Modeling of experts’ divergent prior beliefs for a sequential phase III clinical trial
Abstract
Background: There have been few Bayesian analyses of phase III sequential clinical trials that model divergent expert opinions in a single distribution. Purpose: We used modeling of experts’ opinions to perform additional Bayesian analyses of a randomized clinical trial (designed as a sequential trial), particularly when a bimodal shape is observed. We provide an illustrative example based on a randomized trial conducted in patients aged between 65 and 75 years with multiple myeloma as the case study. Methods: The main endpoint of the trial was overall survival (OS). Prior distribution of the log hazard ratio of death in the experimental versus the control arm ([Formula: see text]) was constructed based on elicitation of experts using a mixture of normal distributions estimated by the Expectation–Maximisation (EM) algorithm. At each interim and terminal analysis, the posterior probability of [Formula: see text] and the resulting increases in median OS in the experimental arm compared to the control were computed. The results were compared to results obtained using either skeptical, enthusiastic, or a mixture of those priors. Finally, we discuss our results in light of the frequentist approach originally designed for the trial. Results: A total of 39 experts reported their opinion on the median OS in the experimental arm compared to the median control survival of 30 months. The resulting pooled distribution of the log hazard ratios exhibited a bimodal profile. When the prior mixture of the normal distribution was fitted to the data sets from the experts, 44% of the experts’ opinions were optimistic and 56% were doubtful. At the final analysis, the percentage of doubting experts dropped to 18%. This corresponded to a posterior probability of an improved OS in the experimental arm compared to the control arm of at least 0.98, regardless of the prior. These findings are in agreement with the original conclusion of the trial regarding the beneficial effect of the experimental treatment in this population. Limitations: Only 39 experts among the 120 questioned physicians responded to the inquiry. Our approach was hybrid because the prior mixture was estimated using the EM algorithm, and a full Bayesian approach may have been used. Conclusions: Bayesian inference allows the quantification of increased survival in terms of probability distributions and provides investigators with an additional tool in the analysis of a randomized phase III clinical trial. Using a mixture of densities appears to be a promising strategy for incorporating the bimodal profile of prior opinion, with actualization of the two components along the trial as an illustration of the evolution of opinions as data are accumulated.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Small trials with inadequate power can produce non-significant P-values despite clinically meaningful effects.
“It is well known that insufficient power accompanying small trials may lead to insignificant P-values even when clinically meaningful effects are observed.2,4”
From A Bayesian Analysis of a Randomized Clinical Trial Comparing Antimetabolite Therapies for Non-Infectious Uveitis (2017) · cites this paper as [2]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Maximum Likelihood from Incomplete Data Via the <i>EM</i> Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444 · see citing works
Regression Models and Life-Tables
Cox, D. R. (1972) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1972.tb00899.x · Cited by 39,793 · see citing works
Regression Models and Life-Tables
Cox, D. R. (1992) · Springer Series in Statistics · doi:10.1007/978-1-4612-4380-9_37 · Cited by 26,297 · see citing works
McLachlan, G., & Peel, D. (2000) · Wiley Series in Probability and Statistics · doi:10.1002/0471721182 · Cited by 10,991 · see citing works
Breslow, N. E., Cox, D. R., & Oakes, D. (1985) · Biometrics · doi:10.2307/2530888 · Cited by 4,382 · see citing works
Chang, E. L., Wefel, J. S., Hess, K. R., Allen, P. K., Lang, F. F., Kornguth, D. G., Arbuckle, R. B., Swint, J. M., Shiu, A. S., Maor, M. H., et al. (2009) · The Lancet Oncology · doi:10.1016/s1470-2045(09)70263-3 · Cited by 2,479 · see citing works
Equipoise and the Ethics of Clinical Research
Freedman, B. (1987) · New England Journal of Medicine · doi:10.1056/nejm198707163170304 · Cited by 2,339 · see citing works
