1. Home
  2. Issues
  3. Volume 2, Issue 1 (2024)
  4. On Bayesian Sequential Clinical Trial De ...

The New England Journal of Statistics in Data Science


On Bayesian Sequential Clinical Trial Designs
Volume 2, Issue 1 (2024), pp. 136–151
Pub. online: 31 January 2023      Type: Cancer Research      Open accessOpen Access
Accepted
24 January 2023
Published
31 January 2023

Abstract

Clinical trials usually involve sequential patient entry. When designing a clinical trial, it is often desirable to include a provision for interim analyses of accumulating data with the potential for stopping the trial early. We review Bayesian sequential clinical trial designs based on posterior probabilities, posterior predictive probabilities, and decision-theoretic frameworks. A pertinent question is whether Bayesian sequential designs need to be adjusted for the planning of interim analyses. We answer this question from three perspectives: a frequentist-oriented perspective, a calibrated Bayesian perspective, and a subjective Bayesian perspective. We also provide new insights into the likelihood principle, which is commonly tied to statistical inference and decision making in sequential clinical trials. Some theoretical results are derived, and numerical studies are conducted to illustrate and assess these designs.

Supplementary material

 Supplementary Material
Supplementary Material to “On Bayesian Sequential Clinical Trial Designs”.

References

[1] 
Anderson, K. (2022). gsDesign: Group Sequential Design. R package version 3.4.0. https://CRAN.R-project.org/package=gsDesign.
[2] 
Armitage, P. (1991). Interim analysis in clinical trials. Statistics in Medicine 10(6) 925–937.
[3] 
Armitage, P., McPherson, C. and Rowe, B. (1969). Repeated significance tests on accumulating data. Journal of the Royal Statistical Society: Series A (General) 132(2) 235–244. https://doi.org/10.2307/2343787. MR0250405
[4] 
Bayarri, M. J. and Berger, J. O. (2004). The interplay of Bayesian and frequentist analysis. Statistical Science 19(1) 58–80. https://doi.org/10.1214/088342304000000116. MR2082147
[5] 
Berger, J. (1980) Statistical Decision Theory: Foundations, Concepts, and Methods. Springer Science & Business Media. MR0580664
[6] 
Berger, J. O. and Sellke, T. (1987). Testing a point null hypothesis: the irreconcilability of P values and evidence. Journal of the American Statistical Association 82(397) 112–122. MR0883340
[7] 
Berger, J. O. and Wolpert, R. L. (1988) The Likelihood Principle (Second Edition). Institute of Mathematical Statistics, Hayward. MR0773665
[8] 
Bernardo, J. M. and Smith, A. F. M. (2000) Bayesian Theory. John Wiley & Sons. https://doi.org/10.1002/9780470316870. MR1274699
[9] 
Berry, D. A. (1985). Interim analyses in clinical trials: classical vs. Bayesian approaches. Statistics in Medicine 4(4) 521–526.
[10] 
Berry, D. A. (1987). Interim analysis in clinical trials: the role of the likelihood principle. The American Statistician 41(2) 117–122. https://doi.org/10.2307/2684222. MR0898268
[11] 
Berry, D. A. (2006). Bayesian clinical trials. Nature Reviews Drug Discovery 5(1) 27–36.
[12] 
Berry, D. A. and Ho, C. q. H. (1988). One-sided sequential stopping boundaries for clinical trials: a decision-theoretic approach. Biometrics 219–227. https://doi.org/10.2307/2531909. MR0931636
[13] 
Berry, D. A. and Hochberg, Y. (1999). Bayesian perspectives on multiple comparisons. Journal of Statistical Planning and Inference 82(1-2) 215–227. https://doi.org/10.1016/S0378-3758(99)00044-0. MR1736444
[14] 
Berry, S. M., Carlin, B. P., Lee, J. J. and Müller, P. (2010) Bayesian Adaptive Methods for Clinical Trials. CRC Press. MR2723582
[15] 
Birnbaum, A. (1962). On the foundations of statistical inference. Journal of the American Statistical Association 57(298) 269–306. MR0138176
[16] 
Chuang-Stein, C., Kirby, S., Hirsch, I. and Atkinson, G. (2011). The role of the minimum clinically important difference and its impact on designing a trial. Pharmaceutical Statistics 10(3) 250–256.
[17] 
Cornfield, J. (1966). A Bayesian test of some classical hypotheses—with applications to sequential clinical trials. Journal of the American Statistical Association 61(315) 577–594. MR0207141
