All patients received dihydroartemisinin-piperaquine tetra-phosphate (Duo Cotecxin, 40 mg/320 mg tablets, Beijing Holley-Cotec Pharmaceuticals, Co., Ltd.) once daily for three days. Drug administration was directly observed and taken with a glass of water under fasting conditions. The number of tablets was based on the patient’s body weight to achieve a daily dose of 20 mg piperaquine tetra-phosphate/kg.
Blood samples were obtained by venous puncture or a three-way tap. PCR, haematology and biochemistry samples were drawn before the first dose and on day 14. Blood samples (2 mL) for pharmacokinetic analysis were drawn pre-dose and at 1.5, 4, 8, 24, 25.5, 28, 32, 48, 49, 50, 52, 56, 60, 72 h after the first dose and on days 5, 7, 14, 21, 28, 35, 42, 49, 56, 63 and 90. The actual time of dosing and sampling were noted and used in the pharmacokinetic analysis. Blood samples were centrifuged at 2000×g for 10 minutes and plasma samples stored in liquid nitrogen until the samples were transferred to Khartoum there they were stored in −80°C.
Pharmacokinetic and statistical analysis
The data were analysed using nonlinear mixed-effects modelling as implemented in NONMEM version VI (Icon Development Solutions, Ellicott City, Maryland, USA) . Piperaquine plasma concentrations were transformed into their natural logarithms to increase the stability of the numeric analysis. Models were fitted to the data using the first-order conditional estimation (FOCE) method with interaction [39–41]. Census, version 1.1 , and Xpose, version 4.04 , library for R was used for model diagnostics. Perl-speaks-NONMEM (PsN), version 3.4.2,  was used to automate the modelling process and for model diagnostics.
Model discrimination was based the on the objective function value (OFV) computed by NONMEM as −2×log likelihood . The OFV is approximately χ2 distributed and a decrease in OFV of 3.84 and 6.64 is considered a significant drop with p<0.05 and p<0.01, respectively, when adding one additional parameter (one degree of freedom between two nested models).
Structural models with one-, two-, three- and four- disposition compartments were fitted to the data. Several alternative absorption models were investigated; first-order absorption, first-order absorption with lag time, zero-order absorption, sequential zero- and first-order absorption, sequential zero- and first-order absorption with lag time, parallel first- and zero-order absorption, parallel first-order absorption and transit compartment absorption with a fixed number of 1–10 transit compartments. The full implementation of the transit compartment absorption model, which allows the number of transit compartments to vary between patients, was also evaluated .
It was assumed that drug elimination took place from the central compartment and the base model was parameterized as elimination clearance, central volume of distribution, inter-compartmental clearance(s) and peripheral distribution volume(s). Bioavailability was added to the model and the population value was fixed to 100%.
The distribution of the individual parameters was assumed to be log-normal and between-subject variability (BSV) was investigated on all parameters as an exponential random effect [Equation 1].
is the individual estimate for a model parameter (e.g. individual drug clearance) in the i
is the population mean of parameter P
is individual i
deviation from the population mean. BSV is estimated from a normal distribution with variance ω2
and zero mean. Between dose occasion variability (BOV) was evaluated on absorption parameters [Equation 2].
Where Pij is the individual parameter estimate for the ith patient on the jth dose occasion, κ is the deviation from the population mean after each dose occasion, taken from a normal distribution with variance Π2 and zero mean. An additive residual error model was assumed since data were transformed into their natural logarithms (i.e. essentially equivalent to an exponential error model on an arithmetic scale). Body weight was tried in the model as a simultaneous incorporation of an allometric function on all clearance (power of 0.75) and volume parameters (power of 1), considering the strong biological prior of this covariate relationship [47–49].
Basic goodness-of-fit plots and simulation-based diagnostics were used to evaluate the final model. Visual and numerical predictive checks  were performed using 2000 simulations at each concentration-time point with binning based on protocol times. The 5th, 50th and 95th percentile of observed data were plotted over the simulated 95% confidence interval of the same percentiles to evaluate the models predictive performance. Bootstrap diagnostics were performed using 1000 re-sampled datasets, stratified on pregnancy.
A Monte Carlo Mapped Power analysis (MCMP)  was conducted based on results from a previously published population analysis . The current study design in terms of sampling times and doses were used to create a modelled data set with 408 pregnant and 408 non-pregnant patients. This data set and the published population pharmacokinetic model was used to estimate the minimum number of individuals needed in each group (i.e. pregnant and non-pregnant) to identify the described covariate relationships (i.e. a 45.0% increase in elimination clearance or a 46.8% increase in bioavailability) at a given power (80%) and significance level (p=0.05). Full power curves were produced by plotting number of patients needed against the power to detect the assumed covariate relationship.
Pregnancy was investigated in the final pharmacokinetic model utilizing a full covariate approach where pregnancy was included as a categorical covariate on all pharmacokinetic parameters. Estimated gestational age (EGA) was evaluated as a continuous covariate on individual parameters using a linear and a power function, and the most appropriate covariate relationship (lowest OFV) was incorporated into a full covariate model for EGA. These two full covariate models were bootstrapped (n=200) to investigate the impact of pregnancy. A pregnancy related change in the parameter estimate of more than 20% was deemed to have clinical relevance.