Research ArticleMalaria

Characterization of an in vivo concentration-effect relationship for piperaquine in malaria chemoprevention

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Science Translational Medicine  29 Oct 2014:
Vol. 6, Issue 260, pp. 260ra147
DOI: 10.1126/scitranslmed.3005311

Abstract

A randomized, placebo-controlled trial conducted on the northwest border of Thailand compared malaria chemoprevention with monthly or bimonthly standard 3-day treatment regimens of dihydroartemisinin-piperaquine. Healthy adult male subjects (N = 1000) were followed weekly during 9 months of treatment. Using nonlinear mixed-effects modeling, the concentration-effect relationship for the malaria-preventive effect of piperaquine was best characterized with a sigmoidal Emax relationship, where plasma concentrations of 6.7 ng/ml [relative standard error (RSE), 23%] and 20 ng/ml were found to reduce the hazard of acquiring a malaria infection by 50% [that is, median inhibitory concentration (IC50)] and 95% (IC95), respectively. Simulations of monthly dosing, based on the final model and published pharmacokinetic data, suggested that the incidence of malaria infections over 1 year could be reduced by 70% with a recently suggested dosing regimen compared to the current manufacturer’s recommendations for small children (8 to 12 kg). This model provides a rational framework for piperaquine dose optimization in different patient groups.

INTRODUCTION

Intermittent preventive therapy (IPT) is a pharmacological intervention aimed at treating and preventing malaria infections, primarily in vulnerable populations such as in infants, children, and pregnant women (1, 2). To prevent malaria effectively, IPT treatment must first eliminate any parasites in the host (presumptive treatment) and then provide sufficiently high circulating drug concentrations to prevent parasite growth to patent densities following new infections [posttreatment prophylactic (PTP) effect] until the next dose is given or risk declines. Given in this way, IPT provides continuous chemoprophylaxis and so has been termed “chemoprevention.” The efficacy of a drug used in IPT will depend on (i) the sensitivity of the prevalent parasites to the drug, (ii) the dosing regimen, and (iii) the pharmacokinetic (PK) properties of the drug. The antimalarial drug traditionally used in IPT treatment, primarily the combination therapy sulphadoxine-pyrimethamine, has become less effective because of emerging drug resistance (24). Piperaquine (PQ) has recently been suggested as an alternative long-acting antimalarial in IPT treatment. PQ has a long terminal elimination half-life (about 30 days), and it is used currently in a fixed-dose combination with dihydroartemisinin (DHA) (5). This combination has demonstrated excellent efficacy and tolerability, with a PTP effect against both Plasmodium falciparum and Plasmodium vivax that is typically sustained for more than 1 month (68). A recent randomized, placebo-controlled trial conducted on the northwest border of Thailand compared prophylactic monthly versus bimonthly (that is, every other month) treatment with a standard 3-day treatment regimen of DHA-PQ (9). In that study, a total of 1000 healthy adult male subjects were followed weekly for 9 months of treatment. The monthly DHA-PQ regimen was superior to both the placebo and the bimonthly regimen and proved to be safe and effective in preventing malaria infections in the studied population (9). By applying a pharmacometric modeling approach (10, 11) to the outcome of this study, it was hypothesized that a concentration-effect relationship could be established and used for translational simulations of dosing in vulnerable populations and in areas with PQ resistance.

RESULTS

Model building

Pharmacokinetics. Final PQ PK parameter estimates are presented in Table 1 and visual predictive checks (VPCs) for the monthly and bimonthly dosing groups are presented separately in Fig. 1. Parameter estimates were based on a three-compartment disposition model and a five-compartment transit absorption model. A frequentist prior based on a previous study (12) was applied to all parameter estimates to support the model structure. This approach allowed previous information on the PK of PQ to support aspects that could not be characterized by the study data alone. Parameter estimates for apparent oral clearance (CL/F), central distribution volume (VC/F), intercompartment clearance between central compartment and the shallow peripheral compartment (Q1/F), shallow peripheral distribution volume (VP1/F), and intercompartment clearance between central compartment and the deep peripheral compartment (Q2/F) were all estimated to be lower than the previous estimates (−20, −10, −30, −15, and −18%, respectively). The deep peripheral distribution volume (VP2/F) and the mean absorption transit time (MTT) were virtually unchanged compared to the applied prior. Between-subject variability (BSV) was in line with the applied previous model estimated for CL/F, VC/F, and Q2/F. Between-occasion variability (BOV) in MTT and relative bioavailability (Frel) were estimated assuming separate occasions for each dosing period. Only small deviations were seen between the estimates and the applied prior on the magnitude of BSV and BOV except for BOV in Frel that was decreased from 52 to 39%. The potential effect of concomitant intake of chocolate milk on the Frel of PQ was investigated but not found to be significant.

