Optimal designs for dose-escalation trials and individual allocations in cohorts
Tóm tắt
Dose escalation trials are crucial in the development of new pharmaceutical products to optimize the amount of drug administered while avoiding undesirable side effects. We adopt the framework established by Bailey (Stat Med 28(30):3721–3738, 2009.
https://doi.org/10.1002/sim.3646
) where the individuals are grouped into cohorts, to the subjects in which the placebo or previously defined doses are administered and responses measured. Successive cohorts allow testing higher doses of drug if negative responses have not been observed in earlier cohorts. We propose Mixed Integer Nonlinear Programming formulations for systematically computing optimal experimental designs for dose escalation. We demonstrate its application with i. different optimality criteria; ii. standard and extended designs; and iii. non-constrained (or traditional), strict halving and uniform halving designs. Additionally, we address the allocation of the individuals in a cohort considering previously known prognostic factors. To handle the problem we propose i. an enumerative algorithm; and ii. a Mixed Integer Nonlinear Programming formulation. We demonstrate the application of the enumeration scheme for allocating individuals on an individual arrival basis, and of the latter formulation for allocation on a within cohort basis.
Tài liệu tham khảo
Anderson, D.A.: Designs with partial factorial balance. Ann. Math. Stat. 43(4), 1333–1341 (1972)
Atkinson, A.C.: Optimum biased coin designs for sequential clinical trials with prognostic factors. Biometrika 69(1), 61–67 (1982)
Atkinson, A.C.: The comparison of designs for sequential clinical trials with covariate information. J. R. Stat. Soc. A. Stat. Soc. 165(2), 349–373 (2002). https://doi.org/10.1111/1467-985X.00564
Atkinson, A.C., Donev, A.N., Tobias, R.D.: Optimum Experimental Designs, with SAS. Oxford University Press, Oxford (2007)
Babb, J., Rogatko, A., Zacks, S.: Cancer phase I clinical trials: efficient dose escalation with overdose control. Stat. Med. 10(10), 1103–1120 (1998)
Bailey, R.A.: Designs for dose-escalation trials with quantitative responses. Stat. Med. 28(30), 3721–3738 (2009). https://doi.org/10.1002/sim.3646
Begg, C.B., Iglewicz, B.: A treatment allocation procedure for sequential clinical trials. Biometrics 36(1), 81–90 (1980)
Boer, E., Hendrix, E.: Global optimization problems in optimal design of experiments in regression models. J. Glob. Optim. 18, 385–398 (2000)
Burman, C.F.: On sequential treatment allocations in clinical trials. Ph.D. thesis, Chalmers of University Technology, Göteborg (1996)
Cheung, Y.K.: Coherence principles in dose-finding studies. Biometrika 92(4), 863–873 (2005)
Dette, H., Bretz, F., Pepelyshev, A., Pinheiro, J.: Optimal designs for dose-finding studies. J. Am. Stat. Assoc. 103(483), 1225–1237 (2008)
Dror, S., Faraggi, D., Reiser, B.: Dynamic treatment allocation adjusting for prognostic factors for more than two treatments. Biometrics 51(4), 1338–1343 (1995)
Drud, A.: CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems. Math. Program. 31, 153–191 (1985)
Duarte, B.P.M., Atkinson, A.C., Granjo, J.F.O., Oliveira, N.M.C.: Optimal design of experiments for implicit models. J. Am. Stat. Assoc. forthcoming, 1–14 (2021). https://doi.org/10.1080/01621459.2020.1862670
Duarte, B.P.M., Granjo, J.F.O., Wong, W.K.: Optimal exact designs of experiments via Mixed Integer Nonlinear Programming. Stat. Comput. 30, 93–112 (2020)
Fedorov, V.V.: Theory of Optimal Experiments. Academic Press, London (1972)
