Background
Despite substantial progress in the last decade, malaria remains a major global health problem [
1]. In 2009 there were an estimated 225 million cases and 781,000 malaria-related deaths [
2]. Artemisinin-based combination therapy (ACT) is recommended as first-line treatment for uncomplicated
falciparum malaria [
3]. The primary antiparasitic agent in ACT is the artemisinin derivative, which is quickly absorbed by and eliminated from the body, and destroys the majority of detectable parasites within the first 3 days of treatment. The partner drug(s) co-administered with the artemisinin derivative is less effective but slowly eliminated, and thus provides residual antiparasitic activity in the patient. Additionally, the partner drug offers protection to the artemsinin derivative from rare mutant parasites that have developed resistance [
3].
Though the artemisinin derivitives are generally effective, it has been observed in Cambodia that the effectiveness of the main artemisinin derivative, artesunate, has been diminished due to parasite resistance [
4]. These findings highlight the necessity and importance of the partner drugs in ACT, and provide impetus for gaining more knowledge of their pharmacokinetic (PK) properties. This knowledge can ultimately be used to optimize dosing regimens, particuarly for high risk groups such as pregnant women and children.
The PK properties of a drug can be characterized for intended target populations via population PK studies. For anti-malarial drugs, these studies need to be large enough and designed in order to be representative for the target population(s) so that the expected concentration-time profile and between-subject variability parameters can be characterized adequately [
5]. From a modelling perspective, it would be ideal to propose study designs with intensive blood sampling, but often this is not realistic for patients presenting with
falciparum malaria. Intensive sampling over the entire follow-up period is logistically difficult, especially in rural settings where outpatients attend few follow-up visits [
5]. However, population PK modelling allows information to be “borrowed” across individuals to obtain parameter estimates [
6,
7]; therefore it is reasonable to propose study designs with fewer samples per patient but a sufficiently large number of patients. The key aspect of such a design lies with the timing of blood samples, since the times at which the samples are taken must provide sufficient information for precise estimation of model parameters.
Optimal design methodology has been developed for designing population PK studies [
8]; the method analytically determines a blood sampling schedule that provides precise estimates of the model parameters. Importantly, the methodology allows economical use of resources [
6], for which in the case of the partner drugs is fewer samples per patient but with more patients enrolled. The overall aim of this work was to determine optimal blood sampling schedules that can be used to study the partner drugs of the most widely used ACT that are economical, efficient, and appropriate for all target populations.
Discussion
This study proposes optimal designs that can be used prospectively to study the population pharmacokinetics of the partner drugs used with the most widely used ACT. The designs were based on models from the literature and the key specifications of 100 patients with five samples per person. The sampling schedules for each drug are applicable to the target populations of non-pregnant adults, pregnant women and children. Sampling windows were derived for each optimal sampling time, which provide flexibility for taking samples in the field and capture standard days of follow-up for clinical studies (days 1, 2, 3, 7, 14, 21, 28, 35, 42, 49, 56 and 63).
The design for mefloquine was based primarily on one-compartment models, which in general displayed acceptable expected and empirical precision for all target populations. The only exception was the BSV of
CL/
F for children in Additional file
1: Table S3, but this result was due to the conservative approach to evaluating the designs. The designs were derived in POPT assuming 100 patients, which means that the expected %RSEs were calculated assuming 100 patients for any given competing model. However, the simulation-estimation procedure was performed on only 33 or 34 patients. To ensure the design provided adequate information for children receiving two doses of mefloquine, the simulation-estimation procedure was performed again with 50 simulated children and resulted in acceptable empirical %RSEs for all parameters. Empirical precision was not ideal for all parameters of the two-compartment model for non-pregnant adults, but again, this was due to the conservative evaluation procedure. The simulation-estimation procedure was performed again with 65 simulated adult patients and resulted in acceptable empirical %RSEs for all parameters. Therefore the proposed design should be sufficient for estimating a two-compartment model for non-pregnant adults, and as more studies are conducted the designs can be updated to provide more information for estimating two-compartment models in all populations.