Table 1. Typical model parameter estimates, BSV, BOV, and associated RSEs.
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Fig. 1. VPC for PQ plasma concentration.

Observed plasma concentrations (open circles), observed median (solid black line), predicted nonparametric 95% confidence intervals for the median (dark-gray field), and observed 90% prediction intervals (dashed black lines) and corresponding predicted nonparametric 95% confidence intervals (light-gray field).

Simulation-based diagnostics in the form of VPCs (Fig. 1) demonstrated a good agreement between observations and model simulations with respect to both the central trend (median) and the BSV (for example, 5th and 95th percentiles in VPC). Overall, 4.8% of the observations were below the model-predicted 5th percentile and 5.2% above the 95th percentile for the monthly dosing; corresponding figures for bimonthly dosing were 5.9 and 4.8%, respectively.

Pharmacodynamics and concentration-effect relationship. One statistically significant seasonal peak (P < 0.01) was identified in the baseline model for the untreated hazard of having a malaria infection. The estimated seasonal peak stretched from the end of April until the beginning of August [see estimates of center of seasonal peak (PT) and duration of seasonal peak (WD) in Table 1] and correlated well with the early rainy season in the region. During this period (season), the hazard of experiencing a malaria infection was increased by 220% [relative standard error (RSE), 30%]. A potential second seasonal peak was hypothesized but did not meet the statistical significance criteria and was therefore not included in the model. The hypothesis of a second seasonal peak was also reassessed with the final model in application to all data but did not meet the statistical significance criteria at this point either.

Comparison of observed and simulated survival curves (Kaplan-Meier curves) suggested that the applied constant hazard model underpredicted the number of events in the initial study period and overpredicted the same during the late study period. This could be explained if the hazard for some reason decreased with time in the study. However, a more plausible explanation is that there was significant BSV in the baseline hazard. Subjects with a high baseline hazard will likely have events early, and the average baseline hazard of the subjects remaining in the study will therefore increase over time. The variability in baseline hazard was found to be described satisfactorily with the assumption of two subpopulations (mixtures). A binomial distribution showed no additional benefit to this simpler bimodal distribution described above. The typical probability of belonging to a low-hazard population was estimated to be 70% (RSE, 20%), and the low-hazard population was estimated to have a 93% lower hazard [0.24 infections per year (RSE, 2%)] compared to the high-hazard population [3.8 infections per year (RSE, 42%)]. A structured covariate model search identified subject age as a significant covariate on the probability of belonging to the low/high-hazard population. Age was normalized to the study median of 32 years, and the best model fit was seen with age as a log-linear additive function on the logit-transformed mixture probability (see Eqs. 6 and 7). The covariate relationship indicated a probability of belonging to the low-hazard population of 50% for a 19-year-old subject and 85% for a 55-year-old subject, respectively (see illustration in fig. S1). No other significant covariate relationships were established in the baseline model on top of the seasonal variation and age.

The inclusion of separate hazards for placebo and monthly and bimonthly dosing was statistically significant (P < 0.001). However, inclusion of a single continuous concentration-effect relationship with a single estimated parameter, median inhibitory concentration (IC50) (Eq. 8, with θγ = 1), outperformed the separate hazards model with two parameters (ΔOFV = −25). The model fit was improved further (P < 0.001) by assuming a sigmoidal concentration-effect relationship (that is, estimated Hill factor). In this nonfinal model, the plasma PQ IC50 was estimated to be 6.3 ng/ml (RSE, 12%), and the Hill factor was estimated to be 3.6 (RSE, 15%). This model demonstrated a good predictive performance across all treatment arms in application of internal validation (Kaplan-Meier plot VPC).

