STATISTICS IN MEDICINE
Statist. Med. 2008; 27:5586–5604
Published online 27 August 2008 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/sim.3381
Bayesian adaptive model selection for optimizing group
sequential clinical trials
J. Kyle Wathen
∗,†
and Peter F. Thall
Department of Biostatistics, University of Texas, M.D. Anderson Cancer Center, Box 447,
1515 Holcombe Boulevard, Houston, TX 77030, U.S.A.
SUMMARY
This article presents a new approach to the problem of deriving an optimal design for a randomized
group sequential clinical trial based on right-censored event times. We are motivated by the fact that,
if the proportional hazards assumption is not met, then a conventional design’s actual power can differ
substantially from its nominal value. We combine Bayesian decision theory, Bayesian model selection
and forward simulation (FS) to obtain a group sequential procedure that maintains targeted false-positive
rate and power, under a wide range of true event time distributions. At each interim analysis, the method
adaptively chooses the most likely model and then applies the decision bounds that are optimal under
the chosen model. A simulation study comparing this design with three conventional designs shows that,
over a wide range of distributions, our proposed method performs at least as well as each conventional
design, and in many cases it provides a much smaller trial. Copyright q 2008 John Wiley & Sons, Ltd.
KEY WORDS: Bayesian clinical trial; Bayesian optimal design; forward simulation; model selection;
sequential clinical trial
1. INTRODUCTION
The use of group sequential designs has become routine in phase III clinical trials. Many authors
have provided general group sequential methods [1–3] and approximately optimal group sequential
procedures [4–9]. Each of these group sequential designs is derived by assuming a sequence of
normally distributed test statistics with unknown mean and known variance, with proportional
hazards usually assumed to accommodate right-censored event times. While these designs are
used routinely in practice, if the proportional hazards assumption is not met, then the design’s
actual power may differ substantially from its nominal value. For example, if the true event time
distribution is lognormal with a hazard that initially increases and then decreases (Figure 1(d)),
∗
Correspondence to: J. Kyle Wathen, Department of Biostatistics, University of Texas, M.D. Anderson Cancer Center,
Box 447, 1515 Holcombe Boulevard, Houston, TX 77030, U.S.A.
†
E-mail: jkwathen@mdanderson.org
Received 6 August 2007
Copyright q 2008 John Wiley & Sons, Ltd. Accepted 28 May 2008

BAYESIAN ADAPTIVE MODEL SELECTION 5587
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(a) (b)
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Figure 1. Summary of potential hazards in M. M
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is generalized gamma(1,
,1), equivalent to an
exponential, which has constant hazard and thus is not shown: (a) M
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;(b)M
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;(c)M
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;and(d)M
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.
then the actual power achieved by the O’Brien and Fleming (OF) [1], Pocock [2] and optimal
Hwang, Shih and De Cani (HSD) [5] designs with nominal power 80 per cent may be as low as
20–40 per cent (Tables I–III). Thus, the trial would be unlikely to identify a true treatment advance.
In contrast, if the true event time distribution is Weibull with an increasing hazard (Figure 1(a)),
then the actual power achieved by the OF, Pocock and HSD designs with nominal power 80
per cent may be as high as 99 per cent (Tables I–III). In this case, these designs each enroll 33
per cent to 50 per cent more patients than the optimal Bayesian design that we will present here.
Copyright q 2008 John Wiley & Sons, Ltd. Statist. Med. 2008; 27:5586–5604
DOI: 10.1002/sim