Peto, R., Pike, M. C., Armitage, P., Breslow, N. E., Cox, D. R., Howard, S. V., Mantel, N., McPherson, K., Peto, J., & Smith, P. G. (1976) · British Journal of Cancer · doi:10.1038/bjc.1976.220 · Cited by 2,294 · see citing works
Sample-Size Formula for the Proportional-Hazards Regression Model
Schoenfeld, D. (1983) · Biometrics · doi:10.2307/2531021 · Cited by 1,100 · see citing works
Combining Probability Distributions: A Critique and an Annotated Bibliography
Genest, C., & Zidek, J. V. (1986) · Statistical Science · doi:10.1214/ss/1177013825 · Cited by 1,000 · see citing works
Facon, T. T. F., Mary, J., Hulin, C., Benboubker, L., Attal, M., Pegourié, B., Renaud, M., Harousseau, J. L., Guillerm, G., Chaleteix, C., et al. (2007) · The Lancet · doi:10.1016/s0140-6736(07)61537-2 · Cited by 865 · see citing works
Self-citationBayesian approaches to randomized trials
Spiegelhalter, D. J., Freedman, L. S., & Parmar, M. K. B. (1994) · Journal of the Royal Statistical Society. Series A (Statistics in Society) · doi:10.2307/2983527 · Cited by 720 · see citing works
Adjuvant Chemotherapy in Older Women with Early-Stage Breast Cancer
Muss, H. B., Berry, D. A., Cirrincione, C., Theodoulou, M., Mauer, A. M., Kornblith, A. B., Partridge, A. H., Dressler, L. G., Cohen, H. J., Becker, H. P., et al. (2009) · New England Journal of Medicine · doi:10.1056/nejmoa0810266 · Cited by 554 · see citing works
The Asymptotic Properties of Nonparametric Tests for Comparing Survival Distributions
Schoenfeld, D. (1981) · Biometrika · doi:10.1093/biomet/68.1.316 · Cited by 505 · see citing works
Bayesian methods in health technology assessment: a review.
Spiegelhalter, Myles, Jones, & Abrams, K. R. (2000) · Health Technology Assessment · doi:10.3310/hta4380 · Cited by 359 · see citing works
The GRIT Study Group, & article, P. A. L. A. T. E. O. T. (2003) · BJOG: An International Journal of Obstetrics & Gynaecology · doi:10.1046/j.1471-0528.2003.02014.x · Cited by 305 · see citing works
Methods to elicit beliefs for Bayesian priors: a systematic review
Johnson, S. R., TOMLINSON, G. A., HAWKER, G. A., Granton, J. T., & Feldman, B. M. (2009) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2009.06.003 · Cited by 183 · see citing works
Tsiatis, A. A. (1981) · Biometrika · doi:10.1093/biomet/68.1.311 · Cited by 162 · see citing works
Comparison of Bayesian with group sequential methods for monitoring clinical trials
Freedman, L. S., & Spiegelhalter, D. J. (1989) · Controlled Clinical Trials · doi:10.1016/0197-2456(89)90001-9 · Cited by 128 · see citing works
O’Hagan, A. (2011) · Environmental Modelling & Software · doi:10.1016/j.envsoft.2011.03.003 · Cited by 124 · see citing works
Interim analyses in clinical trials: Classical vs. bayesian approaches
Berry, D. A. (1985) · Statistics in Medicine · doi:10.1002/sim.4780040412 · Cited by 115 · see citing works
The chart trials: Bayesian design and monitoring in practice
Parmar, M., Spiegelhalter, D. J., & Freedman, L. S. (1994) · Statistics in Medicine · doi:10.1002/sim.4780131304 · Cited by 111 · see citing works
The what, why and how of bayesian clinical trials monitoring
Freedman, L. S., Spiegelhalter, D. J., & Parmar, M. (1994) · Statistics in Medicine · doi:10.1002/sim.4780131312 · Cited by 101 · see citing works
Giles, F. J., Kantarjian, H. M., Cortes, J. E., Garcia‐Manero, G., Verstovšek, S., Faderl, S. H., Thomas, D. A., Ferrajoli, A., O'Brien, S. M., Wathen, J. K., et al. (2003) · Journal of Clinical Oncology · doi:10.1200/jco.2003.11.016 · Cited by 99 · see citing works
A kurtosis-based dynamic approach to Gaussian mixture modeling
Vlassis, N., & Likas, A. C. (1999) · IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans · doi:10.1109/3468.769758 · Cited by 90 · see citing works
An empirical comparison of EM, SEM and MCMC performance for problematic Gaussian mixture likelihoods
Dias, J. G., & Wedel, M. (2004) · Statistics and Computing · doi:10.1023/b:stco.0000039481.32211.5a · Cited by 89 · see citing works
Monitoring of large randomised clinical trials: a new approach with Bayesian methods
Parmar, M., Griffiths, G. O., Spiegelhalter, D. J., Souhami, R. L., Altman, D. G., & van der Scheuren, E. (2001) · The Lancet · doi:10.1016/s0140-6736(01)05558-1 · Cited by 73 · see citing works
BIAS IN THE EVALUATION OF DNA-AMPLIFICATION TESTS FOR DETECTINGCHLAMYDIA TRACHOMATIS
Hadgu, A. (1997) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19970630)16:12 · Cited by 65 · see citing works
Why should clinicians care about Bayesian methods?
