Review Articles

Eight predictive powers with historical and interim data for futility and efficacy analysis

Ying-Ying Zhang ,

Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, People’s Republic of China; Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, People’s Republic of China

Teng-Zhong Rong ,

Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, People’s Republic of China; Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, People’s Republic of China

Man-Man Li

Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, People’s Republic of China; Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, People’s Republic of China

Pages 0 | Received 05 Apr. 2021, Accepted 28 Aug. 2021, Published online: 25 Oct. 2021,
  • Abstract
  • Full Article
  • References
  • Citations

When the historical data of the early phase trial and the interim data of the Phase III trial are available, we should use them to give a more accurate prediction in both futility and efficacy analysis.The predictive power is an important measure of the practical utility of a proposed trial, and it is better than the classical statistical power in giving a good indication of the probability that the trial will demonstrate a positive or statistically significant outcome. In addition to the four predictive powers with historical and interim data available in the literature and summarized in Table 1,we discover and calculate another four predictive powers also summarized in Table 1, for one-sided hypotheses. Moreover, we calculate eight predictive powers summarized in Table 2, for the reversed hypotheses. The combination of the two tables gives us a complete picture of the predictive powers with historical and interim data for futility and efficacy analysis. Furthermore, the eight predictive powers with historical and interim data are utilized to guide the futility analysis in the tamoxifen example. Finally, extensive simulations have been conducted to investigate the sensitivity analysis of priors, sample sizes, interim result and interim time on different predictive powers.

References

  • Chen, M. H., Ibrahim, J. G., Lam, P., Yu, A., & Zhang, Y. Y. (2011). Bayesian design of noninferiority trials for medical devices using historical data. Biometrics, 67(3), 11631170. https://doi.org/10.1111/biom.2011.67.issue-3
  • Choi, S. C., Smith, P. J., & Becker, D. P. (1985). Early decision in clinical trials when the treatment differences are small. Controlled Clinical Trials, 6(4), 280288. https://doi.org/10.1016/0197-2456(85)90104-7
  • Chuang-Stein, C. (2006). Sample size and the probability of a successful trial. Pharmaceutical Statistics, 5(4), 305309. https://doi.org/10.1002/(ISSN)1539-1612 
  • Chuang-Stein, C., & Kirby, S. (2017). Quantitative decisions in drug development. Springer.
  • Deng, Q. Q., Zhang, Y. Y., Roy, D., & Chen, M. H. (2020). Superiority of combining two independent trials in interim futility analysis. Statistical Methods in Medical Research, 29(2), 522540. https://doi.org/10.1177/0962280219840383
  • Dignam, J. J., Bryant, J., Wieand, H. S., Fisher, B., & Wolmark, N. (1998). Early stopping of a clinical trial when there is evidence of no treatment benefit: protocol b-14 of the national surgical adjuvant breast and bowel project. Controlled Clinical Trials, 19(6), 575588. https://doi.org/10.1016/S0197-2456(98)00041-5
  • Dmitrienko, A., & Wang, M. D. (2006). Bayesian predictive approach to interim monitoring in clinical trials. Statistics in Medicine, 25(13), 21782195. https://doi.org/10.1002/(ISSN)1097-0258
  • Ibrahim, J. G., Chen, M. H., Lakshminarayanan, M., Liu, G. F., & Heyse, J. F. (2015). Bayesian probability of success for clinical trials using historical data. Statistics in Medicine, 34(2), 249264. https://doi.org/10.1002/sim.v34.2
  • Jiang, K. (2011). Optimal sample sizes and go/no-go decisions for phase ii/iii development programs based on probability of success. Statistics in Biopharmaceutical Research, 3(3), 463475. https://doi.org/10.1198/sbr.2011.10068
  • Kirby, S., Burke, J., Chuang-Stein, C., & Sin, C. (2012). Discounting phase 2 results when planning phase 3 clinical trials. Pharmaceutical Statistics, 11(5), 373385. https://doi.org/10.1002/pst.1521
  • Lan, K. K. G., & Wittes, J. T. (2012). Some thoughts on sample size: a Bayesian frequentist hybrid approach. Clinical Trials, 9(5), 561569. https://doi.org/10.1177/1740774512453784
  • O'Hagan, A., Stevens, J. W., & Campbell, M. J. (2005). Assurance in clinical trial design. Pharmaceutical Statistics, 4(3), 187201. https://doi.org/10.1002/(ISSN)1539-1612
  • Schmidli, H., Bretz, F., & Racine-Poon, A. (2007). Bayesian predictive power for interim adaptation in seamless phase ii/iii trials where the endpoint is survival up to some specified timepoint. Statistics in Medicine, 26(27), 49254938. https://doi.org/10.1002/(ISSN)1097-0258
  • Spiegelhalter, D. J., Abrams, K. R., & Myles, J. P. (2004). Bayesian approaches to clinical trials and health-care evaluation. Wiley.
  • Spiegelhalter, D. J., Freedman, L. S., & Blackburn, P. R. (1986). Monitoring clinical trials: conditional or predictive power?. Controlled Clinical Trials, 7(1), 817. https://doi.org/10.1016/0197-2456(86)90003-6
  • Trzaskoma, B., & Sashegyi, A. (2007). Predictive probability of success and the assessment of futility in large outcomes trials. Journal of Biopharmaceutical Statistics, 17(1), 4563. https://doi.org/10.1080/10543400601001485
  • Tsiatis, A. A. (1981). The asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time. Biometrika, 68(1), 311315. https://doi.org/10.1093/biomet/68.1.311
  • Wang, S. J., Hung, H. M. J., & O'Neill, R. T. (2006). Adapting the sample size planning of a phase iii trial based on phase ii data. Pharmaceutical Statistics, 5(2), 8597. https://doi.org/10.1002/(ISSN)1539-1612
  • Zhang, J., Carlin, B. P., Neaton, J. D., Soon, G. G., Nie, L., Kane, R., Virnig, B. A., & Chu, H. (2014). Network meta-analysis of randomized clinical trials: reporting the proper summaries. Clinical Trials, 11(2), 246262. https://doi.org/10.1177/1740774513498322
  • Zhang, Y. Y., Rong, T. Z., & Li, M. M. (2020a). The contemplated average success probability for normally distributed models with an application to optimal sample sizes selection. Statistics in Medicine, 39(23), 31733183. https://doi.org/10.1002/sim.v39.23
  • Zhang, Y. Y., Rong, T. Z., & Li, M. M. (2020b). A new expectation identity and its application in the calculations of predictive powers assuming normality. Chinese Journal of Applied Probability and Statistics, 36(5), 523535. https://doi.org/10.3969/j.issn.1001-4268.2020.05.007
  • Zhang, Y. Y., & Ting, N. (2018). Bayesian sample size determination for a phase iii clinical trial with diluted treatment effect. Journal of Biopharmaceutical Statistics, 28(6), 11191142. https://doi.org/10.1080/10543406.2018.1436556
  • Zhang, Y. Y., & Ting, N. (2020). Sample size considerations for a phase iii clinical trial with diluted treatment effect. Statistics in Biopharmaceutical Research, 12(3), 311321. https://doi.org/10.1080/19466315.2019.1599414

To cite this article: Ying-Ying Zhang, Teng-Zhong Rong & Man-Man Li (2021): Eight predictive
powers with historical and interim data for futility and efficacy analysis, Statistical Theory and
Related Fields, DOI: 10.1080/24754269.2021.1991557
To link to this article: https://doi.org/10.1080/24754269.2021.1991557