[18] 
Cornfield, J. (1966). Sequential trials, sequential analysis and the likelihood principle. The American Statistician 20(2) 18–23.
[19] 
DeGroot, M. H. (1970) Optimal Statistical Decisions. John Wiley & Sons. MR0356303
[20] 
Dmitrienko, A. and Wang, M. q. D. (2006). Bayesian predictive approach to interim monitoring in clinical trials. Statistics in Medicine 25(13) 2178–2195. https://doi.org/10.1002/sim.2204. MR2240095
[21] 
Edwards, W., Lindman, H. and Savage, L. J. (1963). Bayesian statistical inference for psychological research. Psychological Review 70(3) 193–242.
[22] 
Emerson, S. S., Kittelson, J. M. and Gillen, D. L. (2007). Bayesian evaluation of group sequential clinical trial designs. Statistics in Medicine 26(7) 1431–1449. https://doi.org/10.1002/sim.2640. MR2359150
[23] 
Evans, M. (2013). What does the proof of Birnbaum’s theorem prove? Electronic Journal of Statistics 7 2645–2655. https://doi.org/10.1214/13-EJS857. MR3121626
[24] 
Fisch, R., Jones, I., Jones, J., Kerman, J., Rosenkranz, G. K. and Schmidli, H. (2015). Bayesian design of proof-of-concept trials. Therapeutic Innovation & Regulatory Science 49(1) 155–162.
[25] 
Food and Drug Administration (2010). Guidance for the Use of Bayesian Statistics in Medical Device Clinical Trials. https://www.fda.gov/media/71512/download.
[26] 
Food and Drug Administration (2019). Adaptive Designs for Clinical Trials of Drugs and Biologics: Guidance for Industry. https://www.fda.gov/media/78495/download.
[27] 
Food and Drug Administration (2020). Interacting with the FDA on Complex Innovative Trial Designs for Drugs and Biological Products. Guidance for Industry. https://www.fda.gov/media/130897/download.
[28] 
Freedman, L. S. and Spiegelhalter, D. J. (1989). Comparison of Bayesian with group sequential methods for monitoring clinical trials. Controlled Clinical Trials 10(4) 357–367.
[29] 
Freedman, L. S., Spiegelhalter, D. J. and Parmar, M. K. (1994). The what, why and how of Bayesian clinical trials monitoring. Statistics in Medicine 13(13-14) 1371–1383.
[30] 
Gandenberger, G. (2015). A new proof of the likelihood principle. British Journal for the Philosophy of Science 66(3) 475–503. https://doi.org/10.1093/bjps/axt039. MR3413356
[31] 
Gandenberger, G. (2017). Differences among noninformative stopping rules are often relevant to Bayesian decisions. arXiv preprint arXiv:1707.00214.
[32] 
Gandenberger, G. S. Two Principles of Evidence and Their Implications for the Philosophy of Scientific Method (2015). PhD thesis, University of Pittsburgh. MR3427387
[33] 
Geller, N. L. and Pocock, S. J. (1987). Interim analyses in randomized clinical trials: ramifications and guidelines for practitioners. Biometrics 213–223.
[34] 
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. and Rubin, D. B. (2013) Bayesian Data Analysis (Third Edition). CRC Press. MR3235677
[35] 
Gerber, F. and Gsponer, T. (2016). gsbDesign: an R package for evaluating the operating characteristics of a group sequential Bayesian design. Journal of Statistical Software 69(11) 1–23.
[36] 
Goldstein, M. (2006). Subjective Bayesian analysis: principles and practice. Bayesian Analysis 1(3) 403–420. https://doi.org/10.1214/06-BA116. MR2221272
[37] 
Harrell, F. (2020). Continuous learning from data: no multiplicities from computing and using Bayesian posterior probabilities as often as desired. https://www.fharrell.com/post/bayes-seq/.
[38] 
Harrell, F. (2020). p-values and Type I Errors are Not the Probabilities We Need. https://www.fharrell.com/post/pvalprobs/.
[39] 
Heitjan, D. F. (1997). Bayesian interim analysis of phase II cancer clinical trials. Statistics in Medicine 16(16) 1791–1802.
[40] 
Hendriksen, A., de Heide, R. and Grünwald, P. (2021). Optional stopping with Bayes factors: a categorization and extension of folklore results, with an application to invariant situations. Bayesian Analysis 16(3) 961–989. https://doi.org/10.1214/20-BA1234. MR4303875
[41] 
Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 186(1007) 453–461. https://doi.org/10.1098/rspa.1946.0056. MR0017504
[42] 
