Download PDF
Methods Inf Med 2016; 55(01): 4-13
DOI: 10.3414/ME14-01-0132
Original Articles
Schattauer GmbH

A Bayesian Hybrid Adaptive Randomisation Design for Clinical Trials with Survival Outcomes[*]

M. Moatti
1   Biostatistics and Clinical Epidemiology Team (ECSTRA) of the Center of Research on Epidemiology and Biostatistics Sorbonne Paris Cité (CRESS; INSERM UMR 1153), Paris Diderot University, Paris, France
,
S. Chevret
1   Biostatistics and Clinical Epidemiology Team (ECSTRA) of the Center of Research on Epidemiology and Biostatistics Sorbonne Paris Cité (CRESS; INSERM UMR 1153), Paris Diderot University, Paris, France
,
S. Zohar
1   Biostatistics and Clinical Epidemiology Team (ECSTRA) of the Center of Research on Epidemiology and Biostatistics Sorbonne Paris Cité (CRESS; INSERM UMR 1153), Paris Diderot University, Paris, France
,
W. F. Rosenberger
2   Department of Statistics, George Mason University, Fairfax, Virginia, USA
3   Institut für Medizinische Statistik, RWTH Aachen University, Aachen, Germany
› Author Affiliations
Further Information

Publication History

Received 04 December 2014

Accepted 21 May 2015

Publication Date:
08 January 2018 (online)

    Permissions and Reprints

Summary

Background: Response-adaptive randomisation designs have been proposed to im -prove the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosen -berger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size. Objectives: The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the esti -mated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by re -designing a clinical trial on multiple myeloma. Methods: To handle continuous monitoring of data, we propose a Bayesian response-adap -tive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simu lationstudy to assess and compare the perform -ance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive – either frequentist or fully Bayesian – designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior dis -tribution of the log hazard ratio were com -puted. The method is then illus trated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts. Results: As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mix -ture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules. Conclusions: Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.

Keywords

Adaptive design - Bayesian - censored data - response-adaptive randomisation - optimal allocation

* Supplementary online material published on our website http://dx.doi.org/10.3414/ME14-01-0132


 

