Brian Whiting

Population Pharmacokinetics Theory and Clinical Application

SummaryGood therapeutic practice should always be based on an understanding of pharmacokinetic variability. This ensures that dosage adjustments can be made to accommodate differences in pharmacokinetics due to genetic, environmental, physiological or pathological factors. The identification of the circumstances in which these factors play a significant role depends on the conduct of pharmacokinetic studies throughout all stages of drug development. Advances in pharmacokinetic data analysis in the last 10 years have opened up a more comprehensive approach to this subject: early traditional small group studies may now be complemented by later population-based studies. This change in emphasis has been largely brought about by the development of appropriate computer software (NONMEM: Nonlinear Mixed Effects Model) and its successful application to the retrospective analysis of clinical data of a number of commonly used drugs, e.g. digoxin, phenytoin, gentamicin, procainamide, mexiletine and lignocaine (lidocaine). Success has been measured in terms of the provision of information which leads to increased efficiency in dosage adjustment, usually based on a subsequent Bayesian feedback procedure. The application of NONMEM to new drugs, however, raises a number of interesting questions, e.g. ‘what experimental design strategies should be employed?’ and ‘can kinetic parameter distributions other than those which are unimodal and normal be identified?’ An answer to the latter question may be provided by an alternative non-parametric maximum likelihood (NPML) approach.Population kinetic studies generate a considerable amount of demographic and concentration-time data; the effort involved may be wasted unless sufficient attention is paid to the organisation and storage of such information. This is greatly facilitated by the creation of specially designed clinical pharmacokinetic data bases, conveniently stored on microcomputers.A move towards the adoption of population pharmacokinetics as a routine procedure during drug development should now be encouraged. A number of studies have shown that it is possible to organise existing, routine data in such a way that valuable information on pharmacokinetic variability can be obtained. It should be relatively easy to organise similar studies prospectively during drug development and, where appropriate, proceed to the establishment of control systems based on Bayesian feedback.

Experimental Design and Efficient Parameter Estimation in Population Pharmacokinetics

A computer simulation technique used to evaluate the influence of several aspects of sampling designs on the efficiency of population pharmacokinetic parameter estimation is described. Although the simulations are restricted to the one-compartment one-exponential model, they provide the basis for a discussion of the structural aspects involved in designing a population study. These aspects include number of subjects required, number of samples per subject, and timing of these samples. Parameter estimates obtained from different sampling schedules based on two- and three-point designs are evaluated in terms of accuracy and precision. These simulated data sets include noise terms for both inter- and intraindividual variability. The results show that the population fixed-effect parameters (mean clearance and mean volume of distribution) for this simple pharmacokinetic model are efficiently estimated for most of the sampling schedules when two or three points are used, but the random-effect parameters (describing inter- and intraindividual variability) are inaccurate and imprecise for most of the sampling schedules when only two points are used. This drawback was remedied by increasing the number of data points per individual to three.

Effect of misspecification of the absorption process on subsequent parameter estimation in population analysis

A prospective simulation study has been carried out to evaluate the effect of potential misspecification of the absorption rate constant (ka) in population pharmacokinetic analysis when few to no concentration-time data were available in the absorption phase and estimation of kawas not possible. Data were simulated for 100 subjects using a one-compartment model at steady state with first-order input. Data were generated over a range of kavalues: kawas misspecified in the NONMEM analysis by factors of 0.25, 0.5,1, 2, 3, and 4. In general, clearance (CL)was typically estimated with a small, constant underprediction, regardless of the range of misspecification of ka or whether data were present in the absorption phase. The same was not true for volume of distribution (V),values were biased and sensitive to the degree of misspecification, but only when the data contained even a little information about absorption. If studies are to be designed in which information absorption is either not required or is of no therapeutic use, then blood samples could be concentrated in the postabsorption phase and the absorption input fixed according to the best a priori information available.

Analysis of animal pharmacokinetic data: Performance of the one point per animal design

A simulation study was carried out to determine the impact of various design factors on the accuracy and precision with which population pharmacokinetic parameters are estimated in preclinical pharmacokinetic studies. A drug given by intravenous bolus injection and having monoexponential disposition characteristics was assumed. The factors investigated were (i) number of animals sampled at specified times with one observation taken per animal, (ii) error in observed concentration measurements, and (iii) doubling the number of observations per animal while varying the number of animals. Data were analyzed with the NONMEM program, and the least number of animals per time point (where each animal supplied one concentration-time point) required for accurate and precise parameter estimation was determined. The one observation per animal design yielded biased and imprecise estimates of variability, and residual variability could not be estimated. Increasing the error in the concentration measurement led to a significant deterioration in the accuracy and precision with which variability was estimated. Obtaining a second sample from each animal practically eliminated bias and facilitated the partitioning of interanimal variability and residual intraanimal variability, by introducing information about the latter. Doubling the total number of observations per animal required using half (i.e., 50) the total number of animals required for accurate and precise parameter estimation with the one sample per animal design.

Variability in the pharmacokinetics of epirubicin: a population analysis

SummaryPopulation pharmacokinetic analysis of the anticancer agent epirubicin was carried out using the program NONMEM. Data were available from 36 patients aged 20–73 years, of whom 23 were women. All subjects exhibited normal liver and renal function. Epirubicin was given as a short-term i. v. infusion over the dose range of 25–100 mg/m2, and an average of 11 plasma samples/subject were taken for a period of up to 72 h after each dose. A Two compartment model was fitted to the data, characterised by the parameters clearance, volume of the central compartment, alpha and beta. Clearance was tested as a linear function of various demographic and/or biochemical features. A significant proportion of the variability in clearance could be attributed to sex, and also to age in women. For example, a 25-year-old man would display an average clearance of 95 l/h, whereas a 70-year-old woman would exhibit an average clerance of 64 l/h. Such differences in clearance might be important in the selection of epirubicin dose regimens.

