Generalisations of a Bayesian decision-theoretic randomisation procedure and the impact of delayed responses. (English) Zbl 1543.62644
Summary: The design of sequential experiments and, in particular, randomised controlled trials involves a trade-off between operational characteristics such as statistical power, estimation bias and patient benefit. The family of randomisation procedures referred to as Constrained Randomised Dynamic Programming (CRDP), which is set in the Bayesian decision-theoretic framework, can be used to balance these competing objectives. A generalisation and novel interpretation of CRDP is proposed to highlight its inherent flexibility to adapt to a variety of practicalities and align with individual trial objectives. CRDP, as with most response-adaptive randomisation procedures, hinges on the limiting assumption of patient responses being available before allocation of the next patient. This forms one of the greatest barriers to their implementation in practice which, despite being an important research question, has not received a thorough treatment. Therefore, motivated by the existing gap between the theory of response-adaptive randomisation (which is abundant with proposed methods in the immediate response setting) and clinical practice (in which responses are typically delayed), the performance of CRDP in the presence of fixed and random delays is evaluated. Simulation results show that CRDP continues to offer patient benefit gains over alternative procedures and is relatively robust to delayed responses. To compensate for a fixed delay, a method which adjusts the time horizon used in the optimisation objective is proposed and its performance illustrated.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62C10 | Bayesian problems; characterization of Bayes procedures |
| 62L05 | Sequential statistical design |
Keywords:
Bayesian decision-theoretic model; clinical trials; delayed responses; dynamic programming; response-adaptive randomisationSoftware:
BinaryBanditReferences:
| [1] | Ahuja, V.; Birge, J. R., An approximation approach for response-adaptive clinical trial design, INFORMS J. Comput., 32, 877-894 (2020) · Zbl 07303812 |
| [2] | Alban, A.; Chick, S. E.; Forster, M., Extending a Bayesian decision-theoretic approach to value-based sequential clinical trial design, (2018 Winter Simulation Conference. 2018 Winter Simulation Conference, WSC (2018), IEEE), 2459-2470 |
| [3] | Armitage, P., The search for optimality in clinical trials, Int. Stat. Rev., 53, 15-24 (1985) · Zbl 0586.62129 |
| [4] | Atkinson, A. C.; Biswas, A., Randomised Response-Adaptive Designs in Clinical Trials (2014), CRC Press · Zbl 1284.62005 |
| [5] | Bai, Z. D.; Hu, F.; Rosenberger, W. F., Asymptotic properties of adaptive designs for clinical trials with delayed response, Ann. Stat., 30, 122-139 (2002) · Zbl 1012.62087 |
| [6] | Bandyopadhyay, U.; Biswas, A., Delayed response in randomized play-the-winner rule: a decision theoretic outlook, Calcutta Stat. Assoc. Bull., 46, 69-88 (1996) · Zbl 0907.62009 |
| [7] | Bellman, R., A problem in the sequential design of experiments, Sankhya, 16, 221-229 (1956) · Zbl 0075.14801 |
| [8] | Berry, D. A.; Stangl, D. K., Bayesian methods in health-related research, (Berry, D. A.; Stangl, D. K., Bayesian Biostatistics (1996), Marcel Dekker), 3-66 |