Jennison, C. and Turnbull, B. W. (1990). Statistical approaches to interim monitoring of medical trials: a review and commentary. Statistical Science 5(3) 299–317. MR1080954
[43] 
Jennison, C. and Turnbull, B. W. (2000) Group Sequential Methods with Applications to Clinical Trials. Chapman & Hall/CRC, Boca Raton. MR1710781
[44] 
Johnson, V. E. and Cook, J. D. (2009). Bayesian design of single-arm phase II clinical trials with continuous monitoring. Clinical Trials 6(3) 217–226.
[45] 
Johnson, V. E. and Rossell, D. (2010). On the use of non-local prior densities in Bayesian hypothesis tests. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72(2) 143–170. https://doi.org/10.1111/j.1467-9868.2009.00730.x. MR2830762
[46] 
Kidwell, K. M., Roychoudhury, S., Wendelberger, B., Scott, J., Moroz, T., Yin, S., Majumder, M., Zhong, J., Huml, R. A. and Miller, V. (2022). Application of Bayesian methods to accelerate rare disease drug development: scopes and hurdles. Orphanet Journal of Rare Diseases 17(1) 1–15.
[47] 
Kim, K. and DeMets, D. L. (1987). Design and analysis of group sequential tests based on the type I error spending rate function. Biometrika 74(1) 149–154. https://doi.org/10.1093/biomet/74.1.149. MR0885927
[48] 
Lan, K. K. G. and DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70(3) 659–663. https://doi.org/10.2307/2336502. MR0725380
[49] 
Lan, K. K. G., Simon, R. and Halperin, M. (1982). Stochastically curtailed tests in long–term clinical trials. Sequential Analysis 1(3) 207–219. https://doi.org/10.1080/07474948208836014. MR0685474
[50] 
Lee, J. J. and Liu, D. D. (2008). A predictive probability design for phase II cancer clinical trials. Clinical Trials 5(2) 93–106.
[51] 
Lewis, R. J. and Berry, D. A. (1994). Group sequential clinical trials: a classical evaluation of Bayesian decision-theoretic designs. Journal of the American Statistical Association 89(428) 1528–1534.
[52] 
Little, R. J. (2006). Calibrated Bayes: a Bayes/frequentist roadmap. The American Statistician 60(3) 213–223. https://doi.org/10.1198/000313006X117837. MR2246754
[53] 
Mayo, D. G. (2014). On the Birnbaum argument for the strong likelihood principle. Statistical Science 29(2) 227–239. https://doi.org/10.1214/13-STS457. MR3264534
[54] 
Müller, P., Berry, D. A., Grieve, A. P., Smith, M. and Krams, M. (2007). Simulation-based sequential Bayesian design. Journal of Statistical Planning and Inference 137(10) 3140–3150. https://doi.org/10.1016/j.jspi.2006.05.021. MR2364157
[55] 
O’Brien, P. C. and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35(3) 549–556.
[56] 
Pampallona, S. and Tsiatis, A. A. (1994). Group sequential designs for one-sided and two-sided hypothesis testing with provision for early stopping in favor of the null hypothesis. Journal of Statistical Planning and Inference 42(1-2) 19–35. https://doi.org/10.1016/0378-3758(94)90187-2. MR1309622
[57] 
Peña, V. and Berger, J. O. (2017). A note on recent criticisms to Birnbaum’s theorem. arXiv preprint arXiv:1711.08093. https://doi.org/10.1002/asmb.2402. MR3915805
[58] 
Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64(2) 191–199.
[59] 
Polack, F. P., Thomas, S. J., Kitchin, N., Absalon, J., Gurtman, A., Lockhart, S., Perez, J. L., Marc, G. P., Moreira, E. D., Zerbini, C. et al. (2020). Safety and efficacy of the BNT162b2 mRNA Covid-19 vaccine. New England Journal of Medicine 383(27) 2603–2615.
[60] 
Robert, C. (2007) The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation (Second Edition). Springer Science & Business Media. MR2723361
[61] 
Robins, J. and Wasserman, L. (2000). Conditioning, likelihood, and coherence: a review of some foundational concepts. Journal of the American Statistical Association 95(452) 1340–1346. https://doi.org/10.2307/2669784. MR1825290
[62] 
Robinson, G. K. (2019). What properties might statistical inferences reasonably be expected to have?–crisis and resolution in statistical inference. The American Statistician 73(3) 243–252. https://doi.org/10.1080/00031305.2017.1415971. MR3989366
[63] 
Rosenbaum, P. R. and Rubin, D. B. (1984). Sensitivity of Bayes inference with data-dependent stopping rules. The American Statistician 38(2) 106–109.
