Robust Bayesian sample size determination for avoiding the range of equivalence in clinical trials. (English) Zbl 1131.62019
Summary: This article considers sample size determination methods based on Bayesian credible intervals for \(\theta \), an unknown real-valued parameter of interest. We consider clinical trials and assume that \(\theta \) represents the difference in the effects of a new and a standard therapy. In this context, it is typical to identify an interval of the parameter value that implies equivalence of the two treatments (range of equivalence). Then, an experiment designed to show superiority of the new treatment is successful if it yields evidence that \(\theta \) is sufficiently large, i.e., if an interval estimate of \(\theta \) lies entirely above the superior limit of the range of equivalence. Following a robust Bayesian approach, we model uncertainty on prior specification with a class \(\varGamma \) of distributions for \(\theta \) and we assume that the data yield robust evidence if, as the prior varies in \(\varGamma \), the lower bound of the credible set inferior limit is sufficiently large. Sample size criteria in the article consist in selecting the minimal number of observations such that the experiment is likely to yield robust evidence. These criteria are based on summaries of the predictive distributions of lower bounds of the random inferior limits of credible intervals. The method is developed for the conjugate normal model and applied to a trial for surgery of gastric cancer.
MSC:
| 62F15 | Bayesian inference |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62F35 | Robustness and adaptive procedures (parametric inference) |
References:
| [1] | Adcock, C. J., Sample size determination: a review, Statistician, 46, 261-283 (1997) |
| [2] | Armitage, P.; Berry, G.; Matthews, J. N.S., Statistical Methods in Medical Research (2002), Blackwell Science: Blackwell Science Oxford |
| [3] | Berger, J. O., The robust Bayesian viewpoint (with discussion), (Kadane, J., Robustness of Bayesian Analysis (1984), North-Holland: North-Holland Amsterdam) |
| [4] | Berger, J. O., Robust Bayesian analysis: sensitivity to the prior, J. Statist. Plann. Inference, 25, 303-328 (1990) · Zbl 0747.62029 |
| [5] | Berger, J. O.; Rios Insua, D.; Ruggeri, F., Bayesian robustness, (Rios, D.; Ruggeri, F., Robust Bayesian analysis, Lecture Notes in Statistics, vol. 152 (2000), Springer: Springer New York), 1-32 · Zbl 1281.62076 |
| [6] | Carlin, B.P., Perez, M.E., 2000. Robust Bayesian analysis in medical and epidemiological settings. In: Rios, D., Ruggeri, F., (Eds.), Robust Bayesian analysis, Lecture Notes in Statistics, vol. 152. Springer-Verlag, New York.; Carlin, B.P., Perez, M.E., 2000. Robust Bayesian analysis in medical and epidemiological settings. In: Rios, D., Ruggeri, F., (Eds.), Robust Bayesian analysis, Lecture Notes in Statistics, vol. 152. Springer-Verlag, New York. · Zbl 1281.62231 |
| [7] | Chaloner, K.; Verdinelli, I., Bayesian experimental design: a review, Statist. Sci., 10, 237-308 (1995) |
| [8] | Clarke, B. S.; Yuan, A., Closed form expressions for Bayesian sample size, Ann. Statist., 34, 3, 1293-1330 (2006) · Zbl 1113.62029 |
| [9] | DasGupta, A., 1996. Review of optimal Bayes designs. Design and analysis of experiments. Handbook of Statistics, vol. 13. pp. 1099-1147.; DasGupta, A., 1996. Review of optimal Bayes designs. Design and analysis of experiments. Handbook of Statistics, vol. 13. pp. 1099-1147. · Zbl 0911.62066 |
| [10] | DasGupta, A.; Mukhopadhyay, S., Uniform and subuniform posterior robustness: the sample size problem, J. Statist. Plann. Inference, 40, 189-200 (1994) · Zbl 0798.62006 |
