RE: "USE OF A BAYESIAN APPROACH TO DECIDE WHEN TO STOP A THERAPEUTIC TRIAL: THE CASE OF A CHEMOPROPHYLAXIS TRIAL IN HUMAN IMMUNODEFICIENCY VIRUS INFECTION"

Paulus A. H. van Noord1 and Ingeborg van der Tweel2

1 Julius Center, Universitaire Medisch Centrum Utrecht, 3508 GA Utrecht, the Netherlands
2 Center for Biostatistics, Utrecht University, 3508 TC Utrecht, the Netherlands

P.A.H.vanNoord{at}UMCUtrecht.nl

We read the article by Kpozèhuoen et al. (1Go) in the March 15, 2005, issue of the Journal with interest. As a methodological exercise, their Bayesian simulations are an important contribution in exploring the impact of different priors on reducing the size of a clinical acquired immunodeficiency syndrome trial. To compare the claimed efficiency gained by means of this Bayesian approach with an alternative method (2Go, 3Go), we performed a sequential statistical analysis using the specifications given in the paper.

The information presented in Kpozèhuoen et al.'s Materials and Methods section (645 subjects required in a fixed-sample-size approach to detect a 30 percent reduction in serious complications with an alpha value of 5 percent, a power of 90 percent, and a 40 percent expected prevalence of serious outcomes in the placebo arm) allowed us to construct sequential boundaries with the PEST software program (Planning and Evaluation of Sequential Trials, University of Reading, Reading, United Kingdom (4Go)). Since no information on survival times was given, we chose a double triangular test for a binary outcome to perform the sequential analysis using the data in Kpozèhuoen et al.'s table 1 (1Go, p. 599) for which we estimated a necessary total fixed sample size of approximately 645 patients based on the data from their Materials and Methods section. The efficiency gain was similar to that obtained by Kpozèhuoen et al. (1Go); the upper boundary was crossed at the second interim analysis (the second x in figure 1), with an efficiency gain of 39–54 percent (394 patients instead of the 645 used or the 730 required by the authors) as compared with a fixed-sample-size approach. Therefore, we take issue with Kpozèhuoen et al.'s statement, "This feature of the Bayesian approach is indeed one of the most interesting compared with the frequentist approach," referring to choosing different priors (1Go, p. 601). We consider sequential statistical approaches just as interesting as, if not more interesting than, a Bayesian approach. For example, sequential approaches allow for better adherence to Good Statistical Practice. In clinical trial planning, the external information as used by Kpozèhuoen et al. to justify their choice of different priors should be used to define, a priori, a single effect size one expects to observe or considers relevant to detect (5Go, 6Go). In a sequential approach, defining a specific difference worth detecting is a stringent requirement before one can start such an analysis. This relevant difference defines, together with the type 1 and type 2 errors, the stopping boundaries (see figure 1). Thus, we can fully agree with Kpozèhuoen et al.'s remark, "Given that stopping rules are so sensitive to the choice of the prior, it is of the utmost importance that this choice be made according to standardized procedures" (1Go, p. 601). However, we think a Bayesian approach that allows the trying-out and changing of prior probabilities even after the data have been collected will facilitate violations of Good Statistical Practice.



View larger version (15K):
[in this window]
[in a new window]
 
FIGURE 1. Sequential interim reanalysis of data from the paper by Kpozèhuoen et al. (Am J Epidemiol 2005;161:595–603). Z is a cumulative measure for the advantage of cotrimazole above placebo in the proportion of severe events; V is the cumulative amount of information after each interim analysis and is proportional to the number of patients enrolled in the trial.