An important issue was identified with a model that relates directly the PQ plasma concentration to the hazard of being diagnosed with malaria. Basic knowledge about the biology of malaria infections indicates that there is no instantaneous relationship between drug plasma concentration and the hazard of being diagnosed with malaria. The crucial time point in the malaria-preventive action of PQ is likely to be when blood stage parasites first emerge from the liver (preerythrocytic schizogony). If the drug concentration at this time is sufficient to suppress parasite growth, and it does not decline rapidly (which PQ does not) thereafter, then no malaria infection will be diagnosed. The lag time between this crucial time point of drug action and diagnosis was taken into account by approximating an event censoring interval based on the parasite count at the time of malaria diagnosis in those who did have breakthrough infections. The interval was based on assumptions of a slow or fast parasite growth rate in combination with a low or high number of parasites at the start of the parasite blood stage (see Materials and Methods and illustration in fig. S2). The model-building procedure was repeated with this interval censoring. This resulted in the same model structure as previously, but with slightly altered parameter estimates. The primary differences were that IC50 increased from 6.3 to 6.7 ng/ml, and the Hill factor decreased from 3.6 to 2.8. This model demonstrated a good predictive performance (Fig. 2) and was regarded as the final model.

Fig. 2. VPC for Kaplan-Meier incidence curves (percentage of the target population remaining malaria-free).

Solid lines represent observed Kaplan-Meier curves; red, placebo; blue, bimonthly dosing; and green, monthly dosing. Shaded areas represent corresponding 90% prediction intervals derived from model simulations.

An attempt to differentiate between P. vivax and P. falciparum infections could not identify any statistically significant differences with regard to either baseline hazard or PQ sensitivity (IC50). However, there was a trend toward a higher baseline hazard and a lower IC50 for P. vivax.

Translational simulations

Pediatric population. Simulations were carried out to compare three different dosing strategies for a pediatric population (see Table 1). The simulations were done with the baseline hazard and concentration-effect relationship according to the final model and pharmacokinetics according to a recent publication (13). Figure 3 illustrates the predicted 1-year incidence curves for a pediatric population of 8 to 34 kg, given the three different dosing strategies. The predicted 1-year incidence (1 − survival) was reduced by about 50% for the recently suggested increased dose regimen (13) compared to the regimens formerly recommended by the World Health Organization (WHO) and the manufacturer Sigma-Tau. The increased dose regimen demonstrated an equal performance across all weight groups, but the other dose regimens performed significantly worse for a low-weight subgroup of 8 to 12 kg. In this subgroup, the 1-year incidence was reduced by about 70% with the increased dosing regimen compared to the Sigma-Tau regimen (2.1% versus 6.6%).

Fig. 3. Simulated incidence curves for 1-year prophylactic treatment with monthly dosing, given three different dosing strategies, in a pediatric population.

The solid lines represent the expected incidence in a pediatric population ranging from 8 to 34 kg with the Sigma-Tau recommended dosing (red), the former WHO recommended dosing (blue), and the dosing recommendations according to Tarning et al. (13) (black). The corresponding dashed lines represent a low-weight group of 8 to 12 kg.

Pregnant population. The predicted difference between pregnant and nonpregnant women was relatively small (8% versus 7% yearly incidence). The yearly incidence for both groups was however predicted to be significantly higher than in the corresponding healthy male study population (3%). This is due to a generally higher clearance reported in the women with malaria. This is thought to be primarily a difference between healthy subjects and malaria-infected subjects and is elaborated on further in the discussion.

PQ resistance. The possible consequences of emerging resistance to PQ on preventive treatment outcome were investigated with simulations based on the final model. The simulated median incidence over 1 year given different assumed IC50 values is presented in Fig. 4.

Fig. 4. Simulated incidence curves for 1-year prophylactic treatment with monthly dosing under the assumption of altered IC50 values (that is, PQ-resistant parasites).

The black line represents the observed IC50 value (7 ng/ml); the gray line represents the placebo response; and the red, green, blue, and yellow lines represent a 2-, 4-, 10-, and 100-fold increased IC50 value, respectively.

Day 7 target concentration. In clinical studies, the plasma concentration of PQ is often measured 1 week (day 7) after the start of treatment. Simulations were carried out to compare the association between plasma concentrations measured on days 7, 14, and 30 and clinical efficacy in terms of 1-month survival in June (that is, peak malaria transmission season). Survival refers to the probability of remaining malaria-free during 1 month of such high malaria transmission. The results of these simulations are presented in Fig. 5 and show that a closer correlation to clinical efficacy can be expected for day 14 rather than day 7 concentrations. Day 7 plasma concentrations of 50 ng/ml indicate a median expected 1-month parasite-free prevalence of 99% with a 95% confidence interval between 94 and 100%. Day 14 and day 30 plasma concentrations of 30 and 20 ng/ml, respectively, resulted in a similar median expected parasite-free prevalence of 99% but were associated with a narrower confidence interval from 97 to 100% parasite-free prevalence.

