Bayesian Experimental Design for Nonlinear Mixed‐Effects Models with Application to HIV Dynamics

Bayesian experimental design is investigated for Bayesian analysis of nonlinear mixed-effects models. Existence of the posterior risk for parameter estimation is shown. When the same prior distribution is used for both design and inference, existence of the preposterior risk for design is also proven. If the prior distribution used in design is different from that used for inference, sufficient conditions are established for existence of the preposterior risk for design. A case study of design for an experiment in population HIV dynamics is provided.

[1]  J. Wakefield.  The Bayesian Analysis of Population Pharmacokinetic Models , 1996 .

[2]  H Wu,et al.  Population HIV‐1 Dynamics In Vivo: Applicable Models and Inferential Tools for Virological Data from AIDS Clinical Trials , 1999, Biometrics.

[3]  Alan S. Perelson,et al.  Bayesian Analysis of a Population HIV Dynamic Model , 2002 .

[4]  Nozer D. Singpurwalla,et al.  On the Evidence Needed to Reach Agreed Action between Adversaries, with Application to Acceptance Sampling , 1991 .

[5]  Alain Mallet,et al.  Optimal design in random-effects regression models , 1997 .

[6]  Joseph B. Kadane,et al.  Optimal Experimental Design for Another's Analysis , 1993 .

[7]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

[8]  Bradley P. Carlin,et al.  BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS , 1996, Stat. Comput..

[9]  Martin A. Nowak,et al.  Viral dynamics in human immunodeficiency virus type 1 infection , 1995, Nature.

[10]  J L Palmer,et al.  Bayesian optimal design in population models for haematologic data. , 1998, Statistics in medicine.

[11]  Peter Müller,et al.  Optimal sampling times in population pharmacokinetic studies , 2001 .

[12]  F. Pukelsheim.  Optimal Design of Experiments , 1993 .

[13]  A. Perelson,et al.  HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time , 1996, Science.

[14]  M Davidian,et al.  Population pharmacokinetic/pharmacodynamic methodology and applications: a bibliography. , 1994, Biometrics.

[15]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[16]  Valerii V. Fedorov,et al.  Design of experiments with unknown parameters in variance , 2002 .

[17]  George G. Woodworth,et al.  t for Two, or Preposterior Analysis for Two Decision Makers: Interval Estimates for the Mean , 1976 .

[18]  Alan S. Perelson,et al.  Effect of drug efficacy and the eclipse phase of the viral life cycle on estimates of HIV viral dynamic parameters. , 2001 .

[19]  A. Perelson,et al.  Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection , 1995, Nature.

[20]  Adrian F. M. Smith,et al.  Bayesian Analysis of Linear and Non‐Linear Population Models by Using the Gibbs Sampler , 1994 .

[21]  D. Cox,et al.  Planning Experiments for Discriminating between Models , 1974 .

[22]  Robert K. Tsutakawa,et al.  Design of Experiment for Bioassay , 1972 .