×

Exact group sequential designs for two-arm experiments with Poisson distributed outcome variables. (English) Zbl 07532103

Summary: We describe and compare two methods for the group sequential design of two-arm experiments with Poisson distributed data, which are based on a normal approximation and exact calculations respectively. A framework to determine near-optimal stopping boundaries is also presented. Using this framework, for a considered example, we demonstrate that a group sequential design could reduce the expected sample size under the null hypothesis by as much as 44% compared to a fixed sample approach. We conclude with a discussion of the advantages and disadvantages of the two presented procedures.

MSC:

62-XX Statistics

Software:

BRENT

References:

[1] Brent, R., Algorithms for minimization without derivatives (1973), Englewood Cliffs, NJ: Prentice-Hall, Englewood Cliffs, NJ · Zbl 0245.65032
[2] Cook, R.; Lawless, J. F., Interim monitoring of longitudinal comparative studies with recurrent event responses, Biometrics, 52, 4, 1311-23 (1996) · Zbl 0925.62460 · doi:10.2307/2532846
[3] Cook, R.; Yi, G.; Lee, K. A., Sequential testing with recurrent events over multiple treatment periods, Statistics in Biosciences, 2, 2, 137-53 (2010) · doi:10.1007/s12561-010-9030-1
[4] Grayling, M. J., Mander, A. P., and J.M.S, W.. 2017. A two-stage fisher exact test for multi-arm studies with binary outcome variables. arXiv:1711.10199v1.
[5] Jennison, C.; Turnbull, B. W., Group sequential methods with applications to clinical trials (2000), Boca Raton, FL: Chapman & Hall/CRC Press, Boca Raton, FL · Zbl 0934.62078
[6] Jiang, W., Group sequential procedures for repeated events data with frailty, Journal of Biopharmaceutical Statistics, 9, 3, 379-99 (1999) · Zbl 0961.62068 · doi:10.1081/BIP-100101183
[7] Johnson, N. L., On ad extension of the connexion between Poisson and \(####\) distributions, Biometrika, 46, 3-4, 352-64 (1959) · Zbl 0101.35805 · doi:10.2307/2333532
[8] Jung, S. H., Randomized phase II cancer clinical trials (2012), Boca Raton, FL: CRC Press, Boca Raton, FL
[9] Lan, K. K. G.; DeMets, D. L., Discrete sequential boundaries for clinical trials, Biometrika, 70, 3, 659-63 (1983) · Zbl 0543.62059 · doi:10.1093/biomet/70.3.659
[10] Lewis, J. W.; Brown, P. E.; Tsagris, M. (2016)
[11] Mander, A. P.; Wason, J. M. S.; Sweeting, M. J.; Thompson, S. G., Admissible two-stage designs for phase II cancer clinical trials that incorporate the expected sample size under the alternative hypothesis, Pharmaceutical Statistics, 11, 2, 91-6 (2012) · doi:10.1002/sim.1600
[12] Mathews, P., Sample size calculations: Practical methods for engineers and scientists (2010), Harbor, OH: Mathews Malnar and Bailey, Inc, Harbor, OH
[13] Menon, S.; Massaro, J.; Lewis, J.; Pencina, M.; Wang, Y. C.; Lavin, P., Sample size calculation for Poisson endpoint using the exact distribution of difference between two Poisson random variables, Statistics in Biopharmaceutical Research, 3, 3, 497-504 (2011) · doi:10.1198/sbr.2011.10015
[14] Mutze, T.; Glimm, E.; Schmidli, H.; Friede, T., Group sequential designs with robust semiparametric recurrent event models, Statistical Methods in Medical Research (2018) · doi:10.1177/0962280218780538
[15] Mutze, T.; Glimm, E.; Schmidli, H.; Friede, T., Group sequential designs for negative binomial outcomes, Statistical Methods in Medical Research (2018) · doi:10.1177/0962280218773115
[16] National Institute for Health and Care Excellence (2008)
[17] Pampallona, S.; Tsiatis, A. A., 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 (1994) · Zbl 0805.62078 · doi:10.1016/0378-3758(94)90187-2
[18] Patel, S. R.; White, D. P.; Malhotra, A.; Stanchina, M. L.; Ayas, N. T., Continuous positive airway pressure therapy for treating sleepiness in a diverse population with obstructive sleep apnea: results of a meta-analysis, Archives of Internal Medicine, 163, 5, 565-71 (2003) · doi:10.1001/archinte.163.5.565
[19] Quinnell, T. G., M. Bennett, J. Jordan, A. L. Clutterbuck-James, M. G. Davies, I. E. Smith, N. Oscroft, M. A. Pittman, M. Cameron, and R. Chadwick, et al. 2014. A crossover randomised controlled trial of oral mandibular advancement devices for obstructive sleep apnoea-hypopnoea (TOMADO). Thorax 69(10):938-45.
[20] Scharfstein, D. O.; Tsiatis, A. A.; Robins, J. M., Semiparametric efficiency and its implication on the design and analysis of group-sequential studies, Journal of the American Statistical Association, 92, 440, 1342-50 (1997) · Zbl 0913.62075 · doi:10.1080/01621459.1997.10473655
[21] Schultz, J. R.; Nichol, F. R.; Elfring, G. L.; Weed, S. D., Multiple-stage procedures for drug screening, Biometrics, 29, 2, 293-300 (1973)
[22] Shan, G.; Chen, J. J.; Ma, C., Boundary problem in Simon’s two-stage clinical trial designs, Journal of Biopharmaceutical Statistics, 27, 1, 25-33 (2017) · doi:10.1080/10543406.2016.1148716
[23] Shiue, W. K.; Bain, L. J., Experiment size and power comparisons for two-sample Poisson tests, Journal of the Royal Statistical Society: Series C (Applied Statistics), 31, 2, 103-34 (1982) · Zbl 0498.62071 · doi:10.2307/2347975
[24] Skellam, J. G., The frequency distribution of the difference between two poisson variates belonging to different populations, Journal of the Royal Statistical Society: Series A (General), 109, 3, 296 (1946) · Zbl 0063.07068
[25] Thode, H. C., Power and sample size requirements for tests of differences between two Poisson rates, Journal of the Royal Statistical Society: Series D (the Statistician), 46, 227-30 (1997) · Zbl 0063.07068 · doi:10.2307/2981372
[26] Wason, J. M. S.; Mander, A. P.; Thompson, S. G., Optimal multistage designs for randomised clinical trials with continuous outcomes, Statistics in Medicine, 31, 4, 301-12 (2012) · doi:10.1111/1467-9884.00078
[27] Weaver, T. E.; Grunstein, R. R., Adherence to continuous positive airway pressure therapy: the challenge to effective treatment, Proceedings of the American Thoracic Society, 5, 2, 173-8 (2008) · doi:10.1513/pats.200708-119MG
[28] Weaver, T. E.; Mancini, C.; Maislin, G.; Cater, J.; Staley, B.; Landis, J. R.; Ferguson, K. A.; George, C. F.; Schulman, D. A.; Greenberg, H., Continuous positive airway pressure treatment of sleepy patients with milder obstructive sleep apnea: results of the CPAP Apnea Trial North American Program (CATNAP) randomized clinical trial, American Journal of Respiratory and Critical Care Medicine, 186, 7, 677-83 (2012) · doi:10.1164/rccm.201202-0200OC
[29] Xia, Q.; Hoover, D. R., A procedure for group sequential comparative Poisson trials, Journal of Biopharmaceutical Statistics, 17, 5, 869-81 (2007) · doi:10.1080/10543400701514015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.