Frequentist and Bayesian Sample Size Determination for Single-Arm Clinical Trials Based on a Binary Response Variable: A Shiny App to Implement Exact Methods
Sample size determination typically relies on a power
analysis based on a frequentist conditional approach. This latter can be seen
as a particular case of the two-priors approach,which allows to build four distinct power functions to select the optimal
sample size. We revise this approach when the focus is on testing a single
binomial proportion. We consider exact methods and introduce a conservative
criterion to account for the typical non-monotonic behavior of the power
functions, when dealing with discrete data. The main purpose of this paper is
to present a Shiny App providing a
user-friendly, interactive tool to apply these criteria. The app also provides
specific tools to elicit the analysis and the designprior
distributions, which are the core of the two-priors approach.
References
[1]
Sambucini, V. (2017) Bayesian vs Frequentist Power Functions to Determine the Optimal Sample Size: Testing One Sample Binomial Proportion Using Exact Methods. In: Tejedor, J.P., Ed., Bayesian Inference, IntechOpen, Rijeka, 77-97.
https://doi.org/10.5772/intechopen.70168
[2]
Wang, F. and Gelfand, A.E. (2002) A Simulation-Based Approach to Bayesian Sample Size Determination for Performance under a Given Model and for Separating Models. Statistical Science, 17, 193-208.
[3]
Sahu, S.K. and Smith, T.M.F. (2006) A Bayesian Method of Sample Size Determination with Practical Applications. Journal of the Royal Statistical Society: Series A, 169, 235-253. https://doi.org/10.1111/j.1467-985X.2006.00408.x
[4]
De Santis, F. (2006) Sample Size Determination for Robust Bayesian Analysis. Journal of the American Statistical Association, 101, 278-291.
https://doi.org/10.1198/016214505000000510
[5]
Brutti, P., De Santis, F. and Gubbiotti, S. (2008) Robust Bayesian Sample Size Determination in Clinical Trials. Statistics in Medicine, 27, 2290-2306.
https://doi.org/10.1002/sim.3175
[6]
Gubbiotti, S. and De Santis, F. (2008) Classical and Bayesian Power Functions: Their Use in Clinical Trials. Biomedical Statistics and Clinical Epidemiology, 2, 201-211.
[7]
Sambucini, V. (2008) A Bayesian Predictive Two-Stage Design for Phase II Clinical Trials. Statistics in Medicine, 27, 1199-1224. https://doi.org/10.1002/sim.3021
[8]
Matano, F. and Sambucini, V. (2016) Accounting for Uncertainty in the Historical Response Rate of the Standard Treatment in Single-Arm Two-Stage Designs Based on Bayesian Power Functions. Pharmaceutical Statistics, 15, 517-530.
https://doi.org/10.1002/pst.1788
[9]
Berchialla, P., Zohar, S. and Baldi, I. (2019) Bayesian Sample Size Determination for Phase IIA Clinical Trials Using Historical Data and Semi-Parametric Prior’s Elicitation. Pharmaceutical Statistics, 18, 198-211. https://doi.org/10.1002/pst.1914
[10]
Turchetta, A., Moodie, E.E.M., Stephens, D.A. and Lambert, S.D. (2023) Bayesian Sample Size Calculations for Comparing Two Strategies in SMART Studies. Biometrics, 3, 2489-2502. https://doi.org/10.1111/biom.13813
[11]
Chernick, M.R. and Liu, C.Y. (2002) The Saw-Toothed Behavior of Power versus Sample Size and Software Solutions: Single Binomial Proportion Using Exact Methods. The American Statistician, 56, 149-155.
https://doi.org/10.1198/000313002317572835
[12]
Gentile, S. and Sambucini, V. (2023) Exact Sample Size Determination for a Single Poisson Random Sample. Biometrical Journal, 25, Article ID: 2200183.
https://doi.org/10.1002/bimj.202200183
[13]
Champely, S. (2020) PWR: Basic Functions for Power Analysis. R Package Version 1.3-0. https://CRAN.R-project.org/package=pwr
[14]
Aberson, C. (2021) pwr2ppl: Power Analyses for Common Designs (Power to the People). R package version 0.5.0.
https://cran.r-project.org/web/packages/pwr2ppl/pwr2ppl.pdf
[15]
Ryan, T.P. (2013) Sample Size Determination and Power. John Wiley & Sons, Hoboken. https://doi.org/10.1002/9781118439241
[16]
Kohl, M. (2020) MKpower: Power Analysis and Sample Size Calculation. R Package Version 0.7. https://cran.rproject.org/web/packages/MKpower/MKpower.pdf
[17]
Ekstrm, C. (2022) MESS: Miscellaneous Esoteric Statistical Scripts. R package Version 0.5.9. https://CRAN.R-project.org/package=MESS
[18]
Millard, S.P. (2013) EnvStats: An R Package for Environmental Statistics. Springer Science & Business Media, Berlin. https://doi.org/10.1007/978-1-4614-8456-1
[19]
Faul, F., Erdfelder, E., Lang, A. and Buchner, A. (2007) G*Power 3: A Flexible Statistical Power Analysis Program for the Social, Behavioral, and Biomedical Sciences. Behavior Research Methods, 39, 175-191. https://doi.org/10.3758/BF03193146
[20]
Lenth, R. V. (2018) Java Applets for Power and Sample Size.
http://homepage.divms.uiowa.edu/~rlenth/Power/
[21]
Chang, W., Cheng, J., Allaire, J.J., Sievert, C., Schloerke, B., Xie, Y., Allen, J., McPherson, J., Dipert, A. and Borges, B. (2021) Shiny: Web Application Framework for R. R package Version 1.7.1. https://CRAN.R-project.org/package=shiny
[22]
Wickham, H. (2021) Mastering Shiny. O’Reilly Media, Inc., Sebastopol.
[23]
Spiegelhalter, D.J., Abrams, K.R. and Myles, J.P. (2004) Bayesian Approaches to Clinical Trials and Health-Care Evaluation. John Wiley & Sons, Hoboken.
https://doi.org/10.1002/0470092602
[24]
Lesaffre, E. and Lawson, A.B. (2012) Bayesian Biostatistics. John Wiley & Sons, Hoboken. https://doi.org/10.1002/9781119942412
[25]
Eaton, M.L., Muirhead, R.J. and Soaita, A.I. (2013) On the Limiting Behavior of the Probability of Claiming Superiority in a Bayesian Context. Bayesian Analysis, 8, 221-232. https://doi.org/10.1214/13-BA809