GAMS Development Corporation: GAMS—A User’s Guide, GAMS Release 24.2.1. GAMS Development Corporation, Washington, DC, USA (2013a)
GAMS Development Corporation: GAMS—The Solver Manuals, GAMS Release 24.2.1. GAMS Development Corporation, Washington, DC, USA (2013b)
Haines, L.M., Clark, A.E.: The construction of optimal designs for dose-escalation studies. Stat. Comput. 24(1), 101–109 (2014). https://doi.org/10.1007/s11222-012-9356-2
Hedayat, A.S., Jacroux, M., Majumdar, D.: Optimal designs for comparing test treatments with controls. Stat. Sci. 3(4), 462–476 (1988)
Holbrook, A.: Differentiating the pseudo determinant. Linear Algebra Appl. 548, 293–304 (2018). https://doi.org/10.1016/j.laa.2018.03.018
Huang, B., Chapell, R.: Three-dose-cohort designs in cancer phase I trials. Stat. Med. 27(12), 2070–2093 (2008). https://doi.org/10.1016/10.1002/sim.3054
Kaye, R., Wilson, R.: Linear Algebra. Oxford Science Publications, Oxford University Press, Oxford (1998)
Lastusilta, T., Bussieck, M., Westerlund, T.: Comparison of some high-performance MINLP solvers. Chem. Eng. Trans. 11, 125–130 (2007)
Le Tourneau, C., Lee, J.J., Siu, L.L.: Dose escalation methods in phase I cancer clinical trials. JNCI: J. Natl. Cancer Inst. 101(10), 708–720 (2009). https://doi.org/10.1093/jnci/djp079
Neuenschwander, B., Branson, M., Gsponer, T.: Critical aspects of the Bayesian approach to phase I cancer trials. Stat. Med. 27, 2420–39 (2008)
O’Brien, R.M.: Mixed models, linear dependency, and identification in age-period-cohort models. Stat. Med. 36(16), 2590–2600 (2017)
O’Quigley, J., Pepe, M., Fisher, L.: Continual reassessment method: a practical design for phase 1 clinical trials in cancer. Biometrics 46(1), 33–48 (1990)
Pearce, S.C.: The Agricultural Field Experiment. A Statistical Examination of Theory and Practice. Wiley, Chichester (1983)
Pukelsheim, F.: Optimal Design of Experiments. SIAM, Philadelphia (1993)
Rosa, S., Harman, R.: Optimal approximate designs for comparison with control in dose-escalation studies. TEST 26, 638–660 (2017). https://doi.org/10.1007/s11749-017-0529-3
Searle, S.R.: On inverting circulant matrices. Linear Algebra Appl. 25, 77–89 (1979). https://doi.org/10.1016/0024-3795(79)90007-7
Senn, S.: Statistical Issues in Drug Development, 2nd edn. Wiley, Chichester (2007). https://doi.org/10.1002/9780470723586
Senn, S., Amin, D., Bailey, R.A., Bird, S.M., Bogacka, B., Colman, P., Garrett, A., Grieve, A., Lachmann, P.: Statistical issues in first-in-man studies. J. R. Stat. Soc. A. Stat. Soc. 170(3), 517–579 (2007). https://doi.org/10.1111/j.1467-985X.2007.00481.x
Sibson, R.: D\(_{\text{A}}\)-optimality and duality. In: Gani, J., Sarkadi, K., Vincze, I. (eds.) Progress in Statistics, Vol. 2-Proceedings of 9th European Meeting of Statisticians, Budapest, pp. 677–692. North-Holland, Amsterdam (1974)
Smith, R.L.: Properties of biased coin designs in sequential clinical trials. Ann. Stat. 12, 1018–1034 (1984)
Smith, R.L.: Sequential treatment allocation using biased coin designs. J. R. Stat. Soc. B 46, 519–543 (1984)
Storer, B.E.: Design and analysis of phase I clinical trials. Biometrics 45(3), 925–937 (1989)
Tawarlamani, M., Sahinidis, N.: Convexification and Global Optimization in Continuous and Mixed Integer Nonlinear Programming, 1st edn. Kluwer Academic Pusblishers, Dordrecht (2002)
Vo-Thanh, N., Jans, R., Schoen, E.D., Goos, P.: Symmetry breaking in mixed integer linear programming formulations for blocking two-level orthogonal experimental designs. Comput. Oper. Res. 97, 96–110 (2018). https://doi.org/10.1016/j.cor.2018.04.001
Williams, H.P.: Model Building in Mathematical Programming, 4th edn. Wiley, Chichester (1999)