Bayesian decision-theoretic group sequential clinical trial design based on a quadratic loss function: a frequentist evaluation
Abstract
The decision to terminate a controlled clinical trial at the time of an interim analysis is perhaps best made by weighing the value of the likely additional information to be gained if further subjects are enrolled against the various costs of that further enrollment. The most commonly used statistical plans for interim analysis (eg, O'Brien–Fleming), however, are based on a frequentist approach that makes no such comparison. A two-armed Bayesian decision-theoretic clinical trial design is developed for a disease with two possible outcomes, incorporating a quadratic decision loss function and using backward induction to quantify the cost of future enrollment. Monte Carlo simulation is used to compare frequentist error rates and mean required sample sizes for these Bayesian designs with the two-tailed frequentist group-sequential designs of, O'Brien–Fleming and Pocock. When the terminal decision loss function is chosen to yield typical frequentist error rates, the mean sample sizes required by the Bayesian designs are smaller than those of the corresponding O'Brien–Fleming frequentist designs, largely due to the more frequent interim analyses typically used with the Bayesian designs and the ability of the Bayesian designs to terminate early and conclude equivalence. Adding stochastic curtailment to the frequentist designs and using the same number of interim analyses results in largely equivalent trials. An example of a Bayesian design for the data safety monitoring of a clinical trial is given. Our design assumes independence of the probabilities of success in the two trial arms. Additionally, we have chosen non-informative priors and selected loss functions to produce trials with appealing frequentist error rates, rather than choosing priors that reflect realistic prior information and loss functions that reflect true costs. Our Bayesian designs allow interpretation of the final results along either Bayesian or frequentist lines. For the Bayesian, they minimize the total cost and allow the direct calculation of the probability density function for the difference in efficacy. For the frequentist, they have well-characterized type I and II error rates and in some cases lead to a reduction in the mean sample size.
Get full access to this article
View all access and purchase options for this article.
References
Pocock SJ. Group sequential methods in the design and analysis of clinical trials . Biometrika 1977; 64: 191-199 .
O'Brien PC, Fleming TR . A multiple testing procedure for clinical trials . Biometrics 1979; 35: 549-556 .
Lan KKG, DeMets DL . Discrete sequential boundaries for clinical trials . Biometrika 1983; 70: 659-663 .
Kim K, DeMets DL . Design and analysis of group sequential tests based on the type I error spending rate function . Biometrika 1987; 74: 149-154 .
Geller NL, Pocock SJ . Interim analyses in randomized clinical trials: Ramifications and guidelines for practitioners . Biometrics 1987; 43: 213-223 .
Whitehead J. The design and analysis of sequential trials, revised 2nd edn. John Wiley & Sons, 1997.
Berry DA. A case for Bayesianism in clinical trials . Statistics in Medicine 1993; 12: 1377-1393 .
Berry DA. Interim analysis in clinical trials: Frequentist vs. Bayesian approaches . Statistics in Medicine 1985; 4: 521-526 .
Berry DA. Interim analysis in clinical trials: The role of the likelihood principle . The American Statistician 1987; 41: 117-122 .
Freedman LS, Spiegelhalter DJ . Comparison of Bayesian with group sequential methods for monitoring clinical trials . Controlled Clinical Trials 1989; 10: 357-367 .
Berry DA. Monitoring accumulating data in a clinical trial . Biometrics 1989; 45: 1197-1211 .
Lewis RJ, Wears RL . An introduction to the Bayesian analysis of clinical trials . Annals of Emergency Medicine 1993; 22: 1328-1336 .
Berry DA, Ho CH . One-sided sequential stopping boundaries for clinical trials: A decision-theoretic approach . Biometrics 1988; 44: 219-227 .
Berry DA, Wolff MC, Sack D . Public health decision making: A sequential vaccine trial (with discussion). In Bernardo JM, Berger JO, Dawid AP, Smith AFM eds. Bayesian statistics 4. Oxford University Press, 1992: 79-96.
Lewis RJ, Berry DA . Group sequential clinical trials: A frequentist evaluation of Bayesian decision-theoretic designs . Journal of the American Statistical Association 1994; 89: 1528-1534 .
Carlin BP, Kadane JB, Gelfand AE . Approaches for optimal sequential decision analysis in clinical trials . Biometrics 1998; 54: 964-975 .
Stangl DK. Bridging the gap between statistical analysis and decision making in public health research . Statistics in Medicine 2005; 24: 503-511 .
Ashby D, Tan SB . Where's the utility in Bayesian datamonitoring of clinical trials? Clinical Trials 2005; 2: 197-205 .
DeGroot MH. Optimal statistical decisions. McGraw-Hill, 1970.
Lan KKG, Simon R, Halperin M . Stochastically curtailed tests in long-term clinical trials . Sequential Analysis 1982; 1: 207-219 .
Whitehead J, Matsushita T . Stopping clinical trials because of treatment ineffectiveness: a comparison of a futility design with a method of stochastic curtailment . Statistics in Medicine 2003; 22: 677-687 .