Fig. 5. Simulations of relationship between observed venous PQ plasma concentration (ng/ml) at day 7 (A), day 14 (B), and day 31 (C) after the start of treatment and expected 1-month parasite-free prevalence (%).

The circles represent simulated individuals, the solid black line represents the median, and the dashed lines represent a 90% prediction interval. The dotted vertical lines indicate the concentration that results in 99% median survival [50 ng/ml (A), 30 ng/ml (B), and 20 ng/ml (C)].

DISCUSSION

The applied PK model described the observed PQ plasma concentrations after both monthly and bimonthly dosing (Fig. 1). The estimated apparent oral clearance (CL/F) was 20% lower than the previous estimate from a female population diagnosed with malaria (12). Also, intercompartmental clearances (Q1/F and Q2/F) and distribution volumes (VC/F and VP1/F) were estimated to be between 10 and 30% lower than the previous estimates. These differences are not thought to be gender-related differences but because of the lower oral bioavailability in malaria-infected subjects. This is in line with previous reports of increasing oral bioavailability as patients recover from their disease (12) as well as the generally lower CL/F and V/F reported in healthy volunteer studies (14, 15) compared to patient studies (16, 17).

The identified seasonal peak in malaria transmission, ranging from the end of April until the beginning of August, is in good agreement with that previously described for this region (18). The estimated 220% increase in hazard is also in line with the previously reported 175% higher incidence during peak season. A second high-transmission season, typically around January, has also been reported, and a corresponding weak trend toward increased hazard during December was seen in this study. However, this was not statistically significant and hence not included in the final model.

It is easy to imagine that the hazard of having a malaria infection varies between subjects in a given population. The difference in baseline hazard can result from not only differences in exposure to malaria-infected mosquito bites but also differences in levels of acquired immunity (which in turn reflect cumulative previous parasite exposure). Indeed, the baseline hazard was characterized as bimodal in the investigated population. However, it is likely that the distribution in reality is more continuous, but this could not be described sufficiently with the collected data. Age was identified as a covariate for the probability of belonging to the high-hazard population (fig. S1), indicating a generally higher hazard for younger subjects. This is likely to be a consequence of working conditions and behavior resulting in higher exposure to mosquito bites, less acquired immunity, or a combination of both of these factors.

The PQ plasma concentration effect on reducing the hazard of having a malaria infection was strong. It had a vastly superior explanatory power over a categorical treatment effect separating the treatment arms by monthly, bimonthly, and placebo treatment. To understand the pharmacokinetics of PQ, it is therefore important to understand what effect to anticipate in a given population. The steep nature of the concentration-response relationship is a consequence of the estimated Hill factor (2.8) and will result in large differences in risk with relatively small differences in plasma concentration. A 95% risk reduction is achieved with a PQ plasma concentration of 20 ng/ml, whereas a 50% risk reduction is achieved with a concentration of 6.7 ng/ml.

The approach of applying an interval to the time of treatment failure was designed to include more of the pathophysiology in the model and hence obtain parameter estimates that would have a more mechanistic relevance. The differences in parameter estimates compared to a model without this consideration were relatively small. This can be explained by the long half-life of PQ. If the same approach is applied for another drug with a shorter half-life, the consequences are anticipated to be greater. Another factor that could make the delay between treatment failure and detection more influential is if the parasite growth rate is slower than the value assumed in the analysis. This could be the case in endemic areas where naturally acquired partial immunity would explain a slower net parasite growth rate (19).

A recent publication by Tarning et al. (13) raised the concern that current DHA-PQ dose recommendations for small children are too low. Dosing recommendations by the manufacturer Sigma-Tau and formerly by the WHO (see Table 2) were predicted to provide relatively low PQ exposures in children between 8 and 12 kg. However, at the time, it was difficult to assess the clinical relevance of this because no continuous exposure-response relationship was available. The empirical observation by Price et al. (20) that day 7 venous plasma concentrations less than 30 ng/ml were associated with an increased risk of recurrent P. falciparum infection (hazard ratio, 6.6) was used as a clinically relevant reference value. However, being categorical, this 30 ng/ml threshold is not very suitable to use for extrapolations into other populations and/or dosing regimens. By applying the continuous concentration-effect relationship established in the present study, it was possible to predict quantitatively the expected clinical outcomes with different DHA-PQ dosing regimens. The presented predictions were made for a scenario with preventive treatment in an environment similar to the study described (Fig. 3). However, the relative difference between the different treatment regimens is expected to be similar for preventing recurrence after treatment of a malaria infection and/or in another region. The safety and tolerability of the new dosing recommendations need to be confirmed in a trial to generate the last missing supporting evidence for changing the treatment recommendations in the pediatric population.

