The Bayesian approach to Population pharmacokinetic/pharmacodynamic modeling
It is one of the principal aims of drug development to discover, for a particular agent, the relationship between dose administered, drug concentrations in the body and efficacy/toxicity. Understanding this relationship leads to the determination of doses which are both effective and safe. Population pharmacokinetic/pharmacodynamic models provide an important aid to this understanding.
Pharmacokinetics considers the absorption, distribution and elimination over time of a drug and its metabolites. Pharmacokinetic data consist of drug concentrations along with (typically) known sampling times and known dosage regimens. A dosage regimen is defined by a route of administration and the sizes and timings of the doses. Pharmacodynamics considers the action of a drug on the body. Pharmacodynamic data consist of a response measure, for example blood pressure, a pain score or a clotting time, and a known dosage regimen. Population data arise when these quantities are measured on a group of individuals, along with subject-specific characteristics (covariates) such as age, sex or the level of a biological marker. When identical doses are administered to a group of individuals large between-individual variability in responses is frequently observed. The mechanisms which cause this variability are complex and include between-individual differences in both pharmacokinetic and pharmacodynamic parameters. The general aim of population studies then is to isolate and quantify the within-and between-individual sources of variability. The explanation of between-individual sources of variability in terms of known covariates is important as it has implications for the determination of dosage regimens for particular covariate-defined subpopulations.
In this chapter we describe the drug development process from a population pharmacokinetic/pharmacodynamic perspective. In particular we describe how the nature of the statistical analysis and the models that are used are modified as the type of data and the aims of the study change through the various phases of development. The Bayesian approach to population modeling is particularly appealing from a biological perspective as it allows informative prior distributions to be incorporated. These priors may arise from previous studies and/or from medical/biological considera-tions. From an estimation standpoint a Bayesian approach is preferable because of the difficulties which a classical approach encounters due to the large numbers of parameters, the nonlinearity of the subject-specific models which are typically used and the large numbers of variance parameters.
We illustrate the population approach to drug development by describing a number of studies which were carried out by Ciba for a particular anti-clotting agent. We also present a detailed analysis for one of the studies.
KeywordsDrug Development Bayesian Approach Subcutaneous Dose Compartmental System Nonlinear Mixed Effect Model
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- Beal, S.L. and Sheiner, L.B. (1982). Estimating population kinetics. CRC Critical Reviews in Biomedical Engineering, 8, 195–222.Google Scholar
- Beal, S.L. and Sheiner, L.B. (1993). NONMEM User’s Guide, University of California, San Fransisco.Google Scholar
- Bennett, J.E., Racine-Poon, A. and Wakefield, J.C. (1996). MCMC for nonlinear hierarchical models. InMarkov Chain Monte Carlo Methods in Practice, (eds. W.R. Gilks, S. Richardson and D.J. Spiegelhalter), 339–357. London: Chapman and Hall.Google Scholar
- Berry, D.A. (1990). Basic principles in designing and analyzing clinical studies. InStatistical Methodology in the Pharmaceutical Sciences, (ed. D.A. Berry), 1–55. Marcel-Dekker, Inc. New York and Basel.Google Scholar
- Colburn, W.A. (1989). Controversy IV: population pharmacokinetics, NONMEM and the pharmacokinetic screen; academic, industrial and regulatory perspectives. J. Clin.Pharmacol., 29, 1–6.Google Scholar
- Davidian, M. and Giltinan, D.M. (1995). Nonlinear Models for Repeated Measurement Data., Chapman and Hall, London.Google Scholar
- Eriksson, B.I., Kalebo, P., Zachrisson, B., Ekman, S., Kerry, R. and Close, P. (1996). Prevention of deep vein thrombosis with recombinant hirudin CGP 39393 in hip prosthesis surgery. Evaluation of three dose levels of recombinant hirudin in comparison with unfractionated heparin. Lancet, 347, 635–39.CrossRefGoogle Scholar
