Comparing non-hierarchical models: Application to non-linear mixed effects modeling

There is no method available to compare the fit of two non-hierarchical non-linear mixed effects models, although the common practice is to select the model with the lower objective function. Bootstrapping the log-likelihood differences (LLDs) of non-hierarchical models and constructing a bootstrap confidence interval on the LLDs is proposed for comparing the goodness-of-fit of such models. This is illustrated with different parameterizations of clearance models for an anti-infective agent in a longitudinal pharmacokinetic study which are compared. Additive and exponential models of creatinine clearance as a predictor of clearance are used as examples.     

A random sampling approach for robust estimation of tissue-to-plasma ratio from extremely sparse data

This study was performed to develop a new nonparametric approach for the estimation of robust tissue-to-plasma ratio from extremely sparsely sampled paired data (ie, one sample each from plasma and tissue per subject). Tissue-to-plasma ratio was estimated from paired/unpaired experimental data using independent time points approach, area under the curve (AUC) values calculated with the naive data averaging approach, and AUC values calculated using sampling based approaches (eg, the pseudoprofile-based bootstrap [PpbB] approach and the random sampling approach [our proposed approach]). The random sampling approach involves the use of a 2-phase algorithm. The convergence of the sampling/resampling approaches was investigated, as well as the robustness of the estimates produced by different approaches. To evaluate the latter, new data sets were generated by introducing outlier(s) into the real data set. One to 2 concentration values were inflated by 10% to 40% from their original values to produce the outliers. Tissue-to-plasma ratios computed using the independent time points approach varied between 0 and 50 across time points. The ratio obtained from AUC values acquired using the naive data averaging approach was not associated with any measure of uncertainty or variability. Calculating the ratio without regard to pairing yielded poorer estimates. The random sampling and pseudoprofile-based bootstrap approaches yielded tissue-to-plasma ratios with uncertainty and variability. However, the random sampling approach, because of the 2-phase nature of its algorithm, yielded more robust estimates and required fewer replications. Therefore, a 2-phase random sampling approach is proposed for the robust estimation of tissue-to-plasma ratio from extremely sparsely sampled data.     

Pharmacokinetics of chloroquine: saliva and plasma levels relationship

The use of saliva levels as an alternative to plasma levels in monitoring chloroquine therapy was studied in five healthy volunteers. Subjects took two (250 mg) tablets of chloroquine diphosphate (300 mg chloroquine base) with 200 ml of water. Saliva and blood samples were collected at intervals over 6 days. Plasma was separated from blood samples after centrifugation while saliva samples were centrifuged to remove mucoid sediments. Both the plasma and saliva samples were analysed for chloroquine by a combination of thin-layer chromatography and spectrophotometry. Regression analysis was used to determine the correlation between saliva and plasma chloroquine levels. A significant correlation (r = 0.97, p less than 0.05) was observed between saliva and plasma levels of chloroquine. The saliva: plasma concentrations ratio was found to be 0.53. From the saliva: plasma relationship, the extent of chloroquine binding to plasma proteins was estimated to be 47%. The Cmax and AUC0-6 day values obtained from saliva data was about half those from plasma, while the Tmax obtained from both fluids remained the same. The saliva clearance rate (Cls/F) of chloroquine was about twice the plasma clearance rate (Cl/F). (Cls/F: 0.46 +/- 0.051/day/kg; 0.27 +/- 0.021/day/kg). However, the predicted Cl/F (0.27 +/- 0.031/day/kg) from saliva data was in agreement with Cl/F from plasma data. This was also true of the volume of distribution. The collection of saliva for measuring chloroquine levels provides a painless, non-invasive alternative to plasma sampling, and it is useful in predicting chloroquine pharmacokinetics.     