| [9] | Biswas, A., Delayed response in randomized play-the-winner rule revisited, Commun. Stat., Simul. Comput., 28, 715-731 (1999) · Zbl 0968.62549 |
| [10] | Biswas, A., Generalized delayed response in randomized play-the-winner rule, Commun. Stat., Simul. Comput., 32, 259-274 (2003) · Zbl 1100.62505 |
| [11] | Biswas, A.; Bandyopadhyay, U.; Bhattacharya, R., Response-adaptive designs in phase III clinical trials, (Biswas, A.; Datta, S.; Fine, J. P.; Segal, M. R., Statistical Advances in the Biomedical Sciences: Clinical Trials, Epidemiology, Survival Analysis, and Bioinformatics. Statistical Advances in the Biomedical Sciences: Clinical Trials, Epidemiology, Survival Analysis, and Bioinformatics, Wiley Series in Probability and Statistics (2008), John Wiley & Sons, Inc.), 22-53 |
| [12] | Biswas, A.; Bhattacharya, R., Response-adaptive designs for continuous treatment responses in phase III clinical trials: a review, Stat. Methods Med. Res., 25, 81-100 (2016) |
| [13] | Biswas, A.; Coad, D. S., A general multi-treatment adaptive design for multivariate responses, Seq. Anal., 24, 139-158 (2005) · Zbl 1073.62068 |
| [14] | Burnett, T.; Mozgunov, P.; Pallmann, P.; Villar, S. S.; Wheeler, G. M.; Jaki, T., Adding flexibility to clinical trial designs: an example-based guide to the practical use of adaptive designs, BMC Med., 18, 1-21 (2020) |
| [15] | Cheng, Y.; Berry, D. A., Optimal adaptive randomized designs for clinical trials, Biometrika, 94, 673-689 (2007) · Zbl 1135.62063 |
| [16] | Cheung, Y. K.; Inoue, L. Y.T.; Wathen, J. K.; Thall, P. F., Continuous Bayesian adaptive randomization based on event times with covariates, Stat. Med., 25, 55-70 (2006) |
| [17] | Chick, S.; Forster, M.; Pertile, P., A Bayesian decision theoretic model of sequential experimentation with delayed response, J. R. Stat. Soc., Ser. B, Stat. Methodol., 79, 1439-1462 (2017) · Zbl 1380.62027 |
| [18] | Chick, S. E.; Gans, N.; Yapar, O., Bayesian sequential learning for clinical trials of multiple correlated medical interventions (2020), INSEAD Working Paper No. 2020/40/TOM/ACGRE |
| [19] | Dallow, N.; Best, N.; Montague, T. H., Better decision making in drug development through adoption of formal prior elicitation, Pharm. Stat., 17, 301-316 (2018) |
| [20] | Donahue, E.; Sabo, R. T., A natural lead-in approach to response-adaptive allocation for continuous outcomes, Pharm. Stat., 20, 563-572 (2021) |
| [21] | Eick, S. G., Gittins procedures for bandits with delayed responses, J. R. Stat. Soc. B, 50, 125-132 (1988) · Zbl 0647.62078 |
| [22] | Eick, S. G., The two-armed bandit with delayed responses, Ann. Stat., 16, 254-264 (1988) · Zbl 0637.62074 |
| [23] | Facey, K. M., A sequential procedure for a phase II efficacy trial in hypercholesterolemia, Control. Clin. Trials, 13, 122-133 (1992) |
| [24] | Flight, L.; Julious, S. A.; Goodacre, S., Can emergency medicine research benefit from adaptive design clinical trials?, J. Emerg. Med., 34, 243-248 (2017) |
| [25] | Hampson, L. V.; Jennison, C., Group sequential tests for delayed responses (with discussion), J. R. Stat. Soc., Ser. B, Stat. Methodol., 75, 3-54 (2013) · Zbl 07555437 |
| [26] | Hardwick, J.; Oehmke, R.; Stout, Q. F., New adaptive designs for delayed response models, J. Stat. Plan. Inference, 136, 1940-1955 (2006) · Zbl 1089.62133 |