- Eriksson, B.I., Ekman, S., Lindbratt, S., Baur, M., Torholm, C., Kalebo, P. and Close, P. (1997a). Prevention of deep vein thrombosis with recombinant hirudin — results of a double-blind multicenter trial comparing the efficacy of desirudin (Revasc) with that of unfractionated heparin in patients having a total hip replacement. J. Bone J. Surg. (Am), 79A, 326–33.Google Scholar
- Eriksson, B.I., Wille-Jorgensen, P., Kalebo, P., Mouret, P., Rosencher, N., Bosch, P., Baur, M., Ekman, S., Bach, D., Lindbratt, S. and Close, P. (1997b). Recombinant hirudin, desirudin, is more effective than a low-molecularweight heparin, enoxaparin, as prophylaxis of major thromboembolic complications after primary total hip replacement. To appear in New England Medical Journal.Google Scholar
- Food and Drug Administration (1989). Guideline for the study of drugs likely to be used in the elderly. Washington, DC.Google Scholar
- Gibaldi, M. and Perrier, D. (1982). Drugs and the Pharmaceutical Sciences, Volume 15 Pharmacokinetics, Second Edition., Marcel Dekker.Google Scholar
- Gilks, W.R., Neal, R.M., Best, N.G. and Tan, K.K.C. (1997). Corrigendum to `Adaptive rejection metropolis sampling within Gibbs sampling’. Applied Statistics, 46, 541–2.Google Scholar
- Godfrey, K.R. (1983). Compartmental Models and their Applications., London, Academic Press.Google Scholar
- Maitre, P., Buhrer, M., Thomson, D., and Stanski, D. (1991). A three-step approach to combining Bayesian regression and NONMEM population analysis. Journal of Pharmacokinetics and Biopharmaceutics, 19, 377–84.Google Scholar
- Muller, P. and Rosner, G.L. (1997). A Bayesian population model with hierarchical mixture priors applied to blood count data. Journal of the American Statistical Association, 92, 1279–92.Google Scholar
- Pinheiro, J. and Bates, D. (1995). Approximations to the loglikelihood function in the nonlinear mixed effects model. Computational and Graphical Statistics, 4, 12–35.Google Scholar
- Racine-Poon, A. and Wakefield, J.C. (1996). Bayesian analysis of population pharmacokinetic and instantaneous pharmacodynamic relationships. InBayesian Biostatistics, (ed. D. Berry and D. Stangl). Marcel-Dekker.Google Scholar
- Rowland, M. and Tozer, T.N. (1995). Clinical Pharmacokinetics: Concepts and Applications, Third Edition., Williams and Wilkins.Google Scholar
- Steimer, J., Vozeh, S., Racine-Poon, A., Holford, N., and O’Neill, R. (1994). The population approach: rationale, methods and applications in clinical pharmacology and drug development. In Handbook of experimental pharmacology, (eds. P. Welling and H. Balant). Springer Verlag.Google Scholar
- Temple, R. (1983). Discussion paper on the testing of drugs in the elderly. Washington, DC: Memorandum of the Food and Drug Administration of Department of Health and Human Service.Google Scholar
- Temple, R. (1985). Food and Drug Administration’s guidelines for clinical testing of drugs in the elderly. Drug Information Journal, 19, 483–486.Google Scholar
- Temple, R. (1989). Dose-response and registration of new drugs. In Dose-response relationships in Clinical Pharmacology., Eds. Lasagne, L., Emill, S. and Naranjo, C.A. Amsterdam, Elsevier, pl45–167.Google Scholar
- Wakefield, J.O. (1996b). Bayesian individualization via sampling based methods. Journal of Pharmacokinetics and Biopharmaceutics, 24, 103–31.Google Scholar
- Wakefield, J.C. and Walker, S.G. (1997). Bayesian nonparametric population model: formulation and comparison with likelihood approaches. Journal of Pharmacokinetics and Biopharmaceutics, 25, 235–53.Google Scholar
- Walker, S.G. and Wakefield, J.C. (1998). Population models with a nonparametric random coefficient distribution. To appear inSankhya, Series B Google Scholar
- Beal, S.L. and Sheiner, L.B. (1993). NONMEM User’s Guide, University of California, San Francisco.Google Scholar
- Bennett, J.E., Wakefield, J.C. and Lacey, L.F. (1997). Modeling of trough plasma bismuth concentrations. Journal of Pharmacokinetics and Biopharmaceutics, 25, 79–106.Google Scholar
- Bennett, J.E. and Wakefield, J.C. (1998). Errors-in-variables in joint PIC/PD modeling. Manuscript under preparation Google Scholar
- Spiegelhalter, D.J., Thomas, A., Best, N.G. and Gilks, W.R. (1994). BUGS: Bayesian Inference Using Gibbs Sampling, Version 3.0., Cambridge: Medical Research Council Biostatistics Unit.Google Scholar
- Wakefield, J.C. and Rahman, N.J. The combination of population pharmacokinetic studies. Submitted for publication Google Scholar