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Sequential Monte Carlo for Bayesian sequentially designed experiments for discrete data. (English) Zbl 1365.62318
Summary: In this paper we present a sequential Monte Carlo algorithm for Bayesian sequential experimental design applied to generalised non-linear models for discrete data. The approach is computationally convenient in that the information of newly observed data can be incorporated through a simple re-weighting step. We also consider a flexible parametric model for the stimulus-response relationship together with a newly developed hybrid design utility that can produce more robust estimates of the target stimulus in the presence of substantial model and parameter uncertainty. The algorithm is applied to hypothetical clinical trial or bioassay scenarios. In the discussion, potential generalisations of the algorithm are suggested to possibly extend its applicability to a wide variety of scenarios.

MSC:
62L05 Sequential statistical design
62K05 Optimal statistical designs
62F15 Bayesian inference
Software:
bnpmr
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[1] Akacha, M.; Benda, N., The impact of dropouts on the analysis of dose-finding studies with recurrent event data, Statistics in Medicine, 29, 15, 1635-1646, (2010)
[2] Amzal, B.; Bois, F. Y.; Parent, E.; Robert, C. P., Bayesian-optimal design via interacting particle systems, Journal of the American Statistical Association, 101, 474, 773-785, (2006) · Zbl 1119.62308
[3] Atkinson, A. C.; Donev, A. N., Optimum experimental designs, (1992), Oxford University Press Inc. · Zbl 0829.62070
[4] Bernardo, J. M.; Smith, A. F.M., Bayesian theory, (1994), Wiley · Zbl 0796.62002
[5] Beskos, A., Crisan, D., Jasra, A., 2011. On the stability of sequential Monte Carlo methods in high dimensions. arXiv:1103.3965v2. · Zbl 1304.82070
[6] Bickel, P., Li, B., Bengtsson, T., 2008. Sharp failure rates for the bootstrap particle filter in high dimensions. In: Bertrand Clarke, Subhashis Ghosal (Eds.) IMS Collections: Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, vol. 3. pp. 318-329.
[7] Biedermann, S.; Woods, D. C., Optimal designs for generalized non-linear models with application to second-harmonic generation experiments, Journal of the Royal Statistical Society: Series C (Applied Statistics), 60, 2, 281-299, (2011)
[8] Bornkamp, B.; Ickstadt, K., Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis, Biometrics, 65, 1, 198-205, (2009) · Zbl 1159.62023
[9] Chaloner, K.; Verdinelli, I., Bayesian experimental design: a review, Statistical Science, 10, 3, 273-304, (1995) · Zbl 0955.62617
[10] Chang, H. H.; Ying, Z., Nonlinear sequential designs for logistic item response theory models with applications to computerized adaptive tests, The Annals of Statistics, 37, 3, 1466-1488, (2009) · Zbl 1160.62073
[11] Chopin, N., A sequential particle filter method for static models, Biometrika, 89, 3, 539-551, (2002) · Zbl 1036.62062
[12] Del Moral, P.; Doucet, A.; Jasra, A., Sequential Monte Carlo samplers, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68, 3, 411-436, (2006) · Zbl 1105.62034
[13] Dror, H. A.; Steinberg, D. M., Sequential experimental designs for generalized linear models, Journal of the American Statistical Association, 103, 481, 288-298, (2008) · Zbl 05564488
[14] Drovandi, C.C., McGree, J.M., Pettitt, A.N., 2012. A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design, Tech. Rep., Queensland University of Technology. http://eprints.qut.edu.au/49601/. · Zbl 06652998
[15] Drovandi, C. C.; Pettitt, A. N., Estimation of parameters for macroparasite population evolution using approximate Bayesian computation, Biometrics, 67, 1, 225-233, (2011) · Zbl 1217.62128
[16] Fearnhead, P., Taylor, B.M., 2010. An adaptive sequential Monte Carlo sampler. arXiv:1005.1193v2. · Zbl 1329.62055