| [27] | Hu, F.; Zhang, L. X.; Cheung, S. H.; Chan, W. S., Doubly adaptive biased coin designs with delayed responses, Can. J. Stat., 36, 541-559 (2008) · Zbl 1166.62059 |
| [28] | Hurvitz, S. A.; Martin, M.; Symmans, W. F.; Jung, K. H.; Huang, C. S.; Thompson, A. M.; Harbeck, N.; Valero, V.; Stroyakovskiy, D.; Wildiers, H.; Campone, M.; Boileau, J. F.; Beckmann, M.; Afenjar, K.; Fresco, R.; Helms, H. J.; Xu, J. X.; Lin, Y. G.; Sparano, J.; Slamon, D., Neoadjuvant trastuzumab, pertuzumab, and chemotherapy versus trastuzumab emtansine plus pertuzumab in patients with HER2-positive breast cancer (KRISTINE): a randomised, open-label, multicentre, phase 3 trial, Lancet Oncol., 19, 115-126 (2018) |
| [29] | Ivanova, A.; Rosenberger, W. F., A comparison of urn designs for randomized clinical trials of \(k > 2\) treatments, J. Biopharm. Stat., 10, 93-107 (2000) |
| [30] | Jacko, P., BinaryBandit: an efficient Julia package for optimization and evaluation of the finite-horizon bandit problem with binary responses (2019), Lancaster University Management School, Working Paper 4 |
| [31] | Jacko, P., The finite-horizon two-armed bandit problem with binary responses: a multidisciplinary survey of the history, state of the art, and myths (2019), Lancaster University Management School, Working Paper |
| [32] | Kaibel, C.; Biemann, T., Rethinking the gold standard with multi-armed bandits: machine learning allocation algorithms for experiments, Organ. Res. Methods, 24, 78-103 (2021) |
| [33] | Langenberg, P.; Srinivasan, R., On the Colton model for clinical trials with delayed observations — normally-distributed responses, Biometrics, 37, 143-148 (1981) · Zbl 0473.62099 |
| [34] | Langenberg, P.; Srinivasan, R., On the Colton model for clinical trials with delayed observations — dichotomous responses, Biom. J., 24, 287-296 (1982) · Zbl 0491.62092 |
| [35] | Magirr, D., Block response-adaptive randomization in clinical trials with binary endpoints, Pharm. Stat., 10, 341-346 (2011) |
| [36] | Mozgunov, P.; Jaki, T., An information theoretic approach for selecting arms in clinical trials, J. R. Stat. Soc., Ser. B, Stat. Methodol., 82, 1223-1247 (2020) · Zbl 07554790 |
| [37] | Muir, K. W.; Ford, G. A.; Messow, C. M.; Ford, I.; Murray, A.; Clifton, A.; Brown, M. M.; Madigan, J.; Lenthall, R.; Robertson, F.; Dixit, A.; Cloud, G. C.; Wardlaw, J.; Freeman, J.; White, P., Endovascular therapy for acute ischaemic stroke: the pragmatic ischaemic stroke thrombectomy evaluation (PISTE) randomised, controlled trial, J. Neurol. Neurosurg. Psychiatry, 88, 38-44 (2017) |
| [38] | Ovbiagele, B.; Lyden, P. D.; Saver, J. L., Disability status at 1 month is a reliable proxy for final ischemic stroke outcome, Neurology, 75, 688-692 (2010) |
| [39] | Pallmann, P.; Bedding, A. W.; Choodari-Oskooei, B.; Dimairo, M.; Flight, L.; Hampson, L. V.; Holmes, J.; Mander, A. P.; Sydes, M. R.; Villar, S. S.; Wason, J. M.S.; Weir, C. J.; Wheeler, G. M.; Yap, C.; Jaki, T., Adaptive designs in clinical trials: why use them, and how to run and report them, BMC Med., 16, 29 (2018) |
| [40] | Pertile, P.; Forster, M.; Torre, D. L., Optimal Bayesian sequential sampling rules for the economic evaluation of health technologies, J. R. Stat. Soc., Ser. A, Stat. Soc., 177, 419-438 (2014) |