Effect of ranitidine on chloroquine disposition

Ten healthy, male volunteers (aged 19-27 yr; weight 62-67 kg) were randomly distributed into control and test groups of five subjects each in a controlled study on the effect of ranitidine on chloroquine disposition. The control group subjects received two tablets of chloroquine sulfate (300-mg base) only. The test group subjects received ranitidine 250 mg hs for four days prior to the administration of chloroquine sulfate and throughout the sample collection period. Blood samples (5 ml) were collected from the time of the chloroquine administration to the seventh day after drug administration. The samples were analyzed for chloroquine content by a combination of thin-layer chromatography and ultraviolet spectrophotometry. The Wilcoxon test at 0.05 significance level was used to compare the disposition parameters between control and test groups. Ranitidine therapy was associated with no significant alterations in chloroquine oral clearance rate, elimination rate constant, and apparent volume of distribution. Unlike cimetidine, ranitidine does not interact pharmacokinetically with chloroquine. Ranitidine, therefore, may be the H2-receptor antagonist of choice for ulcer patients receiving chloroquine.     

Designing population pharmacokinetic studies: performance of mixed designs.

The interplay of the following factors: population design (PDN), the cost function in terms of maximum cost (Max. C) (i.e., maximum number of samples/sample size), sample size, and intersubject variability [restricted (30%) to moderate (60%)] on the estimation of pharmacokinetic parameters from population pharmacokinetic data sets obtained using mixed designs was investigated in a simulation study. A two compartment model with multiple bolus intravenous inputs was assumed, and the residual variability was set at 15%. The sample size (N) investigated ranged from 30 to 200 with the associated cost function varying accordingly with the five individual and sixteen population designs studied. Accurate and precise estimates of structural model parameters were obtained for N > or = 50 (Max. C > or = 150) irrespective of the intersubject variability (ITV) and PDN investigated. When ITV was 30%, all structural model parameters were well estimated irrespective of the PDN. Robust estimates of clearance and its variability were obtained for all N at all levels of ITV with Max. C > or = 90 (PDN > or = 4). Imprecise estimates of ITV in V1, V2, and Q were obtained at 60% ITV irrespective of N, PDN, or Max. C. Positive bias was associated with the estimation of variability in V1, V2, and Q with PDN < or = 4 (Max. C < or = 150). This was due in part to a greater proportion of subjects sampled only once. Correspondingly, residual variability was underestimated. It is of utmost importance to avoid this artifact by ensuring that at least a moderate subset of subjects contributing data to a population pharmacokinetic study contribute data more than once. Given a sample size and ITV, the cost function must be considered in designing a population pharmacokinetic study using mixed designs.     

Estimating inestimable standard errors in population pharmacokinetic studies: the bootstrap with Winsorization.

A simulation study was performed to determine how inestimable standard errors could be obtained when population pharmacokinetic analysis is performed with the NONMEM software on data from small sample size phase I studies. Plausible sets of concentration-time data for nineteen subjects were simulated using an incomplete longitudinal population pharmacokinetic study design, and parameters of a drug in development that exhibits two compartment linear pharmacokinetics with single dose first order input. They were analyzed with the NONMEM program. Standard errors for model parameters were computed from the simulated parameter values to serve as true standard errors of estimates. The nonparametric bootstrap approach was used to generate replicate data sets from the simulated data and analyzed with NONMEM. Because of the sensitivity of the bootstrap to extreme values, winsorization was applied to parameter estimates. Winsorized mean parameters and their standard errors were computed and compared with their true values as well as the non-winsorized estimates. Percent bias was used to judge the performance of the bootstrap approach (with or without winsorization) in estimating inestimable standard errors of population pharmacokinetic parameters. Winsorized standard error estimates were generally more accurate than non-winsorized estimates because the distribution of most parameter estimates were skewed, sometimes with heavy tails. Using the bootstrap approach combined with winsorization, inestimable robust standard errors can be obtained for NONMEM estimated population pharmacokinetic parameters with > or = 150 bootstrap replicates. This approach was also applied to a real data set and a similar outcome was obtained. This investigation provides a structural framework for estimating inestimable standard errors when NONMEM is used for population pharmacokinetic modeling involving small sample sizes.