 
The need to be able to draw conclusions about new, potentially beneficial treatments as soon as possible, or with as few patients as possible, promotes the development of methodological improvements to reduce the size and/or duration of clinical trials (5Go). This has been the topic of several papers (3Go, 4Go, 8Go–10Go) and recent discussions (7Go, 11Go–13Go) focusing on more efficient statistical strategies. We have suggested that future claims of efficiency gains should include at least a percentage or the mean/median expected gain in order to allow evaluation of new strategies (3Go). Apart from gains in efficiency, the number and objectivity of the assumptions required for proposed alternative methods of increasing efficiency should be an additional criterion in comparing claims of the advantages of potential new methods. We defend the thesis that sequential approaches, in addition to their gain in efficiency, have as an additional advantage the fact that they require fewer—though more stringent—assumptions (14Go) than Bayesian methods and several other methods proposed (1Go, 3Go, 6Go, 9Go).

ACKNOWLEDGMENTS

Conflict of interest: none declared.

NOTES

Editor's note: In accordance with Journal policy, Kpozèhuoen et al. were asked whether they wished to reply to this letter, but they chose not to do so.

References

  1. Kpozèhuoen A, Alioum A, Anglaret X, et al. Use of a Bayesian approach to decide when to stop a therapeutic trial: the case of a chemoprophylaxis trial in human immunodeficiency virus infection. Am J Epidemiol 2005;161:595–603.[Abstract/Free Full Text]
  2. van der Tweel I, van Noord PAH. Sequential analysis of matched dichotomous data from prospective case-control studies. Stat Med 2000;189:3449–64.[CrossRef]
  3. van der Tweel I, van Noord PAH. Early stopping in clinical trials and epidemiological studies for "futility": conditional power versus sequential analysis. J Clin Epidemiol 2003;56:610–17.[CrossRef][ISI][Medline]
  4. Medical and Pharmaceutical Statistics Research Unit, University of Reading. PEST 4: operating manual. Reading, United Kingdom: University of Reading, 2000.
  5. Whitehead J. The design and analysis of sequential clinical trials. Rev 2nd ed. New York, NY: John Wiley & Sons, Inc, 1997.
  6. Whitehead J. Stopping clinical trials by design. Nat Rev Drug Discov 2004;3:973–7.[CrossRef][ISI][Medline]
  7. Horrobin DF. Are large clinical trials in rapid lethal diseases usually unethical? Lancet 2003;361:685–7.
  8. Kaaks R, van der Tweel I, van Noord PAH, et al. Efficient use of biological banks for biochemical epidemiology: exploratory hypothesis testing by means of a sequential t-test. Epidemiology 1994;5:429–38.[ISI][Medline]
  9. Stromberg U. A method for deciding early stopping of inconclusive case-control studies in settings where the data are stratified. Stat Med 1997;16:2327–37.[CrossRef][ISI][Medline]
  10. Groeneveld GJ, van der Tweel I, Wokke JH, et al. Sequential designs for clinical trials in amyotrophic lateral sclerosis. Amyotroph Lateral Scler Other Motor Neuron Disord 2004;5:202–7.[CrossRef][ISI][Medline]
  11. Baksh MF, Todd S, Whitehead J, et al. Design considerations in the sequential analysis of matched case-control data. Stat Med 2005;24:853–67.[CrossRef][ISI][Medline]
  12. Bacchetti P, Wolf LE, Segal MR, et al. Ethics and sample size. Am J Epidemiol 2005;161:105–10.[Abstract/Free Full Text]
  13. Prentice R. Invited commentary: ethics and sample size—another view. Am J Epidemiol 2005;161:111–12.[Free Full Text]
  14. van der Tweel I, van Noord PAH. A method for deciding early stopping of inconclusive case-control studies in settings where data are stratified. (Letter). Stat Med 1999;18:361–2.




This Article
Extract
Full Text (PDF)
All Versions of this Article:
162/10/1033-a    most recent
kwi319v1
Alert me when this article is cited
Alert me if a correction is posted
Services
Email this article to a friend
Similar articles in this journal
Similar articles in ISI Web of Science
Similar articles in PubMed
Alert me to new issues of the journal
Add to My Personal Archive
Download to citation manager
Disclaimer
Request Permissions
Google Scholar
Articles by van Noord, P. A. H.
Articles by van der Tweel, I.
PubMed
PubMed Citation
Articles by van Noord, P. A. H.
Articles by van der Tweel, I.