Reboussin DM, DeMets DL, Kyung Mann K, Lan KKG . Programs for computing group sequential boundaries using the Lan-DeMets method - Version 2. Technical Report Number 95, Department of Biostatistics, University of Wisconsin-Madison, 1995.
Gausche M, Lewis RJ, Stratton SJ et al. Effect of out-of-hospital pediatric endotracheal intubation on survival and neurological outcome: A controlled trial . JAMA 2000; 283: 783-790 .
Gausche-Hill M, Lewis RJ, Gunter CS, Henderson DP, Haynes BE, Stratton SJ . Design and implementation of a controlled trial of pediatric endotracheal intubation in the out-of-hospital setting . Annals of Emergency Medicine 2000; 36: 356-365 .
Food and Drug Administration . Guidance for the use of Bayesian statistics in medical device clinical trials - draft guidance for industry and FDA staff. http://www.fda.gov/cdrh/osb/guidance/1601.html. Accessed 30 September 2006.
Kadane JB. Bayesian methods for health-related decision making . Statistics in Medicine 2005; 24: 563-567 .
Smith AFM, Roberts GO . Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods . Journal of the Royal Statistical Society B 1993; 55: 3-23 .
Cheng Y, Shen Y . Bayesian adaptive designs for clinical trials . Biometrika 2005; 92: 633-646 .
Brockwell AE, Kadane JB . A gridding method for Bayesian sequential decision problems . Journal of Computational and Graphical Statistics 2003; 12: 566-584 .
Berger JO. Statistical decision theory and Bayesian analysis. Springer-Verlag, 1985.
Ferguson TS. Mathematical statistics: a decision theoretic approach. Academic Press, 1967: 100-100, 104-104.
Cite article
Cite article
Cite article
OR
Download to reference manager
If you have citation software installed, you can download article citation data to the citation manager of your choice
Information, rights and permissions
Information
Published In
Article first published: February 2007
Issue published: February 2007
PubMed: 17327241
Authors
Metrics and citations
Metrics
Article usage*
Total views and downloads: 221
*Article usage tracking started in December 2016
Altmetric
See the impact this article is making through the number of times it’s been read, and the Altmetric Score.
Learn more about the Altmetric Scores
Articles citing this one
Receive email alerts when this article is cited
Web of Science: 31 view articles Opens in new tab
Crossref: 33
-
Network node grouping algorithm and evaluation model based on clusteri...
-
Bayesian Sequential Learning for Clinical Trials of Multiple Correlate...
-
A decision-theoretic approach to Bayesian clinical trial design and ev...
-
Bayesian adaptive decision-theoretic designs for multi-arm multi-stage...
-
Effects of simulated sample sizes on the mortality effect estimates in...
-
Bayesian Methods in Regulatory Science
-
Sequential monitoring of response-adaptive randomized clinical trials ...
-
Bayesian decision theory for clinical trials: Utility and sample size ...
-
Second-Generation P-Values, Shrinkage, and Regularized Models
-
The Performance of Fixed-Horizon, Look-Ahead Procedures Compared to Ba...
-
A Review of Clinical Trials With an Adaptive Design and Health Economi...
-
Adaptive designs in clinical trials: why use them, and how to run and ...
-
Multicolour versus monocolour inking specimens after pancreaticoduoden...
-
A Bayesian Decision Theoretic Model of Sequential Experimentation with...
-
A Bayesian sequential design with adaptive randomization for 2‐sided h...
-
Optimal Interim Decision Rules Based on a Binary Surrogate Outcome for...
-
Bayesian randomized clinical trials: From fixed to adaptive design
-
Clinical Trials for New Drug Development: Optimal Investment and Appli...
-
A Bayesian approach to sequential meta‐analysis
-
Decision-theoretic designs for small trials and pilot studies: A revie...
-
Optimal sequential sampling with delayed observations and unknown vari...
-
Optimal Decision Rules for Biomarker-Based Subgroup Selection for a Ta...
-
Bayesian Designs and the Control of Frequentist Characteristics: A Pra...
-
Bayesian Adaptive Randomization Designs for Clinical Trial
-
Optimizing Sedative Dose in Preterm Infants Undergoing Treatment for R...
-
Bayesian sequential meta‐analysis design in evaluating cardiovascular ...
-
Optimal Bayesian Sequential Sampling Rules for the Economic Evaluation...
-
A practical guide to Bayesian group sequential designs
-
Do Bayesian adaptive trials offer advantages for comparative effective...
-
Response‐adaptive decision‐theoretic trial design: operating character...
-
Can Rodent Longevity Studies be Both Short and Powerful?
-
Adaptive group sequential design for phase II clinical trials: A Bayes...
-
Comments on ‘Bayesians in clinical trials: Asleep at the switch’ by Le...
Figures and tables
Figures & Media
Tables
View Options
Get access
Access options
If you have access to journal content via a personal subscription, university, library, employer or society, select from the options below:
loading institutional access options
SCT members can access this journal content using society membership credentials.
SCT members can access this journal content using society membership credentials.
Alternatively, view purchase options below:
Purchase 24 hour online access to view and download content.
Access journal content via a DeepDyve subscription or find out more about this option.
