Discussion and References

Table of Links

Abstract and 1 Introduction: BayesPPDSurv

2 Theoretical Framework

2.1 The Power Prior and the Normalized Power Prior

2.2 The Piecewise Constant Hazard Proportional Hazards (PWCH-PH) Model

2.3 Power Prior for the PWCH-PH Model

2.4 Implementing the Normalized Power Prior for the PWCH-PH Model

2.5 Bayesian Sample Size Determination

2.6 Data Simulation for the PWCH-PH Model

3 Using BayesPPDSurv

3.1 Sampling Priors

4 Case Study: Melanoma Clinical Trial Design

5 Discussion and References

5 Discussion

BayesPPDSurv facilitates Bayesian power and type I error rate calculations using the power and normalized power prior for time-to-event outcomes using a PWCH-PH model. We implement a flexible stratified version of the model, where the historical data can be used to inform the treatment effect, the effect of other covariates in the regression model, as well as the baseline hazard parameters. We develop a novel algorithm for approximating the normalized power prior that eliminates the need to compute the normalizing constant. The package also has features that semi-automatically generate the sampling priors from the historical data.

Future versions of the package will accommodate cure rate models. Another possible feature is the computation of optimal hyperparameters for the beta prior on a0 to ensure that the normalized power prior adapts in a desirable way to prior-data conflict or prior-data agreement, based on the work of Shen et al. (2024).

References

Alt, E. (2022). hdbayes: Bayesian Analysis of Generalized Linear Models with Historical Data. R package version 0.0.0.9000.

Anderson, K. (2024). gsDesign: Group Sequential Design. R package version 3.6.1, https://github.com/keaven/gsDesign.

Balcome, S., D. Musgrove, T. Haddad, and G. L. Hickey (2021). bayesDP: Tools for the Bayesian Discount Prior Function. R package version 1.3.4.

Benaglia, T., D. Chauveau, D. R. Hunter, and D. Young (2009). mixtools: An R package for analyzing finite mixture models. Journal of Statistical Software 32(6), 1–29.

Carvalho, L. M. and J. G. Ibrahim (2021, Jul). On the normalized power prior. Statistics in Medicine 40(24), 5251–5275.

Chandereng, T., D. Musgrove, T. Haddad, G. Hickey, T. Hanson, and T. Lystig (2020). bayesCT: Simulation and Analysis of Adaptive Bayesian Clinical Trials. R package version 0.99.3.

Chen, C.-F. (1985). On asymptotic normality of limiting density functions with Bayesian implications. Journal of the Royal Statistical Society. Series B (Methodological) 47(3), 540–546.

Chen, M.-H. and J. Ibrahim (2006, 09). The relationship between the power prior and hierarchical models. Bayesian Analysis 1.

Chen, M.-H., J. G. Ibrahim, P. Lam, A. Yu, and Y. Zhang (2011, Sep). Bayesian design of noninferiority trials for medical devices using historical data. Biometrics 67(3), 1163–1170.

Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological) 34(2), 187–220.

Duan, Y., K. Ye, and E. P. Smith (2006, feb). Evaluating water quality using power priors to incorporate historical information. Environmetrics (London, Ont.) 17(1), 95–106.

Eddelbuettel, D. and R. Francois (2011). Rcpp: Seamless R and C++ integration. Journal of Statistical Software 40(8), 1–18.

Eggleston, B. S., J. G. Ibrahim, B. McNeil, and D. Catellier (2021). BayesCTDesign: an R package for bayesian trial design using historical control data. Journal of Statistical Software 100(21).

Friedman, M. (1982, Mar). Piecewise exponential models for survival data with covariates. The Annals of Statistics 10(1), 101–113.

Frumento, P. (2024). pch: Piecewise Constant Hazard Models for Censored and Truncated Data. R package version 2.1.

Han, Z., T. Bai, and K. Ye (2021). NPP: Normalized Power Prior Bayesian Analysis. R package version 0.4.0.

Ibrahim, J., M.-H. Chen, and D. Sinha (2001). Bayesian Survival Analysis. New York: Springer.

Ibrahim, J. G. and M.-H. Chen (2000, feb). Power prior distributions for regression models. Statistical Science 15(1), 46–60.

Ibrahim, J. G., M.-H. Chen, Y. Gwon, and F. Chen (2015, dec). The power prior: theory and applications. Statistics in Medicine 34(28), 3724–3749.

Ibrahim, J. G., M.-H. Chen, and D. Sinha (2003, mar). On optimality properties of the power prior. Journal of the American Statistical Association 98(461), 204–213.

Kirkwood, J. M., J. G. Ibrahim, V. K. Sondak, J. Richards, L. E. Flaherty, M. S. Ernstoff, T. J. Smith, U. Rao, M. Steele, and R. H. Blum (2000, Jun). High- and low-dose interferon alfa-2b in high-risk melanoma: first analysis of intergroup trial e1690/s9111/c9190. Journal of Clinical Oncology 18(12), 2444–2458.

Kirkwood, J. M., M. H. Strawderman, M. S. Ernstoff, T. J. Smith, E. C. Borden, and R. H. Blum (1996). Interferon alfa-2b adjuvant therapy of high-risk resected cutaneous melanoma: the eastern cooperative oncology group trial est 1684. Journal of Clinical Oncology 14, 7–17.

Neal, R. M. (2003). Slice sampling. Ann. Statist. 31(3), 705–767.

Psioda, M. A. and J. G. Ibrahim (2019, Jul). Bayesian clinical trial design using historical data that inform the treatment effect. Biostatistics 20(3), 400–415.

Psioda, M. A., M. Soukup, and J. G. Ibrahim (2018, Nov). A practical bayesian adaptive design incorporating data from historical controls. Statistics in Medicine 37(27), 4054–4070.

Shen, Y., L. M. Carvalho, M. A. Psioda, and J. G. Ibrahim (2024). Optimal priors for the discounting parameter of the normalized power prior. Statistica Sinica. Preprint.

Shen, Y., M. A. Psioda, L. M. Carvalho, and J. G. Ibrahim (2024). Exploring the connection between the normalized power prior and bayesian hierarchical models. arXiv preprint.

Shen, Y., M. A. Psioda, and J. G. Ibrahim (2023a). BayesPPD: An R package for Bayesian sample size determination using the power and normalized power prior for generalized linear models. The R Journal 14, 335–351. https://doi.org/10.32614/RJ-2023-016.

Shen, Y., M. A. Psioda, and J. G. Ibrahim (2023b). BayesPPD: Bayesian Power Prior Design. R package version 1.1.2.

Shen, Y., M. A. Psioda, and J. G. Ibrahim (2024). BayesPPDSurv: Bayesian Power Prior Design for Survival Data. R package version 1.0.2.

Viele, K., S. Berry, B. Neuenschwander, B. Amzal, F. Chen, N. Enas, B. Hobbs, J. G. Ibrahim, N. Kinnersley, S. Lindborg, and et al. (2014, Feb). Use of historical control data for assessing treatment effects in clinical trials. Pharmaceutical Statistics 13(1), 41–54.

Wang, F. and A. E. Gelfand (2002, May). A simulation-based approach to bayesian sample size determination for performance under a given model and for separating models. Statistical Science 17(2), 193–208.

Wang, Y.-B., M.-H. Chen, L. Kuo, and P. O. Lewis (2018). A new monte carlo method for estimating marginal likelihoods. Bayesian Analysis 13(2), 311–333.