belies the ‘Elementary’ of thetitle, requiring a good knowledge of probability
Copyright r 2009 John Wiley & Sons, Ltd. Pharmaceut. Statist. 2009; 8: 255–258DOI: 10.1002/pst
Book Reviews 257
distributions and calculus, for example knowingthat integration is permitted through a summa-tion.
The book is well written. The ideas areintroduced and developed easily with clearlyworked examples in each relevant chapter. How-ever, no examples were given which showed how aBayesian would analyse a clinical trial data andcompare active treatment against placebo. Theadvanced level of the mathematical derivationsmay limit the target audience to practicingstatisticians. While the book is good at introducingBayesian statistical techniques, it may not be sosuccessful in convincing frequentists that these
techniques translate into methods that they couldapply in practice or replace those they use already.
In particular, the concept of confidence intervalis never mentioned and is not even in the index.Bearing in mind that Chapter 5 was devoted todifferences between Bayesian and frequentist, thisomission justifies an explanation. Although it doesnot cover all the information, the book provides agood selection of Bayesian techniques that couldbe applied in the right circumstances.
John Hughes,(DOI: 10.1002/pst.350)
Copyright r 2009 John Wiley & Sons, Ltd. Pharmaceut. Statist. 2009; 8: 255–258DOI: 10.1002/pst
258 Book Reviews