Matthews, R. (2001) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(00)00232-9 · Cited by 62 · see citing works
Komárek, A. (2009) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2009.05.006 · Cited by 53 · see citing works
Early Stopping of a Clinical Trial When There is Evidence of No Treatment Benefit
Dignam, J. J., Bryant, J., Wieand, H. S., et al. (1998) · Controlled Clinical Trials · doi:10.1016/s0197-2456(98)00041-5 · Cited by 50 · see citing works
Bayesian sample size calculations in phase II clinical trials using a mixture of informative priors
Gajewski, B. J., & Mayo, M. S. (2005) · Statistics in Medicine · doi:10.1002/sim.2450 · Cited by 45 · see citing works
Tan, S. B., Chung, Y. F. A., Tai, B., et al. (2003) · Controlled Clinical Trials · doi:10.1016/s0197-2456(02)00318-5 · Cited by 39 · see citing works
Nathan, P. C., TOMLINSON, G. A., Dupuis, L. L., et al. (2005) · Supportive Care in Cancer · doi:10.1007/s00520-005-0875-7 · Cited by 35 · see citing works
Hiance, A., Chevret, S., & Lévy, V. (2008) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2008.04.009 · Cited by 34 · see citing works
Self-citationMixtures of prior distributions for predictive Bayesian sample size calculations in clinical trials
Brutti, P., Santis, F. D., & Gubbiotti, S. (2009) · Statistics in Medicine · doi:10.1002/sim.3609 · Cited by 22 · see citing works
Norman, P. H., Thall, P. F., Purugganan, R. V., et al. (2009) · Cancer · doi:10.1002/cncr.24108 · Cited by 18 · see citing works
Sequential causal inference: Application to randomized trials of adaptive treatment strategies
Dawson, R., & Lavori, P. W. (2007) · Statistics in Medicine · doi:10.1002/sim.3039 · Cited by 15 · see citing works
Chen, Y., & Smith, B. J. (2009) · Statistics in Medicine · doi:10.1002/sim.3711 · Cited by 12 · see citing works
Pressman, A. R., Avins, A. L., Hubbard, A., & Satariano, W. A. (2011) · Contemporary Clinical Trials · doi:10.1016/j.cct.2011.03.010 · Cited by 9 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- Fayers PM, Ashby D, Parmar MK. Tutorial in biostatis- tics Bayesian data monitoring in clinical trials. Stat Med 1997; 16: 1413-30.
Cited by
Sorted by citations
Browne, E. N., Rathinam, S. R., Kanakath, A., Thundikandy, R., Babu, M., Lietman, T. M., & Acharya, N. R. (2017) · Ophthalmic Epidemiology · doi:10.1080/09286586.2016.1255764 · Cited by 11 · see citing works
- Authors
- Moatti, M., Zohar, S., Facon, T., Moreau, P., Mary, J.-Y., & Chevret, S.
- Affiliations
- Inserm (FR)
- Centre Hospitalier Universitaire de Lille (FR)
- Centre Hospitalier Universitaire de Nantes (FR)
- Venue
- Clinical Trials
- Publisher
- SAGE Publications
- Published
- 2013-07-02
- Volume
- 10
- Issue
- 4
- Pages
- 505-514
- ISSN
- 1740-7745 (ISSN-L)
- 1740-7753
- OpenAlex
- W2096317974
- Cited by
- 11
- References
- 40
- Citations by year
- 2024: 1 · 2021: 1 · 2019: 1 · 2017: 4 · 2016: 3 · 2015: 1
- FWCI
- 1.18
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Clinical Trials (publishedVersion)
- PubMed (publishedVersion)
- HAL (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Sociology and Political Science › Delphi Technique in Research
- Keywords
- expert elicitation, mixture of normal distributions, expectation-maximization algorithm, overall survival, multiple myeloma, interim analysis
- MeSH terms
- Aged, Bayes Theorem, Drug Therapy, Combination, Expert Testimony, Humans, Melphalan, Multiple Myeloma, Prednisone, Surveys and Questionnaires, Thalidomide, Models, Statistical, Survival Analysis, Antineoplastic Agents, Hormonal, Myeloablative Agonists, Angiogenesis Inhibitors, Stem Cell Transplantation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