[17] Friel, N.; Pettitt, A. N., Marginal likelihood estimation via power posteriors, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70, 3, 589-607, (2008) · Zbl 05563360
[18] Gasparini, M.; Eisele, J., A curve-free method for phase I clinical trials, Biometrics, 56, 2, 609-615, (2000) · Zbl 1060.62611
[19] Gramacy, R. B.; Polson, N. G., Particle learning of Gaussian process models for sequential design and optimization, Journal of Computational and Graphical Statistics, 20, 1, 102-118, (2011)
[20] Houede, N.; Thall, P. F.; Nguyen, H.; Paoletti, X.; Kramar, A., Utility-based optimization of combination therapy using ordinal toxicity and efficacy in phase I/II trials, Biometrics, 66, 2, 532-540, (2010) · Zbl 1192.62224
[21] Kullback, S.; Leibler, R. A., On information and sufficiency, The Annals of Mathematical Statistics, 22, 1, 79-86, (1951) · Zbl 0042.38403
[22] Lewi, J.; Butera, R.; Paninski, L., Sequential optimal design of neurophysiology experiments, Neural Computation, 21, 3, 619-687, (2009) · Zbl 1180.68219
[23] Liu, G.; Rosenberger, W. F.; Haines, L. M., Sequential designs for ordinal phase I clinical trials, Biometrical Journal, 51, 2, 335-347, (2009)
[24] Loeppky, J. L.; Moore, L. M.; Williams, B. J., Batch sequential designs for computer experiments, Journal of Statistical Planning and Inference, 140, 6, 1452-1464, (2010) · Zbl 1185.62142
[25] MacKay, D. J.C., Probable networks and plausible predictions—a review of practical Bayesian methods for supervised neural networks, Network: Computation in Neural Systems, 6, 3, 469-505, (1995) · Zbl 0834.68098
[26] McCullagh, P.; Nelder, J. A., (Generalized Linear Models, Monographs on Statistics and Applied Probability, vol. 37, (1989), Chapman Hall London) · Zbl 0744.62098
[27] McGree, J. M.; Drovandi, C. C.; Thompson, M. H.; Eccleston, J. A.; Duffull, S. B.; Mengerson, K.; Pettitt, A. N.; Goggin, T., Adaptive Bayesian compound designs for dose finding studies, Journal of Statistical Planning and Inference, 142, 6, 1480-1492, (2012) · Zbl 1242.62120
[28] Mukhopadhyay, S., Bayesian nonparametric inference on the dose level with specified response rate, Biometrics, 56, 1, 220-226, (2000) · Zbl 1060.62642
[29] Müller, P., Simulation-based optimal design, (Berger, J.; Bernardo, J.; Dawid, A.; Smith, A., Bayesian Statistics 6: Proceedings of the Sixth Valencia International Meeting, Vol. 6, June 6-10, 1998, (1999), Oxford University Press USA), 459-474 · Zbl 0974.62058
[30] Müller, P.; Berry, D. A.; Grieve, A. P.; Smith, M.; Krams, M., Simulation-based sequential Bayesian design, Journal of Statistical Planning and Inference, 137, 10, 3140-3150, (2007) · Zbl 1114.62076
[31] O’Quigley, J.; Pepe, M.; Fisher, L., Continual reassessment method: a practical design for phase I clinical trials in cancer, Biometrics, 46, 33-48, (1990) · Zbl 0715.62242
[32] Pavel, H.; Miroslav, Š., Sequential optimal experiment design for neural networks using multiple linearization, Neurocomputing, 73, 3284-3290, (2010)
[33] Robert, C. P.; Casella, G., Monte Carlo statistical methods, (2004), Springer Science + Business Media, LLC New York · Zbl 1096.62003
[34] Russell, K. G.; Woods, D. C.; Lewis, S. M.; Eccleston, J. A., \(D\)-optimal designs for Poisson regression models, Statistica Sinica, 19, 721-730, (2009) · Zbl 1168.62367
[35] Tian, Y.; Wang, D., Sequential Bayesian design for estimation of edp, (The 2nd International Conference on Biomedical Engineering and Informatics, 2009, BMEI’09, (2009), IEEE), 1-3
[36] Whitehead, J.; Brunier, H., Bayesian decision procedures for dose determining experiments, Statistics in Medicine, 14, 885-893, (1995)
[37] Yin, G.; Li, Y.; Ji, Y., Bayesian dose-finding in phase I/II clinical trials using toxicity and efficacy odds ratios, Biometrics, 62, 3, 777-787, (2006) · Zbl 1111.62114
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