| [41] | Pocock, S. J., Clinical Trials: A Practical Approach (1983), John Wiley & Sons |
| [42] | Robertson, D. S.; Lee, K. M.; Lopez-Kolkovska, B. C.; Villar, S. S., Response-adaptive randomization in clinical trials: from myths to practical considerations (2020) |
| [43] | Robinson, D., A comparison of sequential treatment allocation rules, Biometrika, 70, 492-495 (1983) |
| [44] | Rosenberger, W. F., Randomized play-the-winner clinical trials: review and recommendations, Control. Clin. Trials, 20, 328-342 (1999) |
| [45] | Rosenberger, W. F.; Lachin, J., Randomization in Clinical Trials: Theory and Practice (2016), John Wiley & Sons · Zbl 1329.92004 |
| [46] | Rosenberger, W. F.; Sverdlov, O.; Hu, F., Adaptive randomization for clinical trials, J. Biopharm. Stat., 22, 719-736 (2012) |
| [47] | Royston, P.; Altman, D. G.; Sauerbrei, W., Dichotomizing continuous predictors in multiple regression: a bad idea, Stat. Med., 25, 127-141 (2006) |
| [48] | Shrestha, S.; Jain, S., A Bayesian-bandit adaptive design for N-of-1 clinical trials, Stat. Med. (2021) |
| [49] | Simon, R., Adaptive treatment assignment methods and clinical trials, Biometrics, 33, 743-749 (1977) |
| [50] | Smith, A. L.; Villar, S. S., Bayesian adaptive bandit-based designs using the Gittins index for multi-armed trials with normally distributed endpoints, J. Appl. Stat., 45, 1052-1076 (2018) · Zbl 1516.62607 |
| [51] | Sully, B. G.; Julious, S. A.; Nicholl, J., A reinvestigation of recruitment to randomised, controlled, multicenter trials: a review of trials funded by two UK funding agencies, Trials, 14, 166 (2013) |
| [52] | Sutton, R. S., Generalization in reinforcement learning: successful examples using sparse coarse coding, Adv. Neural Inf. Process. Syst., 8, 1038-1044 (1996) |
| [53] | Sutton, R. S.; Barto, A. G., Reinforcement Learning: An Introduction (2018), MIT Press: MIT Press Cambridge, MA · Zbl 1407.68009 |
| [54] | Sverdlov, O.; Ryeznik, Y.; Wong, W. K., Doubly adaptive biased coin designs for balancing competing objectives in time-to-event trials, Stat. Interface, 5, 401-413 (2012) · Zbl 1383.62293 |
| [55] | Tamura, R. N.; Faries, D. E.; Andersen, J. S.; Heiligenstein, J. H., A case study of an adaptive clinical trial in the treatment of out-patients with depressive disorder, J. Am. Stat. Assoc., 89, 768-776 (1994) |
| [56] | Thompson, W. R., On the likelihood that one unknown probability exceeds another in view of the evidence of two samples, Biometrika, 25, 285-294 (1933) · JFM 59.1159.03 |
| [57] | Thrun, S., The role of exploration in learning control, (White, D.; Sofge, D., Handbook for Intelligent Control: Neural, Fuzzy and Adaptive Approaches (1992), Van Nostrand Reinhold: Van Nostrand Reinhold Florence, Kentucky), 41022 |
| [58] | Thrun, S. B., Efficient Exploration in reinforcement learning (1992), Carnegie-Mellon University: Carnegie-Mellon University Pittsburgh, Pennsylvania, Technical Report CMU-CS-92-102 265 |
| [59] | Upton, G. J.G.; Lee, R. D., The importance of the patient horizon in the sequential analysis of binomial clinical trials, Biometrika, 63, 335-342 (1976) · Zbl 0329.62065 |
| [60] | Upton, G. J.G.; Lee, R. D., Discussion of ‘Randomized allocation of treatments in sequential experiments’ (by J.A. Bather), J. R. Stat. Soc. B, 43, 291 (1981) |