Table 2. Body weight–based dosing guidelines for DHA-PQ in children were used for simulations of pediatric outcome after 3 days of repeated dosing every month.
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Simulations comparing outcome in a pregnant and nonpregnant population indicated no major impact of pregnancy on the risk of experiencing a malaria infection during IPT. The overall expected incidence of malaria infections was predicted to be higher in the female pregnant/nonpregnant population compared to the population in this study. This is thought to result from lower oral bioavailability in malaria-infected subjects. Hence, again, the actual predicted incidence for the pregnant/nonpregnant population might be slightly overpredicted for a preventive treatment setting, but the relative effect of pregnancy should still be the same. However, pregnancy may reduce the exposure to DHA, which would result in a larger residuum of parasites needing to be killed by PQ. More information is urgently needed in pregnant patients (12, 21).

PQ resistance has been reported to increase the in vitro IC50 value up to 100-fold both when resistance was induced in vitro and observed in the field (22). The simulations presented in Fig. 4 indicate that such resistance would make the treatment completely ineffective. The simulations also show that already a much smaller decrease in sensitivity, such as a doubling of the IC50 (14 ng/ml), would lead to a drastically decreased utility in chemoprevention. The coadministered DHA is therefore important in protecting against the development of PQ resistance when the combination is used for prophylactic purposes.

Especially in clinical studies, the plasma concentration of PQ is often measured 1 week (day 7) after start of treatment. This concentration has been used to link PQ exposure to clinical efficacy. One study has concluded that patients with day 7 PQ concentrations less than 30 ng/ml were more likely to have a recurrence of P. falciparum (hazard ratio, 6.6) (16). Simulations based on the final model presented in this paper (Fig. 5) suggest that a closer relationship could be expected if day 14 or day 30 concentrations were used. If observed concentrations at day 7, 14, or 30 are to be used to guide whether the PQ exposure is sufficient, the limits of 50, 30, and 20 ng/ml may be used. These concentrations correspond to a 96% risk reduction compared to placebo under the investigated conditions (in a high-transmission season). These limits are primarily intended for the use of DHA-PQ in preventive treatment, but there is little reason to believe that they would not also be applicable when the combination is used in treatment of a malaria infection. This is based on the reasoning that the relatively low number of parasites left to be suppressed by PQ after the initial potent DHA effect is similar to the number of parasites present at the start of the parasite blood stage in a newly acquired infection.

In conclusion, an in vivo concentration-effect relationship for the malaria-preventive effect of PQ has been established. The established model was useful in translating observed results from a healthy male population to that expected in other populations and under other circumstances.

MATERIALS AND METHODS

Study population and study design

A clinical trial including a total of 1000 healthy adult males whose occupation puts them at high risk of malaria was conducted in northwestern Thailand on the border to Myanmar (9). All volunteers were more than 18 years of age and had neither malaria nor malaria treatment during 6 months before study entry. The study compared outcomes after a prophylactic monthly treatment regimen of DHA-PQ (387 subjects) to that of a bimonthly regimen (383 subjects) and a matched placebo treatment (199 subjects). DHA-PQ was dosed according to a standard adult dose of 120 mg of DHA and 960 mg of PQ phosphate (three tablets) once daily for 3 days. This yielded an average DHA dose of 2.3 mg/kg (range, 1.5 to 3.0) and an average PQ phosphate dose of 18.1 mg/kg (range, 12.2 to 24.0 mg/kg). All dosing was observed by study staff. Study subjects were randomized to the three treatment arms and split between dosing with and without 200 ml of chocolate milk. Double-blind conduct of the trial was ensured by identical placebo matching with the monthly treatment. Volunteers were followed up monthly at the clinic, and trained workers visited each volunteer at home weekly. Blood smears, hematocrit samples, and PQ plasma concentrations were obtained at each visit. Study subjects presenting with microscopically confirmed malaria had an additional venous blood sample taken for plasma PQ concentrations. Translated written study information was provided in the languages of the participants, and informed consent was signed by each volunteer. Ethical approval for the study was obtained from the Ethics Review Board of the Faculty of Tropical Medicine, Mahidol University, Bangkok, and the Oxford Tropical Research Ethics Committee, Oxford University. This study was registered in the International Standard Randomised Controlled Trial Number (ISRCTN) Register under controlled trial no. ISRCTN65524939.