| [11] | DasGupta, A.; Studden, W. J., Robust Bayesian experimental designs in normal linear models, Ann. Statist., 19, 3, 1244-1256 (1991) · Zbl 0744.62099 |
| [12] | De Santis, F., Sample size determination for robust Bayesian analysis, J. Amer. Statist. Assoc., 101, 473, 278-291 (2006) · Zbl 1118.62314 |
| [13] | De Santis, F., Perone Pacifico, M., 2003. Two experimental settings in clinical trials: predictive criteria for choosing the sample size in interval estimation. In: Di Bacco, M., et al. (Eds.), Applied Bayesian Statistical Studies in Biology and Medicine. Kluwer Academic Publishers, Norwell, MA, USA.; De Santis, F., Perone Pacifico, M., 2003. Two experimental settings in clinical trials: predictive criteria for choosing the sample size in interval estimation. In: Di Bacco, M., et al. (Eds.), Applied Bayesian Statistical Studies in Biology and Medicine. Kluwer Academic Publishers, Norwell, MA, USA. |
| [14] | Etzioni, R.; Kadane, J. B., Optimal experimental design for another’s analysis, J. Amer. Statist. Assoc., 88, 424, 1404-1411 (1993) · Zbl 0792.62062 |
| [15] | Fayers, P. M.; Cuschieri, A.; Fielding, J.; Craven, J.; Uscinska, B.; Freedman, L. S., Sample size calculation for clinical trials: the impact of clinicians beliefs, British J. Cancer, 82, 213-219 (2000) |
| [16] | Greenhouse, J. B.; Wasserman, L., Robust Bayesian methods for monitoring clinical trials, Statist. Med., 14, 1379-1391 (1995) |
| [17] | Ianus, I., 2000. Approximate robust Bayesian inference with applications to sample size calculation. Ph.D Thesis, Department of Statistics, Carnegie Mellon University.; Ianus, I., 2000. Approximate robust Bayesian inference with applications to sample size calculation. Ph.D Thesis, Department of Statistics, Carnegie Mellon University. |
| [18] | Joseph, L.; Belisle, P., Bayesian sample size determination for normal means and difference between normal means, Statistician, 46, 209-226 (1997) |
| [19] | Joseph, L.; du Berger, R.; Belisle, P., Bayesian and mixed Bayesian/likelihood criteria for sample size determination, Statist. Med, 16, 769-781 (1997) |
| [20] | Julious, S. A., Sample sizes for clinical trials for normal data, Statist. Med., 23, 1921-1986 (2004) |
| [21] | Kass, R. E.; Wasserman, L., A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion, J. Amer. Statist. Assoc., 90, 928-934 (1995) · Zbl 0851.62020 |
| [22] | Lindley, D. V., The choice of sample size, Statistician, 46, 129-138 (1997) |
| [23] | O’Hagan, A.; Stevens, J. W., Bayesian assessment of sample size for clinical trials for cost effectiveness, Med. Decision Making, 21, 219-230 (2001) |
| [24] | Sahu, S. K.; Smith, T. M.F., A Bayesian method of sample size determination with practical applications, J. Roy. Statist. Soc. Ser. A, 169, 2, 235-253 (2006) |
| [25] | Spiegelhalter, D. J.; Freedman, L. S., A predictive approach to selecting the size of a clinical trial, based on subjective clinical opinion, Statist. Med., 5, 1-13 (1986) |
| [26] | Spiegelhalter, D. J.; Abrams, K. R.; Myles, J. P., Bayesian Approaches to Clinical Trials and Health-Care Evaluation (2004), Wiley: Wiley New York |
| [27] | Tsutakawa, R. K., Design of experiment for bioassay, J. Amer. Statist. Assoc., 67, 339, 584-590 (1972) · Zbl 0251.62051 |
| [28] | Wang, F.; Gelfand, A. E., A simulation-based approach to Bayesian sample size determination for performance under a given model and for separating models, Statist. Sci., 17, 2, 193-208 (2002) · Zbl 1013.62025 |
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