Abstract
In this article, we consider some up-and-down designs that are discussed in Ivanova et al. (2003) for estimating the maximum tolerated dose (MTD) in phase I trials: the biased coin design, k-in-a-row rule, Narayana rule, and continual reassessment method (CRM). A large-scale Monte Carlo simulation study, which is substantially more extensive than Ivanova et al. (2003), is conducted to examine the performance of these five designs for different sample sizes and underlying dose-response curves. For the estimation of MTD, we propose a modified maximum likelihood estimator (MMLE) in addition to those in Ivanova et al. (2003). The selection of different dose-response curves and their parameters allows us to evaluate the robustness features of the designs as well as the performance of the estimators. The results obtained, in addition to revealing that the new estimator performs better than others in many situations, enable us to make recommendations on designs.
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References
Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D. (1972). Statistical Inference under Order Restrictions, John Wiley & Sons, New York.
Clogg, C. C., Rubin, D. B., Schenker, N., Schultz, B., and Weidman, L. (1991). Multiple imputation of industry and occupation codes in census public-use samples using Bayesian logistic regression, Journal of the American Statistical Association, 86, 68–78.
Crowley, J. (2001). Handbook of Statistics in Clinical Oncology, Marcel Dekker, New York.
Durham, S. D., and Flournoy, N. (1994). Random walks for quantile estimation, In Statistical Decision Theory and Related Topics V (Eds., S. S. Gupta and J. O. Berger), pp. 467–476, Springer-Verlag, New York.
Durham, S. D., and Flournoy, N. (1995). Up-and-down designs I. Stationary treatment distributions, In Adaptive Designs (Eds., N. Flournoy and W. F. Rosenberger), pp. 139–157, Institute of Mathematical Statistics, Hayward, California.
Durham, S. D., Flournoy, N., and Rosenberger, W. F. (1997). A random walk rule for phase I clinical trials, Biometrics, 53, 745–760.
Faries, D. (1994). Practical modifications of the continual reassessment method for phase I cancer clinical trials. Journal of Biopharmaceutical Statistics, 4, 147–164.
Gezmu, M. (1996). The geometric up-and-down design for allocating dosage levels, Ph.D. Dissertation, American University, Washington, DC.
Ivanova, A., Montazer-Haghighi, A., Mohanty, S. G., and Durham, S. D. (2003). Improved up-and-down designs for phase I trails, Statistics in Medicine, 22, 69–82.
Korn, E. L., Midthune, D., Chen, T. T., Rubinstein, L. V., Christian, M. C., and Simon, R. M. (1994). A comparison of two phase I trial designs, Statistics in Medicine, 13, 1799–1806.
Narayana, T. V. (1953). Sequential procedures in the probit analysis, Ph.D. Dissertation, University of North Carolina, Chapel Hill, NC.
O’Quigley, J., Pepe, M., and Fisher, L. (1990). Continual reassessment method: a practical design for phase I clinical trials in cancer, Biometrics, 46, 33–48.
Robertson, T., Wright, F. T., and Dykstra, R. L. (1988). Order Restricted Statistical Inference, John Wiley & Sons, New York.
Storer, B. E. (1989). Design and analysis of phase I clinical trials, Biometrics, 45, 925–937.
Stylianou, M., and Flournoy, N. (2002). Dose finding using the biased coin up-and-down design and isotonic regression, Biometrics, 58, 171–177.
Stylianou, M., Proschan, M., and Flournoy, N. (2003). Estimating the probability of toxicity at the target dose following an up-and-down design, Statistics in Medicine, 22, 535–543.
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Ng, H.K.T., Mohanty, S.G., Balakrishnan, N. (2007). An Assessment of Up-and-Down Designs and Associated Estimators in Phase I Trials. In: Auget, JL., Balakrishnan, N., Mesbah, M., Molenberghs, G. (eds) Advances in Statistical Methods for the Health Sciences. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4542-7_24
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DOI: https://doi.org/10.1007/978-0-8176-4542-7_24
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