| [61] | U. S. Food and Drug Administration, Adaptive designs for clinical trials of drugs and biologics: draft guidance for industry (2018) |
| [62] | Villar, S. S., Bandit strategies evaluated in the context of clinical trials in rare life-threatening diseases, Probab. Eng. Inf. Sci., 32, 229-245 (2018) · Zbl 1462.62691 |
| [63] | Villar, S. S.; Bowden, J.; Wason, J., Multi-armed bandit models for the optimal design of clinical trials: benefits and challenges, Stat. Sci., 30, 199-215 (2015) · Zbl 1332.62267 |
| [64] | Villar, S. S.; Bowden, J.; Wason, J., Response-adaptive randomisation for multi-arm clinical trials using the forward looking Gittins index rule, Biometrics, 71, 969-978 (2015) · Zbl 1419.62465 |
| [65] | Villar, S. S.; Bowden, J.; Wason, J., Response-adaptive designs for binary responses: how to offer patient benefit while being robust to time trends?, Pharm. Stat., 17, 182-197 (2018) |
| [66] | Villar, S. S.; Rosenberger, W. F., Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule, Biometrics, 74, 49-57 (2018) · Zbl 1415.62141 |
| [67] | Wang, J., Response-adaptive trial designs with accelerated Thompson sampling, Pharm. Stat., 20, 645-656 (2021) |
| [68] | Wang, X., A bandit process with delayed responses, Stat. Probab. Lett., 48, 303-307 (2000) · Zbl 0959.62067 |
| [69] | Wang, X., Asymptotic properties of bandit processes with geometric responses, Stat. Probab. Lett., 60, 211-217 (2002) · Zbl 1092.62572 |
| [70] | Wason, J. M.S.; Brocklehurst, P.; Yap, C., When to keep it simple — adaptive designs are not always useful, BMC Med., 17, 1-7 (2019) |
| [71] | Watkins, C., Learning from delayed rewards (1989), University of Cambridge, Ph.D. thesis |
| [72] | Wei, L. J.; Durham, S., The randomized play-the-winner rule in medical trials, J. Am. Stat. Assoc., 73, 840-843 (1978) · Zbl 0391.62076 |
| [73] | Whitehead, J., Application of sequential methods to a phase III clinical trial in stroke, Drug Inf. J., 27, 733-740 (1993) |
| [74] | Williams, C. J.; Wilson, K. J.; Wilson, N., A comparison of prior elicitation aggregation using the classical method and shelf, J. R. Stat. Soc., Ser. A, Stat. Soc., 184, 920-940 (2021) |
| [75] | Williamson, S. F., Bayesian bandit models for the design of clinical trials (2020), University of Lancaster, Ph.D. thesis |
| [76] | Williamson, S. F.; Jacko, P.; Villar, S. S.; Jaki, T., A Bayesian adaptive design for clinical trials in rare diseases, Comput. Stat. Data Anal., 113, 136-153 (2017) · Zbl 1464.62183 |
| [77] | Williamson, S. F.; Villar, S. S., A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes, Biometrics, 76, 197-209 (2020) · Zbl 1451.62147 |
| [78] | Xu, J.; Yin, G., Two-stage adaptive randomization for delayed response in clinical trials, J. R. Stat. Soc., Ser. C, Appl. Stat., 63, 559-578 (2014) |
| [79] | Zhang, L.; Rosenberger, W. F., Response-adaptive randomization for survival trials: the parametric approach, J. R. Stat. Soc., Ser. C, Appl. Stat., 56, 153-165 (2007) · Zbl 1490.62390 |
| [80] | Zhang, Y.; Trippa, L.; Parmigiani, G., Frequentist operating characteristics of Bayesian optimal designs via simulation, Stat. Med., 38, 4026-4039 (2019) |
| [81] | Wei, L. J., Exact two-sample permutation tests based on the randomized play-the-winner rule, Biometrika, 75, 3, 603-606 (1988) · Zbl 0657.62086 |
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