Experimental Design and Efficient Parameter Estimation in Preclinical Pharmacokinetic Studies

Monte Carlo simulation technique used to evaluate the effect of the arrangement of concentrations on the efficiency of estimation of population pharmacokinetic parameters in the preclinical setting is described. Although the simulations were restricted to the one compartment model with intravenous bolus input, they provide the basis of discussing some structural aspects involved in designing a destructive (“quantic”) preclinical population pharmacokinetic study with a fixed sample size as is usually the case in such studies. The efficiency of parameter estimation obtained with sampling strategies based on the three and four time point designs were evaluated in terms of the percent prediction error, design number, individual and joint confidence intervals coverage for parameter estimates approaches, and correlation analysis. The data sets contained random terms for both inter- and residual intra-animal variability. The results showed that the typical population parameter estimates for clearance and volume were efficiently (accurately and precisely) estimated for both designs, while interanimal variability (the only random effect parameter that could be estimated) was inefficiently (inaccurately and imprecisely) estimated with most sampling schedules of the two designs. The exact location of the third and fourth time point for the three and four time point designs, respectively, was not critical to the efficiency of overall estimation of all population parameters of the model. However, some individual population pharmacokinetic parameters were sensitive to the location of these times.

Modeling of Drug Response in Individual Subjects

Pharmacokinetic and drug response data from individual subjects are analyzed empirically by two different mathematical techniques. The drugs involved are the antiarrhythmic agent disopyramide, whose kinetics can be described by a two-compartment model, and two cardiac glycosides, digoxin and β-methyl digoxin, for which three-compartment models are appropriate. The first analytical approach uses multiple linear regression to describe response in terms of the amount of drug in several kinetic compartments. The second approach describes response in terms of the drug concentration in an “effect” compartment. Both approaches describe the data equally well and require the same number of parameters for model specification.

The pharmacokinetics and pharmacodynamics of lignocaine and MEGX in healthy subjects

Lignocaine clearance declines during continuous intravenous infustion in man and in vitrostudies suggest that this may partly be due to inhibition by MEGX, a metabolite of lignocaine, MEGX is pharmacologically active in animals, but this is not yet proven in man. This study examined the pharmacokinetics and pharmacodynamics of lignocaine and MEGX in eight healthy male volunteers given lignocaine HCl 120mg, MEGX HCl 120 mg, lignocaine HCl 120 mg+MEGX HCl 120 mg, and placebo, administered according to a randomized double-blind protocol. One-, two-, or three-compartment models were fitted to drug and metabolite blood concentration-time profiles and clearance, volume (Vss), andhalf-life values were calculated and compared by paired t-test. Systolic time intervals and QTinterval were recorded and compared by repeated measures ANOVA. When administered in combination with MEGX, lignocaine clearance was significantly reduced from 58±18 to 48±13 L hr(su−1) (p <0.02). The V(inss) was unchanged and there was a trend toward an increase in terminal half-life. Lignocaine, MEGX, and the combination significantly reduced QTinterval up to 30 min after injection and this was maintained to 2 hr with the lignocaine and the combination. Transient side effects were experienced with all active treatments, but were most pronounced with the combination. Thus, lignocaine clearance was inhibited by MEGX, which was pharmacologically active in man.

Enhancement of Methotrexate Absorption by Subdivision of Dose

SummaryA comparison was made in fasting patients between a single 100 mg oral dose of methotrexate formulated as its sodium salt in a palatable syrup and the same total quantity of drug administered in four divided doses of 25 mg taken at 2-h intervals. Allocation to the order of these treatment schedules was on a random basis. The area under the serum methotrexate concentration-time curve until 50 h was found to be considerably greater after the divided dose regimen, the mean ratio AUC 25 mg x 4/AUC 100 mg being 1.86 (±0.90). There was no significant difference in peak serum methotrexate concentrations or methotrexate half-life estimates between the two regimens, however.The results of this study are consistent with saturation of an intestinal transport process when methotrexate is administered orally in a single large dose.

Interpretation of Simulation Studies for Efficient Estimation of Population Pharmacokinetic Parameters

OBJECTIVE: To develop new approaches for evaluating results obtained from simulation studies used to determine sampling strategies for efficient estimation of population pharmacokinetic parameters. METHODS: One-compartment kinetics with intravenous bolus injection was assumed and the simulated data (one observation made on each experimental unit [human subject or animal]), were analyzed using NONMEM. Several approaches were used to judge the efficiency of parameter estimation. These included: (1) individual and joint confidence intervals (CIs) coverage for parameter estimates that were computed in a manner that would reveal the influence of bias and standard error (SE) on interval estimates; (2) percent prediction error (%PE) approach; (3) the incidence of high pair-wise correlations; and (4) a design number approach. The design number (Φ) is a new statistic that provides a composite measure of accuracy and precision (using SE). RESULTS: The %PE approach is useful only in examining the efficiency of estimation of a parameter considered independently. The joint CI coverage approach permitted assessment of the accuracy and reliability of all model parameter estimates. The Φ approach is an efficient method of achieving an accurate estimate of parameter(s) with good precision. Both the Φ for individual parameter estimation and the overall Φ for the estimation of model parameters led to optimal experimental design. CONCLUSIONS: Application of these approaches to the analyses of the results of the study was found useful in determining the best sampling design (from a series of two sampling times designs within a study) for efficient estimation of population pharmacokinetic parameters.