The lumefantine design resulted in precise estimation of the two-compartment model parameters for pregnant women. The design yielded acceptable precision for the estimable parameters for the non-pregnant adults, but was not optimized for
k
a
or the BSVs of
k
a
or
V
p
/
F for this group due to a structural identifiability problem with the model reported in [
15]. This issue was explored in POPT by increasing the number of samples to eight per patient, but still resulted in unacceptably high expected %RSEs for these parameters. This model was entered into POPT since it was the only published model for non-pregnant adults, however it is likely that other two-compartment profiles exist for this group. Therefore, it is recommended to vary sampling within the windows for non-pregnant adults to investigate other plausible parameter values. For the children, the design provided adequate information for most of the one-compartment model parameters reported in [
17], however, the reported model was estimated from concentrations that were taken only up to 72 h, which is well before the distribution phase is complete (approximately 14 days). Thus there may be other plausible structural PK models for children (e.g. a two-compartment model, which is quite likely given the adult profiles), and it is, therefore, recommended to vary sampling within the windows to provide means for exploring alternative structural models for this group. As more population PK studies of lumefantrine are performed, this design will be updated to account for other reported models in all study populations, particularly those in children and non-pregnant adults.
The piperaquine design was based on two-compartment models and exhibited acceptable expected precision of all estimable parameters for all study populations. For the non-pregnant adults, the empirical %RSEs for
k
a
and the BSVs of
CL/
F Q/F and
V
p
/F were slightly greater than the target values, but as with the mefloquine design this was due to the conservative approach to evaluation. The simulation-estimation procedure was repeated for this group with 50 patients per simulated dataset and resulted in acceptable %RSEs for all parameters. The two-compartment models fitted to data simulated from models reported in [
27] for pregnant and non-pregnant women yielded acceptable empirical precision for all parameters. The simulation models used for these evaluations provided a detailed description of the PK for these groups (three compartment models with n-transit absorption), and under the proposed design allowed the two-compartment models to be fitted with a lag-time (fixed) as well as covariances on the BSVs (
CL/
F V
c
/
F Q/
F and
V
p
/
F). This empirical result provides evidence that the proposed sampling schedules should be sufficient for estimating two-compartment models in these patient groups. The design was not optimized for the BSVs of
V
c
/
F Q/
F and
V
p
/
F reported in [
18] for children since POPT gave unacceptably high expected %RSEs. However, these parameters were reported to have additive between-subject variability, thus these BSVs were declared as additive in POPT. Though it is possible that the between-subject variability for these parameters is truly additive, it is biologically plausible and thus common practice to assume exponential between-subject variability for all PK parameters. Consequently, the simulation-estimation procedure for children was performed assuming exponential between-subject variability, and resulted in acceptable empirical precision for all parameters except the BSV of
V
c
/
F. Again, this result was due to the conservative approach to evaluating the designs, and when repeated with 50 patients per simulated dataset all parameters displayed acceptable %RSEs. The two-compartment model fitted to the simulated paediatric data from [
26] yielded acceptable empirical precision for all parameters. As with the adults, the simulation model used for this evaluation provided a detailed description of the PK for this group, and under the proposed design allowed estimation of covariances between the BSV parameters. Therefore the proposed optimal design should provide reasonable means for estimating two-compartment models in all patient populations, and it is recommended to vary sampling within the windows to gain more knowledge of their PK profiles.
The design for desethylamodiaquine resulted in acceptable expected and empirical precision for children and adults. However, it is important to note that the model reported for adults was estimated from pregnant and post-partum women with
Plasmodium vivax malaria. Therefore, it is possible that adult patients with
Plasmodium falciparum malaria may display different PK profiles than those simulated, and men may display different profiles than non-pregnant women. Furthermore, Stepniewska
et al.[
21] only reported a BSV for
CL/
F, but BSVs for the other PK parameters may well exist in children. Thus the proposed sampling schedule should be considered a truly “initial” optimal design, and it is, therefore, recommended to vary sampling within the windows to provide flexibility for the exploration of alternative values for the PK and BSV parameters in all patients with uncomplicated
falciparum malaria. Furthermore, taking additional samples, if possible, may aid this exploration. As more studies of amodiaquine and desethylamodiaquine are performed, the sampling schedules proposed in this paper will be revised to provide designs that take into account newly reported values of PK, BSV and residual error parameters.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
JAS and KMJ conceived the project. KMJ, JAS and SBD implemented the designs in POPT. KMJ wrote the first draft of the manuscript. JAS, SBD, JT, NL, and NJW revised the manuscript critically for important intellectual content. All authors read and approved the final manuscript.