Modelling and data handling
Concentration–time data of chloroquine and desethylchloroquine, transformed into their natural logarithms, were analysed using the mixed-effects modelling in NONMEM
® (version 7.12; ICOM Development Solutions, Ellicot City, MD, USA) and the output results and graphical plots were handled using the statistical analysis programs R (version 2.15.1; Free Software Foundation, Boston, MA, USA) and R-package Xpose (version 4.3.5; Uppsala University, Uppsala, Sweden). The observations that were below the limit of quantification were excluded from the pharmacokinetic analysis. The first-order conditional estimation (FOCE) method was used throughout the modeling. Model evaluation was based on visual inspection of diagnostic plots, precision of parameters and the objective function value (OFV; proportional to −2 Log likelihood) [
25]. For nested models, the difference in OFV is approximately Chi squared distributed and it can therefore be used in model discrimination.
For a one parameter difference between models, 3.84 correspond to a
p value of 0.05. Population pharmacokinetic models were constructed to evaluate the concentration–time data for chloroquine and desethylchloroquine and to identify any covariates that could describe between subject variability (BSV). A metabolite model was implemented to describe the pharmacokinetics of chloroquine and desethylchloroquine. One, two-and three compartment models were initially investigated both for the parent drug and metabolite. Different models for the elimination of chloroquine and its metabolite were evaluated. A first-order absorption model and a transit compartment absorption model with 1–10 transit compartments were investigated to describe the absorption of chloroquine. Relative bioavailability was added with a typical value of 100 % with an estimate of between-subject variability. Between-subject variability was added exponentially, resulting in log-normal distributed parameters:
$${\text{P}}_{\text{i}} = {\text{P}}_{\text{p}} {\text{e}}^{{{\upeta}_{\text{i}} }}$$
where Pi is the true value of the parameter for the individual and Pp is the typical or population value of the parameter. Pp is the fixed effect parameter estimated from the structural model and \(\upeta_{\text{i}}\) represents the difference between Pi and Pp.
An additive residual variability (RUV) model was applied according to:
$${\text{C}}_{\text{obs}} = {\text{C}}_{\text{p}} + \varepsilon_{\text{ad}}$$
where Cobs is the observed drug or metabolite concentration and Cp is the concentration predicted by the model and εad represents the difference between these values. An additive model on log-transformed data is equivalent to an exponential model.
The most adequate structural model with random effects (base model) was further developed to include covariates using a stepwise forward addition (
p = 0.05) of covariates, followed by a stepwise backward elimination procedure (
p = 0.001). Relationships between all parameters estimated in the base model and covariates
, i.e., body weight (BW), age, sex, parasite clearance time (PCT) and fever clearance time (FCT) were evaluated. The covariate was retained in the final model if its removal resulted in an increase in the objective function of ≥10.83 points (
p < 0.001) from the full model. BW was applied as a covariate on all CL and V values as a power model according to equation:
$${\text{P}}_{{\text{t}}} = {{\uptheta }}_{1} \cdot \left( {\frac{{{\text{BW}}}}{{{\text{median BW}}}}} \right)^{{{{\uptheta }}_{2} }}$$
where Pt is the typical population value of the parameter for the population; θ1 represents the estimate of P in an individual with median BW; and θ2 is the fractional change in Pt with each kilogram change in BW from median BW. BW was allometrically scaled and θ2 was defined as 0.75 and 1 when applied on CL and V, respectively.
The covariate model for continuous covariates such as FCT was exemplified by the following equation:
$${\text{VP}}_{{\text{t}}} = {{\uptheta }}_{1} \cdot \left[ {1 \,+\, {{\uptheta }}_{2} {\mkern 1mu} \,\times\, {\mkern 1mu} ({\text{FCT}} \,-\, {\text{median FCT}})} \right]$$
where Pt is the typical value of parameter P; θ1 represents the estimate of P in an individual with median FCT; and θ2 the fractional change in P with each change in unit of FCT from median FCT.
All clearance and distribution parameters are reported as the ratio of the parameter and bioavailability since oral dosing was not accompanied by an intravenous dose. The pharmacokinetic population parameters estimated from the final covariate model were used to calculate terminal half-life for chloroquine and desethylchloroquine.
Bootstrap diagnostics were performed using 1000 re-sampled datasets. The precision was described as a relative standard error. A visual predictive check (VPC) is a tool for the evaluation of the predictive ability and the appropriateness of a model and was done by performing simulations of 1000 observations at each time point for the real observations in the data set with the final covariate model. The median and 95 % prediction intervals of the simulated data and the true observations were plotted against time. The predictive ability of the model was assumed to be adequate if less than 10 % of the observed concentrations fell outside the prediction interval.