[64] 
Rosner, G. L. and Berry, D. A. (1995). A Bayesian group sequential design for a multiple arm randomized clinical trial. Statistics in Medicine 14(4) 381–394.
[65] 
Rosner, G. L. and Tsiatis, A. A. (1988). Exact confidence intervals following a group sequential trial: a comparison of methods. Biometrika 75(4) 723–729.
[66] 
Ross, S. M. (1996) Stochastic Processes (Second Edition). John Wiley & Sons. MR1373653
[67] 
Royall, R. (1997) Statistical Evidence: A Likelihood Paradigm. Chapman & Hall/CRC. MR1629481
[68] 
Rubin, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. The Annals of Statistics 12(4) 1151–1172. https://doi.org/10.1214/aos/1176346785. MR0760681
[69] 
Ryan, E. G., Brock, K., Gates, S. and Slade, D. (2020). Do we need to adjust for interim analyses in a Bayesian adaptive trial design? BMC Medical Research Methodology 20(1) 1–9.
[70] 
Saville, B. R., Connor, J. T., Ayers, G. D. and Alvarez, J. (2014). The utility of Bayesian predictive probabilities for interim monitoring of clinical trials. Clinical Trials 11(4) 485–493.
[71] 
Shi, H. and Yin, G. (2019). Control of type I error rates in Bayesian sequential designs. Bayesian Analysis 14(2) 399–425. https://doi.org/10.1214/18-BA1109. MR3934091
[72] 
Simon, R. (1994). Problems of multiplicity in clinical trials. Journal of Statistical Planning and Inference 42(1-2) 209–221.
[73] 
Sjölander, A. and Vansteelandt, S. (2019). Frequentist versus Bayesian approaches to multiple testing. European Journal of Epidemiology 34(9) 809–821.
[74] 
Slud, E. and Wei, L. J. (1982). Two-sample repeated significance tests based on the modified Wilcoxon statistic. Journal of the American Statistical Association 77(380) 862–868. MR0686410
[75] 
Snapinn, S., Chen, M. q. G., Jiang, Q. and Koutsoukos, T. (2006). Assessment of futility in clinical trials. Pharmaceutical Statistics 5(4) 273–281.
[76] 
Spiegelhalter, D. J., Freedman, L. S. and Parmar, M. K. (1994). Bayesian approaches to randomized trials. Journal of the Royal Statistical Society: Series A (Statistics in Society) 157(3) 357–387. https://doi.org/10.2307/2983527. MR1321308
[77] 
Stallard, N., Thall, P. F. and Whitehead, J. (1999). Decision theoretic designs for phase II clinical trials with multiple outcomes. Biometrics 55(3) 971–977.
[78] 
Stallard, N., Todd, S., Ryan, E. G. and Gates, S. (2020). Comparison of Bayesian and frequentist group-sequential clinical trial designs. BMC Medical Research Methodology 20(1) 1–14.
[79] 
Storey, J. D. (2003). The positive false discovery rate: a Bayesian interpretation and the q-value. The Annals of Statistics 31(6) 2013–2035. https://doi.org/10.1214/aos/1074290335. MR2036398
[80] 
Thall, P. F. and Simon, R. (1994). Practical Bayesian guidelines for phase IIB clinical trials. Biometrics 50(2) 337–349. https://doi.org/10.2307/2533377. MR1294683
[81] 
Ventz, S. and Trippa, L. (2015). Bayesian designs and the control of frequentist characteristics: a practical solution. Biometrics 71(1) 218–226. https://doi.org/10.1111/biom.12226. MR3335366
[82] 
Wagenmakers, E. q. J. (2007). A practical solution to the pervasive problems of p values. Psychonomic Bulletin & Review 14(5) 779–804.
[83] 
Whitehead, J. (1997) The Design and Analysis of Sequential Clinical Trials. John Wiley & Sons. MR0793018
[84] 
Zhou, Y., Lin, R. and Lee, J. J. (2021). The use of local and nonlocal priors in Bayesian test-based monitoring for single-arm phase II clinical trials. Pharmaceutical Statistics 20(6) 1183–1199.
[85] 
Zhu, H. and Yu, Q. (2017). A Bayesian sequential design using alpha spending function to control type I error. Statistical Methods in Medical Research 26(5) 2184–2196. https://doi.org/10.1177/0962280215595058. MR3712227

Full article Related articles PDF XML
Full article Related articles PDF XML

Copyright
© 2024 New England Statistical Society
Open access article under the CC BY license.

Keywords
Adaptive design Interim analysis Likelihood principle Multiplicity Optional stopping Sequential hypothesis testing

Metrics
since December 2021
1161

Article info
views

 518

Full article
views
395

PDF
downloads

 82

XML
downloads


Share


RSS