  • References

  • 1 Luce BR, Kramer JM, Goodman SN, Connor J, Tunis S, Whicher D, Schwartz JS. Rethinking randomized clinical trials for comparative effectiveness research: the need for transformational change. Ann Intern Med 2009; 151: 206-209.
    CrossrefPubMedGoogle Scholar
  • 2 Rosenberger WF, Lachin JM. Randomisation in Clinical Trials: Theory and Practice. New York: Wiley; 2002
    Google Scholar
  • 3 Chow SC, Chang M. Adaptive Design Methods in Clinical Trials. New York: Chapman and Hall/CRC Press, Taylor and Francis; 2006
    Google Scholar
  • 4 Louis TA. Sequential allocation in clinical trials comparing two exponential survival curves. Biometrika 1977; 33: 627-634.
    PubMedGoogle Scholar
  • 5 Rosenberger WF, Seshaiyer P. Adaptive survival trials. Journal of Biopharmaceutical Statistics 1997; 7: 617-624.
    CrossrefPubMedGoogle Scholar
  • 6 Bandyopadhyay U, Biswas A, Bhattacharya R. A Bayesian adaptive design for two-stage clinical trials with survival data. Lifetime Data Analysis 2009; 15: 468-492.
    CrossrefPubMedGoogle Scholar
  • 7 Eick GE. The two-armed bandit with delayed responses. The Annals of Statistics 1988; 16: 254-264.
    CrossrefPubMedGoogle Scholar
  • 8 Sverdlov O, Tymofyeyev Y, Wong WK. Optimal response-adaptive randomized designs for multi-armed survival trials. Stat Med 2011; 30: 2890-2910.
    CrossrefPubMedGoogle Scholar
  • 9 Sverdlov O, Ryeznik Y, Wong WK. Efficient and ethical response-adaptive randomisation designs for multi-arm clinical trials with Weibull time-to-event outcomes. Journal of Biopharmaceutical Statistics 2014; 24: 732-754.
    CrossrefPubMedGoogle Scholar
  • 10 Rosenberger WF, Stallard N, Ivanova A, Harper CN, Ricks ML. Optimal adaptive designs for binary response trials. Biometrics 2001; 57: 909-913.
    CrossrefPubMedGoogle Scholar
  • 11 Rosenberger WF. Maximizing power and minimizing treatment failures in clinical trials. Clin Trials 2004; 1: 141-147.
    CrossrefPubMedGoogle Scholar
  • 12 Atkinson AC, Biswas A. Bayesian adaptive biased-coin designs for clinical trials with normal responses. Biometrics 2005; 61: 118-125.
    CrossrefPubMedGoogle Scholar
  • 13 Hu F, Rosenberger WF. The Theory of Response-Adaptive Randomisation in Clinical Trials. New York: Wiley; 2006
    Google Scholar
  • 14 Eisele J. The doubly adaptive biased coin design for sequential clinical trials. Journal of Statistical Planning and Inference 1994; 38: 249-261.
    CrossrefPubMedGoogle Scholar
  • 15 Zhang L, Rosenberger WF. Response-adaptive randomisation for survival trials: the parametric approach. Journal of the Royal Statistical Society C 2007; 56: 153-165.
    CrossrefPubMedGoogle Scholar
  • 16 Cheung YK, Inoue LYT, Wathen JK, Thall PF. Continuous Bayesian adaptive randomisation based on event times with covariates. Stat Med 2006; 25: 55-70.
    CrossrefPubMedGoogle Scholar
  • 17 Lecoutre B, Derzko G, Elqasyr K. Frequentist performance of Bayesian inference with response-adaptive designs. Stat Med 2010; 29: 3219-3231.
    CrossrefPubMedGoogle Scholar
  • 18 Hu F, Zhang L-X. Asymptotic properties of doubly adaptive biased coin designs for multitreatment clinical trials. The Annals of Statistics 2004; 32: 268-301.
    PubMedGoogle Scholar
  • 19 Parmar MK, Spiegelhalter DJ, Freedman LS. The CHART trials: Bayesian design and monitoring in practice. Stat Med 1994; 13: 1297-1312.
    CrossrefPubMedGoogle Scholar
  • 20 Spiegelhalter DJ, Freedman LS, Parmar MK. Bayesian approaches to randomized trials. Journal of the Royal Statistical Society A 1994; 157: 357-416.
    CrossrefPubMedGoogle Scholar
  • 21 Tsiatis AA. The asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time. Biometrika 1981; 68: 311-315.
    CrossrefPubMedGoogle Scholar
  • 22 Freedman LS. Tables of the number of patients required in clinical trials using the logrank test. Stat Med 1982; 1: 121-129.
    CrossrefPubMedGoogle Scholar
  • 23 Moatti M, Zohar S, Facon T, Moreau P, Mary J-Y, Chevret S. Modeling of experts’ divergent prior beliefs for a sequential phase III clinical trial. Clinical Trials 2013; 10: 505-514.
    CrossrefPubMedGoogle Scholar
  • 24 Brutti P, De Santis F, Gubbiotti S. Mixtures of prior distributions for predictive Bayesian sample size calculations in clinical trials. Stat Med 2009; 28: 2185-2201.
    CrossrefPubMedGoogle Scholar
  • 25 Zhao L, Woodworth G. Bayesian decision sequential analysis with survival endpoint in phase II clinical trials. Stat Med 2009; 28: 1339-1352.
    CrossrefPubMedGoogle Scholar
  • 26 Peto R, Pike MC, Armitage P, Breslow NE, Cox DR, Howard SV, Mantel N, McPherson K, Peto J, Smith PG. Design and analysis of randomized clinical trials requiring prolonged observation of each patient. Introduction and design. British Journal of Cancer 1976; 34: 585-612.
    CrossrefPubMedGoogle Scholar
  • 27 Ji Y, Bekele BN. Adaptive randomisation for multi-arm comparative clinical trials based on joint efficacy/toxicity outcomes. Biometrics 2009; 65: 876-884.
    CrossrefPubMedGoogle Scholar
  • 28 Xie F, Ji Y, Tremmel L. A Bayesian adaptive design for multi-dose, randomized, placebo-controlled phase I/II trials. Contemporary Clin Trials 2012; 33: 739-748.
    PubMedGoogle Scholar
  • 29 Pan H, Xie F, Liu P, Xia J, Ji Y. A phase I/II seamless dose escalation/expansion with adaptive randomisation scheme (SEARS). Clin Trials 2014; 11: 49-59.
    CrossrefPubMedGoogle Scholar
  • 30 Schoenfeld DA, Richter JR. Nomograms for calculating the number of patients needed for a clinical trial with survival as an endpoint. Biometrics 1982; 38: 163-170.
    CrossrefPubMedGoogle Scholar
  • 31 Facon T, Mary JY, Hulin C, Benboubker L, Attal M, Pegourie B, Renaud M, Harousseau JL, Guillerm G, Chaleteix C, Dib M, Voillat L, Maisonneuve H, Troncy J, Véronique Dorvaux V, Monconduit M, Martin C, Casassus P, Jau-bert J, Jardel H, Doyen C, Kolb B, Anglaret B, Grosbois B, Yakoub-Agha I, Mathiot C, Avet Loiseau H. Melphalan and prednisone plus thalidomide versus melphalan and prednisone alone or reduced-intensity autologous stem cell transplantation in elderly patients with multiple myeloma (IFM 99–06): a randomised trial. Lancet 2007; 370: 1209-1218.
    CrossrefPubMedGoogle Scholar
  • 32 Maurer W. Creative and Innovative Statistics in Clinical Research and Development. Methods of Information in Medicine 2005; 44 (Suppl. 04) 551-560.
    Article in Thieme ConnectPubMedGoogle Scholar
  • 33 Hiance A, Chevret S, Levy V. A practical approach for eliciting expert prior beliefs about cancer survival in phase III randomized trial. Journal of Clinical Epidemiology 2009; 62: 431-437.
    CrossrefPubMedGoogle Scholar
  • 34 Spiegelhalter DJ, Freedman LS, Blackburn PR. Monitoring clinical trials: conditional or predictive power?. Controlled Clinical Trials 1986; 7: 8-17.
    CrossrefPubMedGoogle Scholar
  • 35 Schmidli H, Bretz F, Racine-Poon A. Bayesian predictive power for interim adaptation in seamless phase II/III trials where the endpoint is survival up to some specified timepoint. Stat Med 2007; 26: 4925-4938.
    CrossrefPubMedGoogle Scholar
  • 36 Sverdlov O, Rosenberger WF, Ryeznick Y. Utility of covariate-adjusted response-adaptive randomisation in survival trials. Statistics in Biopharmaceutical Research 2013; 5: 38-53.
    CrossrefPubMedGoogle Scholar