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. 2020 Jan 7;20(1):4.
doi: 10.1186/s12874-019-0892-8.

Comparison of Bayesian and Frequentist Group-Sequential Clinical Trial Designs

Free PMC article

Comparison of Bayesian and Frequentist Group-Sequential Clinical Trial Designs

Nigel Stallard et al. BMC Med Res Methodol. .
Free PMC article


Background: There is a growing interest in the use of Bayesian adaptive designs in late-phase clinical trials. This includes the use of stopping rules based on Bayesian analyses in which the frequentist type I error rate is controlled as in frequentist group-sequential designs.

Methods: This paper presents a practical comparison of Bayesian and frequentist group-sequential tests. Focussing on the setting in which data can be summarised by normally distributed test statistics, we evaluate and compare boundary values and operating characteristics.

Results: Although Bayesian and frequentist group-sequential approaches are based on fundamentally different paradigms, in a single arm trial or two-arm comparative trial with a prior distribution specified for the treatment difference, Bayesian and frequentist group-sequential tests can have identical stopping rules if particular critical values with which the posterior probability is compared or particular spending function values are chosen. If the Bayesian critical values at different looks are restricted to be equal, O'Brien and Fleming's design corresponds to a Bayesian design with an exceptionally informative negative prior, Pocock's design to a Bayesian design with a non-informative prior and frequentist designs with a linear alpha spending function are very similar to Bayesian designs with slightly informative priors.This contrasts with the setting of a comparative trial with independent prior distributions specified for treatment effects in different groups. In this case Bayesian and frequentist group-sequential tests cannot have the same stopping rule as the Bayesian stopping rule depends on the observed means in the two groups and not just on their difference. In this setting the Bayesian test can only be guaranteed to control the type I error for a specified range of values of the control group treatment effect.

Conclusions: Comparison of frequentist and Bayesian designs can encourage careful thought about design parameters and help to ensure appropriate design choices are made.

Keywords: Adaptive design; Interim analysis; Sequential analysis; Sequential design; Type I error rate.

Conflict of interest statement

The authors declare that they have no competing interests.


Fig. 1
Fig. 1
Densities for range of prior distributions for Bayesian sequential designs for Example 1
Fig. 2
Fig. 2
Stopping boundaries for Bayesian sequential tests with 5 looks using prior distributions from Figure 1 (∘). Solid lines give boundaries for O’Brien and Fleming test (steep sloping lines), Pocock test (horizontal lines) and for frequentist test with α(t)=αt (shallow sloping lines)
Fig. 3
Fig. 3
Cumulative type I error spent for Bayesian sequential tests shown in Fig. 2 (∘). Solid lines give boundaries for O’Brien and Fleming test (lower line), Pocock test (upper line) and for frequentist test with α(t)=αt (middle line)
Fig. 4
Fig. 4
Type I error rate for Bayesian test with K=5 and p1=⋯=p5=0.9884 for range of true μ0 values along with density (not to scale) for the prior distribution for μ0

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