The hybrid frequentist-Bayesian approach to sample size determination is based on the expectation of the power function of a test with respect to a design prior for the unknown parameter value. In clinical trials this quantity is often called probability of success (PoS). Determination of the limiting value of PoS as the number of observa- tions tends to infinity, that is crucial for well defined sample size criteria, has been considered in previous articles. Here, we focus on the asymptotic behavior of the whole distribution of the power function induced by the design prior. Under mild conditions, we provide asymptotic results for the three most common classes of hypotheses on a scalar parameter. The impact of the design parameters choice on the distribution of the power function and on its limit is discussed.

On the limit distribution of the power function induced by a design prior / DE SANTIS, Fulvio; Gubbiotti, Stefania. - In: STATISTICAL PAPERS. - ISSN 0932-5026. - (2023), pp. 1-19. [10.1007/s00362-023-01462-9]

On the limit distribution of the power function induced by a design prior

Fulvio De Santis;Stefania Gubbiotti
2023

Abstract

The hybrid frequentist-Bayesian approach to sample size determination is based on the expectation of the power function of a test with respect to a design prior for the unknown parameter value. In clinical trials this quantity is often called probability of success (PoS). Determination of the limiting value of PoS as the number of observa- tions tends to infinity, that is crucial for well defined sample size criteria, has been considered in previous articles. Here, we focus on the asymptotic behavior of the whole distribution of the power function induced by the design prior. Under mild conditions, we provide asymptotic results for the three most common classes of hypotheses on a scalar parameter. The impact of the design parameters choice on the distribution of the power function and on its limit is discussed.
2023
bayesian design; clinical trials; probability of success; sample size determination
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On the limit distribution of the power function induced by a design prior / DE SANTIS, Fulvio; Gubbiotti, Stefania. - In: STATISTICAL PAPERS. - ISSN 0932-5026. - (2023), pp. 1-19. [10.1007/s00362-023-01462-9]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1686184
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