Descriptive statistics for study population baseline characteristics are presented in table S1, and more details on the study design and descriptive statistics of the study outcome have been presented in full elsewhere (9).

Model building

Software. Data analysis was performed with a nonlinear mixed-effects approach as implemented in the NONMEM software version 7.2.0 (23) and run on a Linux cluster with a Red Hat 9 operating system using openMosix and a g77 Fortran compiler. Laplace estimation method with η-ε interaction and the ADVAN13 (general nonlinear kinetics) subroutine were applied for parameter estimation. SEs for parameter estimates (covariance variance matrix) were obtained with importance sampling. NONMEM output files for the final PK and PK–PD (pharmacodynamic) models are provided in Supplementary text files. The PsN toolkit version 3.5.5 (24, 25) was used in conjunction with NONMEM for automation and postprocessing purposes. The Xpose 4.3.5 (25, 26) package in R (27) was used for graphical diagnostics. Simulations with the final model were carried out with the software Berkeley Madonna (28).

Pharmacokinetics. Plasma PQ concentrations were sampled monthly throughout the study and quantified using solid-phase extraction followed by liquid chromatography with detection by tandem mass spectrometry according to a published method (9, 29). The limit of quantification (LOQ) was set to 1.5 ng/ml.

Because of the sparse sampling of PQ plasma concentrations, an informative prior was applied to support the estimation of PK parameters. A recent rich-sampling PK study in pregnant and nonpregnant women conducted at the same location concluded that a three-compartment disposition model and a five-compartment transit absorption model described the pharmacokinetics of PQ well (12). The model structure, parameter estimates, and associated precisions for the nonpregnant group were applied as a frequentist prior (30) for the PK analysis. The number of observations below LOQ was very few (<1%), and these were therefore omitted during parameter estimation. The model structure and the final parameter estimates were evaluated with standard model diagnostics including VPCs (31).

Pharmacodynamics and concentration-effect relationship. A time-to-event (TTE) modeling approach was applied to describe the occurrence of malaria infections over time. At first, the placebo cohort of the study was analyzed separately to characterize the natural time course without influence of DHA-PQ treatment. When a satisfactory baseline (placebo) model was established, the treatment cohorts were included, and models for relating PQ exposure to a malaria-preventive effect were explored. Estimation of the exposure response parameters was conducted with individual PK parameters set to previous final estimates.

A TTE model with an estimated constant baseline hazard (θBHz) was applied initially (Eq. 1) to describe the time to malaria infection in the placebo subgroup. The survival, S(t), is here a function of the cumulative hazard and describes the probability of not having an event (malaria infection) until time t (Eq. 2). The probability density function for having an event at a specific time point, P(t), is given by multiplying the survival and hazard in that particular moment (Eq. 3).

Embedded Image(1)Embedded Image(2)Embedded Image(3)

It is well known that malaria transmission in northwestern Thailand is seasonal and that one and sometimes two seasonal peaks occur each year. To characterize these seasonal variations, one or two surge functions [Season(t)] with the base equal to 1 and estimated amplitude (θAMP), point of inflection (θPT), and duration (θWD) were multiplied to the constant baseline hazard (Eq. 5).

The steepness/shape factor (shp) of this function was set to a fix value of 4 because estimation was found to cause unstable performance of the minimization algorithm. Inclusion of a seasonal function was conditioned on a decrease in objective function value (OFV) by more than 7.81 (χ2 distribution and 3 df).

Embedded Image(4)Embedded Image(5)

Visual diagnostics showed that the predicted survival curve (Kaplan-Meier) was not in good agreement with the observed survival curve under the assumptions of the applied constant hazard model. The observed survival curve had a steeper initial slope than the predicted. This could be explained by a gradually decreasing hazard, but this explanation was rejected in favor of an alternative hypothesis that was judged to be more plausible given the very uneven transmission intensities and the location, work, and behavior of the subjects in the study. The alternative hypothesis featured two subpopulations, one with a higher baseline hazard than the other (32). The individual probability of belonging to either the high- or low-hazard mixture was estimated using a logit transformation to allow for testing covariates on the probability of belonging to either mixture (Eq. 7).

