Jean-Michel Gries, Pharm.D, Ph.D.(1), Davide Verotta, Ph.D.(2), Lewis B. Sheiner, M.D.(3)
1) Hoechst Marion Roussel, Inc., Clinical Pharmacology, PO Box 6800, Bridgewater, NJ 08807 2) Department of Biopharmaceutical Sciences, School of Pharmacy, University of California, San Francisco, and Department of Epidemiology and Biostatistics, University of California, San Francisco, CA 94143 3) Department of Laboratory Medicine, School of Medicine, University of California, San Francisco, CA 94143
In clinical trials, like ACTG 175 (Hammer, Katzenstein et al. 1996), drug levels in patients, if sampled at all, are generally sampled only once or twice during the whole study. However, one may wish to estimate individual drug exposure in order to relate it to observed outcome.
In general, exposure is dependent on drug taking behavior (compliance) and drug disposition (i.e., pharmacokinetics). We assume that compliance can be estimated (see (Urquhart 1994) for a recent review of methods), and we concern ourselves with estimating pharmacokinetics (PK). When prior knowledge of population PK parameters is available, posterior bayes estimates of PK can be obtained from sparse samples, leading to individual exposure estimates (Bernardo and Smith 1994). However, such estimates are questionable if a subject does not comply prior to the time of PK sampling. For example, an observation taken two population-average half-lives after the stated time of the last previous dose may be reported as below the quantification limit (QL). Such a result is compatible with two different interpretations: the subject has an unusually rapid half-life, or he has a normal half-life, but he took the drug earlier than stated (Lim 1992).
We describe a methodology to handle PK parameter estimation in such a situation. To do so, we assume the following: (i) population PK estimates are available from previous studies, (ii) sparse sampling shortly after a dose, with one or more drug measurements per occasion, is available, (iii) the drug has a short half-life, and is dosed at an interval >3 half-lives (so that if no drug is taken shortly before a clinic visit then the assumption that the drug level will be essentially zero is credible), and (iv) the timing of the PK samples is accurate. These apparently restrictive requirements are, in fact, often met, for example in AIDS clinical trials of reverse transcriptase inhibitors.
A mixture pharmaco-statistical model is proposed that expresses the likelihood of the observed concentration under 3 mutually exclusive events: the prescribed dose was not taken at all, the prescribed dose was taken at the specified time, or a dose of unspecified size was taken at an unspecified time. The individual’s pharmacokinetic parameter estimates are Bayes estimates given the above model and an informative prior distribution on all parameters.
The methodology performs better (less error and greater precision) than other ones that resemble current practice. The extreme sparse sampling considered (one or two observations per individual) coupled with the possible non-compliance leads to large errors in individual PK estimates. This suggests the need for more PK sampling than usual for sparse sampling when compliance cannot be assured.
References
[1]. Bernardo, J. M. and A. F. M. Smith (1994). Bayesian Theory. New York, Wiley.
[2]. Hammer, S. M., D. A. Katzenstein and M. D. Hughes (1996). “A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 per cubic millimeter.” New England Journal of Medicine 335(15): 1081-1089.
[3]. Lim, L. L. (1992). “Estimating compliance to study medication from serum drug levels: application to an AIDS clinical trial of zidovudine.” Biometrics 48(2): 619-30.
[4]. Urquhart, J. (1994). “Role of patient compliance in clinical pharmacokinetics. A review of recent research.” Clinical Pharmacokinetics 27(3): 202-15.
Reference: PAGE 7 (1998) Abstr 671 [www.page-meeting.org/?abstract=671]
Poster: oral presentation