On the limit distribution of the power function induced by a design prior. (English) Zbl 07887506
Summary: 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 observations 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.
MSC:
| 62-XX | Statistics |
References:
| [1] | Ansley, C.; Newbold, P., On the finite sample distribution of residual autocorrelations in autoregressive-moving average models, Biometrika, 66, 547-553, 1979 · doi:10.1093/biomet/66.3.547 |
| [2] | Bartels, R., On the power function of the Durbin-Watson test, J Econom, 51, 101-112, 1992 · doi:10.1016/0304-4076(92)90031-L |
| [3] | Brown, B.; Herson, J.; Atkinson, E., Projection from previous studies: a Bayesian and frequentist compromise, Controlled Clin Trials, 8, 29-44, 1987 · doi:10.1016/0197-2456(87)90023-7 |
| [4] | Brutti P, De Santis F, Gubbiotti S (2008) Robust Bayesian sample size determination in clinical trials. Stat Med 27:2290-2306 |
| [5] | Brutti P, De Santis F, Gubbiotti S (2014) Bayesian-frequentist sample size determination: a game of two priors. Metron 72:133-151 · Zbl 1316.62117 |
| [6] | Chuang-Stein, C., Sample size and the probability of a successful trial, Pharm Stat, 5, 305-309, 2006 · doi:10.1002/pst.232 |
| [7] | Ciarleglio, MM; Arendt, CD; Makuch, RW, Selection of the treatment effect for sample size determination in a superiority clinical trial using a hybrid classical and bayesian procedure, Contemporary Clin Trials, 41, 160-171, 2015 · doi:10.1016/j.cct.2015.01.002 |
| [8] | Dallow, N.; Fina, P., The perils with the misuse of predictive power, Pharm Stat, 10, 311-317, 2011 · doi:10.1002/pst.467 |
| [9] | Eaton, M.; Muirhead, R.; Soaita, A., On the limiting behavior of the “probability of claiming superiority” in a Bayesian context, Bayesian Anal, 8, 221-232, 2013 · Zbl 1329.62126 · doi:10.1214/13-BA809 |
| [10] | Joseph, L.; du Berger, R.; Belisle, P., Bayesian and mixed Bayesian/likelihood criteria for sample size determination, Stat Med, 16, 769-781, 1997 · doi:10.1002/(SICI)1097-0258(19970415)16:7<769::AID-SIM495>3.0.CO;2-V |
| [11] | Kunzmann, K.; Grayling, MJ; Lee, KM, A review of Bayesian perspectives on sample size derivation for confirmatory trials, Am Stat, 75, 4, 424-432, 2021 · Zbl 07632881 · doi:10.1080/00031305.2021.1901782 |
| [12] | Liu, F., An extension of Bayesian expected power and its application in decision making, J Biopharm Stat, 20, 941-953, 2010 · doi:10.1080/10543401003618967 |
| [13] | Muirhead, R.; Soaita, A., On an approach to Bayesian sample sizing in clinical trials, Adv Mod Stat Theory Appl, 10, 126-138, 2013 · Zbl 1327.62155 |
| [14] | O’Hagan, A.; Stevens, J., Bayesian assessment of sample size for clinical trials for cost effectiveness, Med Decis Mak, 21, 219-230, 2001 · doi:10.1177/02729890122062514 |
| [15] | Rufibach, K.; Burger, H.; Abt, M., Bayesian predictive power: choice of prior and some recommendations for its use as probability of success in drug development, Pharm Stati, 15, 438-446, 2016 · doi:10.1002/pst.1764 |
| [16] | Sahu, S.; Smith, T., A Bayesian method of sample size determination with practical applications, JRSSA, 169, 235-253, 2006 |
| [17] | Spiegelhalter, D.; Freedman, L., A predictive approach to selecting the size of a clinical trial, based on subjective clinical opinion, Stat Med, 5, 1-13, 1986 · doi:10.1002/sim.4780050103 |
| [18] | Spiegelhalter, D.; Abrams, K.; Myles, J., Bayesian approaches to clinical trials and health-care evaluation, 2004, New York: Wiley, New York |
| [19] | Tillman, J., The power of the Durbin-Watson test, Econometrica, 43, 959-974, 1975 · Zbl 0322.62027 · doi:10.2307/1911337 |
| [20] | van der Vaart, A., Asymptotic statistics, 1998, Cambridge: Cambridge University Press, Cambridge · Zbl 0910.62001 · doi:10.1017/CBO9780511802256 |
| [21] | Wan, A.; Zou, G.; Banerjee, A., The power of autocorrelation tests near the unit root in models with possibly mis-specified linear restrictions, Econ Lett, 94, 213-219, 2007 · Zbl 1255.62286 · doi:10.1016/j.econlet.2006.06.032 |
| [22] | Wang, F.; Gelfand, A., A simulation-based approach to Bayesian sample size determination for performance under a given model and for separating models, Stat Sci, 17, 193-208, 2002 · Zbl 1013.62025 |
| [23] | Wang, Y.; Fu, H.; Kulkarni, P., Evaluating and utilizing probability of study success in clinical development, Clin Trials, 10, 407-413, 2013 · doi:10.1177/1740774513478229 |
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