A stepwise forward inclusion (P < 0.05) and backward exclusion (P < 0.01) covariate search (33) was carried out to investigate the potential impact of covariates on baseline hazard (Eq. 1) and the mixture probability (Eq. 7). The investigated covariates were subject age, subject weight, previous malaria history (yes/no), enrolment status (resident/worker/visitor), study site, and study year. Covariates were investigated using linear, exponential, or power relationships to the baseline hazard. For the mixture probability, covariates were investigated using additive linear or log-linear relationships on the logit scale (exemplified for Age in Eqs. 6 and 7).Embedded Image(6)Embedded Image(7)where θAGE-PMIX is the estimated parameter that governs the relationship between age (years) and the probability of belonging to the low-hazard population (MIXi = 2), with the relationship parameterized as age over the median age of 32 years. The estimate of θPMIX2 is the population typical (median) probability of belonging to mixture 2 (low-hazard population).

After the covariate model search, the baseline model was considered established, and the model was applied to data from all treatment arms simultaneously. The PQ malaria chemopreventive effect was explored initially with a categorical treatment effect [that is, relative baseline hazard (θBHz) for any PQ treatment or separate relative baseline hazard for monthly and bimonthly treatments compared to placebo]. The categorical effect parameterization was compared to a continuous concentration-effect relationship, where the individually predicted PQ plasma concentrations modulated the hazard of acquiring a malaria infection. The PQ plasma concentration was related to the hazard via an inhibitory Emax relationship (Eqs. 8 and 9).Embedded Image(8)Embedded Image(9)where Def(t) is the relative effect of PQ plasma concentration [C(t)] acting on the hazard of having a malaria infection at time t. The estimated parameter Embedded Image corresponds to the PQ plasma concentration that results in a 50% decrease in baseline malaria infection hazard. An additional complexity to the inhibitory Emax model was investigated by estimating the parameter θγ, which governs the steepness (sigmoidicity) of the exposure-response relationship. Both the seasonal variation function [Season(t)] and the drug effect function [Def(t)] were assumed to have the same relative effect on baseline hazard in mixtures 1 and 2 (Embedded Image and Embedded Image).

With this exposure-response relationship, the maximum effect of infinite concentrations of PQ was assumed to be complete inhibition of the hazard (that is, no possibility of malaria infection). This assumption was justified by the fact that resistant parasites have been described only to have a decreased sensitivity and not to be completely insensitive to PQ and furthermore that such resistant parasites were not prevalent at the time of the study.

For a blood stage–suppressive antimalarial, the drug needs to be effective at the start of the parasite blood stage just after emergence from the liver (2). If the drug concentrations are sufficiently above the minimum inhibitory concentration at this point and remain above it, there will be no parasite multiplication that can result in malaria illness. If the drug concentrations are insufficient, parasite multiplication will occur, and parasitemia may reach pyrogenic densities, although there will be a considerable lag time before the subject is diagnosed with malaria. Not accounting for this lag time was judged likely to harm the mechanistic interpretation of the estimated concentration-effect parameters and limit the possibility for accurate extrapolations. The lag time between the start of the parasite blood stage and the time of diagnosis was approximated on the basis of the observed parasite count (PARobserved) at the time of diagnosis. Instead of making a single approximation of the lag time, an interval was constructed from the earliest plausible time to the last plausible time of the start of the parasite blood stage infection. This was done to account for the uncertainty both with regard to number of parasites at the start of the blood stage and their growth rates (34, 35). The growth rate is particularly uncertain because the PQ concentrations might not completely inhibit parasite growth but slow it down. The start of the interval (Eq. 10) was approximated on the basis of an initial low total number of parasites (104) and a slow growth rate (5-fold increase every 48 hours, Kslow growth = 0.8 day−1), whereas the end of the interval (Eq. 11) was based on a relatively high number of parasites (105) and a fast growth rate (10-fold increase every 48 hours, Kfast growth = 1.15 day−1). The interval censoring with regard to the time of the event was handled with conventional methodology, treating the start of the interval as a censoring event with the probability equal to the survival at that time (Eq. 2) and the probability for the event having taken place at the end of the interval [Pinterval (a,b)] equal to 1 minus the probability of survival during the interval (Eq. 12).

