A review of Bayesian perspectives on sample size derivation for confirmatory trials

Kunzmann, Kevin; Grayling, Michael J.; Lee, Kim May; Robertson, D. S.; Rufibach, Kaspar; Wason, James

doi:10.48550/arxiv.2006.15715

Cited by 1 publication

(5 citation statements)

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“…differs slightly from the one proposed by 1 in that we condition on a positive effect size Θ > 0. This is more consistent with the notion of frequentist power as discussed in 11 , although the difference is only of practical relevance when a substantial fraction of the a priori probability mass is concentrated on the null hypothesis. We now compare ACP, OCP, and PP by means of a concrete example.…”

Section: Monitoring Powersupporting

confidence: 83%

“…Monitoring the power of the remainder of an ongoing trial constitutes an estimation problem since the conditional power is a function of the unknown treatment effect. An often overlooked aspect of this estimation problem is that it is conditional on a positive treatment effect since the notion of power is conditional on there being an non-null effect 11 . In many practical situations where the prior mass is concentrated on non-null effects the effect of conditioning is negligible but its importance increases with the vagueness of a the prior.…”

Section: Discussionmentioning

confidence: 99%

“…In any other case, the Bayesian predictive power allows a priori information to be incorporated in a more fine-grained way and guarantees optimal mean-squared-error performance. If an unconditional measure for the probability to reject the null hypothesis is sought, a conditional version of the probability of success (or assurance) can be derived in an analogue way 11 . Great care should be taken when predictive power or another estimator of conditional power is used to modify an ongoing trial's sample size.…”

Section: Discussionmentioning

confidence: 99%

“…This effectively constitutes an estimation problem where the estimand is the conditional probability of rejecting the null hypothesis given Z m = z m and θ > 0. Here the conditioning on a positive effect is crucial to justify the notion of 'power' in contrast to the unconditional 'probability of success' 11 .…”

Section: Monitoring Powermentioning

confidence: 99%

“…The conditional type-I error rate constraint is not relaxed to comply with the conditional error principle. This approach is closely related to the formulation of the optimal-design problem given in 15 and the utility perspective on sample size derivation presented in 11 . In contrast to the situation analyzed by 15 , however, λ h does depend on z m .…”

Section: Consistent Unplanned Recalculationmentioning

confidence: 99%

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Conditional Power and Friends: The Why and How of (Un)planned, Unblinded Sample Size Recalculations in Confirmatory Trials

Kunzmann¹,

Grayling²,

Lee³

et al. 2020

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Adapting the final sample size of a trial to the evidence accruing during the trial is a natural way to address planning uncertainty.Designs with adaptive sample size need to account for their optional stopping to guarantee strict type-I error-rate control. A variety of different methods to maintain type-I error-rate control after unplanned changes of the initial sample size have been proposed in the literature. This makes interim analyses for the purpose of sample size recalculation feasible in a regulatory context. Since the sample size is usually determined via an argument based on the power of the trial, an interim analysis raises the question of how the final sample size should be determined conditional on the accrued information. Conditional power is a concept often put forward in this context. Since it depends on the unknown effect size, we take a strict estimation perspective and compare assumed conditional power, observed conditional power, and predictive power with respect to their properties as estimators of the unknown conditional power. We then demonstrate that preplanning an interim analysis using methodology for unplanned interim analyses is ineffective and naturally leads to the concept of optimal two-stage designs. We conclude that unplanned design adaptations should only be conducted as reaction to trial-external new evidence, operational needs to violate the originally chosen design, or post hoc changes in the objective criterion. Finally, we show that commonly discussed sample size recalculation rules can lead to paradoxical outcomes and propose two alternative ways of reacting to newly emerging trial-external evidence.

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Section: Monitoring Powersupporting

confidence: 83%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Monitoring Powermentioning

confidence: 99%