Embedded Image(10)Embedded Image(11)Embedded Image(12)

An attempt was also made to differentiate between P. vivax and P. falciparum infections (two cases of Plasmodium ovale were treated as similar to P. falciparum). This was done to test the hypothesis that the two species could have different sensitivities to PQ. The model was extended to separate the probability of having a P. vivax infection, a P. falciparum infection, or a simultaneous infection of both species (two observed cases). The model was constructed so that the observation of a P. vivax event was also the time of censoring for any P. falciparum event. From the raw data, it could be seen that the two species had a similar seasonal peak, and for this reason, the model for seasonal variation was not reassessed. The statistical significance of assuming different baseline hazard (θBHz) and/or PQ sensitivity (Embedded Image) for the two species was assessed with a likelihood ratio test.

Translational simulations

The established PD model and exposure-response relationship were used for translational simulations into different settings (see below headings). Unless stated otherwise, simulations were performed according to the final model and standard monthly dosing with a 3-day regimen. The dosing was assumed to start on 1 January in all individuals, and subjects were followed up for 1 year or until their first malaria infection.

Pediatric population. A recent publication described the pharmacokinetics of PQ in children with uncomplicated P. falciparum malaria in Burkina Faso (13). The model and PK parameter estimates from this study were used to simulate a pediatric population. A total population of 5000 subjects with a uniform body weight distribution of 8 to 34 kg were simulated. Parallel simulations were performed assuming three different dosing strategies with respect to body weight (see Table 1). The same simulations were also performed for a narrower weight range of 8 to 12 kg. An alternative simulation scenario with a higher baseline hazard of 12 infections per year was also carried out for both the 8- to 34-kg and the 8- to 12-kg weight range.

Pregnant population. Simulations were carried out on the basis of a publication on population pharmacokinetics of PQ in pregnant and nonpregnant women with uncomplicated malaria (12). A total of 5000 individuals were simulated assuming reported PK parameters for pregnant, nonpregnant, and healthy male subjects (that is, PK parameters from the current study), respectively. All simulations were carried out assuming a subject of 20 years of age and with a body weight of 50 kg.

PQ resistance. On the basis of the final PK-PD model, simulations were carried out with altered IC50 values aiming to reflect emerging PQ resistance. IC50 values of 7 (estimated), 14 (×2), 28 (×4), 70 (×10), and 700 (×100) ng/ml were assumed, and 5000 subjects were simulated in each scenario.

Day 7 target concentration. The final PK-PD model was used to simulate a standard 3-day treatment followed by a 1-month follow-up. The simulation was carried out assuming a high-transmission season (June) and a wide dose range from 15 to 1500 mg. Predicted PQ plasma concentrations at days 7 and 14 after start of treatment were plotted versus the associated predicted 1-month survival. The results were also summarized by binning the 1-month survival in bins of 400 data points and calculating the median and 90% prediction interval (5th and 95th percentile) for the associated plasma concentrations.

SUPPLEMENTARY MATERIALS

www.sciencetranslationalmedicine.org/cgi/content/full/6/260/260ra147/DC1

Table S1. Descriptive statistics for study population baseline characteristics.

Fig. S1. Illustration of covariate relationship between age (years) and the probability of belonging to the low-hazard population (PMIX2).

Fig. S2. Illustration of the relationship between parasite count at the time of diagnosis and the approximated event censoring interval.

Text file. NONMEM output file: Pharmacokinetics.

Text file. NONMEM output file: Pharmacokinetics-Pharmacodynamics.

REFERENCES AND NOTES

  1. Acknowledgments: We thank the subjects who participated in the study and the staff of Shoklo Malaria Research Unit (SMRU) for a well-conducted clinical trial. The article is dedicated to the memory of Dr. Niklas Lindegårdh, who was instrumental in initiating the collaboration between Uppsala University and Mahidol Oxford University Research Unit (MORU). Funding: M.B. was supported by a grant from the Swedish Research Council (521-2011-3442). SMRU is part of the MORU, Mahidol University, Bangkok, Thailand, supported by the Wellcome Trust of Great Britain. Author contributions: M.B. developed the PK-PD model and coordinated the writing of the manuscript. F.N. was the principal investigator of the clinical trial and provided clinical experience to the interpretation of the results. K.M.L. was the primary research physician during the clinical trial and was responsible for raw data preparation. M.O.K. provided expert input on the modeling and simulation approach. N.J.W. provided expert input with regard to malaria pathology and therapy. J.T. initiated the research project, developed the PK model fitted to the plasma concentration data, and co-authored the manuscript. Competing interests: J.T. received a travel award from Beijing Holley-Cotec Pharmaceuticals that produces Duo-Cotecxin (PQ-DHA). The other authors declare no competing interests.
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