Parasitology

Research Article

18 May 2021

Development and Validation of an In Silico Decision Tool To Guide Optimization of Intravenous Artesunate Dosing Regimens for Severe Falciparum Malaria Patients

ABSTRACT

Most deaths from severe falciparum malaria occur within 24 h of presentation to a hospital. Intravenous (i.v.) artesunate is the first-line treatment for severe falciparum malaria, but its efficacy may be compromised by delayed parasitological responses. In patients with severe malaria, the life-saving benefit of the artemisinin derivatives is their ability to clear circulating parasites rapidly, before they can sequester and obstruct the microcirculation. To evaluate the dosing of i.v. artesunate for the treatment of artemisinin-sensitive and reduced ring stage sensitivity to artemisinin severe falciparum malaria infections, Bayesian pharmacokinetic-pharmacodynamic modeling of data from 94 patients with severe malaria (80 children from Africa and 14 adults from Southeast Asia) was performed. Assuming that delayed parasite clearance reflects a loss of ring stage sensitivity to artemisinin derivatives, the median (95% credible interval) percentage of patients clearing ≥99% of parasites within 24 h (PC24≥99%) for standard (2.4 mg/kg body weight i.v. artesunate at 0 and 12 h) and simplified (4 mg/kg i.v. artesunate at 0 h) regimens was 65% (52.5% to 74.5%) versus 44% (25% to 61.5%) for adults, 62% (51.5% to 74.5%) versus 39% (20.5% to 58.5%) for larger children (≥20 kg), and 60% (48.5% to 70%) versus 36% (20% to 53.5%) for smaller children (<20 kg). The upper limit of the credible intervals for all regimens was below a PC24≥99% of 80%, a threshold achieved on average in clinical studies of severe falciparum malaria infections. In severe falciparum malaria caused by parasites with reduced ring stage susceptibility to artemisinin, parasite clearance is predicted to be slower with both the currently recommended and proposed simplified i.v. artesunate dosing regimens.

INTRODUCTION

Despite major advances in malaria control over the last decade, an estimated 405,000 patients died from malaria in 2018 (1). The majority of these deaths are in African children under 5 years of age with Plasmodium falciparum malaria (1). Most deaths from severe falciparum malaria occur within the first 24 h of presentation to a hospital (2). Early diagnosis and treatment with a highly effective antimalarial treatment are key to prevent severe malaria and death (3).

The current global policy for the treatment of both uncomplicated and severe falciparum malaria (referred to as uncomplicated and severe malaria henceforth) relies on the artemisinin derivatives. The World Health Organization (WHO) treatment guidelines recommend artemisinin combination therapy (ACT) for uncomplicated malaria and intravenous (i.v.) or intramuscular (i.m.) artesunate for severe malaria (3). The reliability and rapid effectiveness of these drugs in the Greater Mekong Subregion is now compromised by resistance to the ACT partner drugs and by Pfkelch13 mutant parasites that have the delayed parasite clearance phenotype (4, 5). Optimizing the dosing regimens for artemisinin-based therapies is crucial to extend the life span of these drugs and prevent the spread of parasites with decreased sensitivity to artemisinin derivatives across Asia and to Africa.

Patients with severe malaria generally have a higher sequestered parasite biomass than those with uncomplicated malaria resulting from efficient multiplication at high densities (6). Decreased sensitivity to artemisinin derivatives is characterized by delayed parasitological responses (7). The life-saving benefit of the artemisinin compounds in severe malaria results from the rapid killing and clearance of circulating parasites before they can sequester and obstruct the microcirculation (8). There is also evidence that patients with severe malaria have higher parasite multiplication rates that contribute to the higher biomass found in severe disease, further highlighting the importance of artemisinin derivatives to clear circulating parasites rapidly (6). Hence, delayed parasite clearance (reflecting reduced ring stage killing and clearance) is a major concern for the treatment of severe malaria (9).

The WHO treatment guidelines for severe malaria recommend that the artemisinin derivative, artesunate, should be given at 0, 12, and 24 h and then daily if required at a parenteral dose of 2.4 mg/kg body weight for adults and larger children (≥20 kg) and, because of lower exposures in younger children, at a dose of 3 mg/kg for smaller children (<20 kg) (9). Once the patient can tolerate oral therapy, treatment is completed with 3 days of an ACT. In Africa, a regimen not requiring a 12-h dose was proposed to have significant practical advantages in resource-poor settings and remote health facilities (10, 11).

The parasite clearance rate is an informative pharmacodynamic variable, and in silico pharmacokinetic-pharmacodynamic (PK-PD) modeling offers an informative approach to explore new dosing strategies. This approach has been used to simulate parasite clearance within the first 24 h for patients with severe malaria. Model-based findings suggest that for patients with artemisinin-sensitive infections, a simplified regimen of i.m. artesunate (4 mg/kg at 0, 24, and 48 h) is comparable in efficacy to the WHO regimen (12). While the WHO-recommended regimen was predicted to be less efficacious in patients infected with parasites with decreased artemisinin sensitivity compared to sensitive parasites, the efficacy of the simplified regimen has yet to be evaluated against parasites with decreased artemisinin sensitivity.

In this study, we fitted a within-host PK-PD model within a Bayesian framework to drug concentration and parasite count data from patients with severe malaria treated with two different i.v. artesunate regimens and performed an external validation. Simulations based on the joint posterior distribution of the PK-PD parameters were performed to compare the parasitological outcomes between hypothetical patients with either artemisinin-sensitive or reduced ring stage sensitivity to artemisinin severe falciparum malaria infections.

RESULTS

Parasitemia (the number of parasites/μl of blood) profiles were available for 94 patients with severe malaria (80 children from Africa and 14 adults from Southeast Asia) treated intravenously with 2.4 mg/kg of artesunate. Details of the trials are provided in Table 1 and published reports (10, 13). Since parasite sampling after 48 h was sparse, parasitemia profiles were modeled only from data collected up to and including 48 h (see Fig. S1a and b in the supplemental material). Baseline patient characteristics and the number of blood samples quantifying parasitemia are summarized in Table 2.

TABLE 1

TABLE 1 Study site, population, design, dosing scheme, and parasitemia sampling times for each study

Characteristic	Data for research team:
Characteristic	Kremsner et al. (10)	Maude et al. (13)
Site	Gabon, Malawi	Bangladesh
Population	Children with severe malaria	Adults with severe malaria
Design	Randomized controlled trial	Clinical study
Dosing regimen	2.4 mg/kg i.v. at 0, 12, 24, 48, and 72 h^a	2.4 mg/kg i.v. at 0, 12, and 24 h and then every 24 h as required
4 mg/kg i.v. at 0, 24, and 48 h
Sampling times
ARS/DHA concentration	2 samples/patient taken from times^b 0.083, 0.167, 0.25, 0.5, 1, 2, 4, and 6 h	0, 0.167, 0.5, 1, 2, and 4 h
Parasitemia	0, 6, 12, 18, and 24 h and then every 6 h until there were 2 consecutive negative^c slides	0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 18, and 24 h and then every 6 h until parasite clearance

Only these patients were included in the analysis.

Patients were randomly allocated to one of eight different sampling groups, where each sampling group had two time points (e.g., group 1 to 5 min, 2 h post-first dose).

Negative slide was defined as the number of circulating parasitized blood cells below the limit of detection (50 parasites/μl of blood).

TABLE 2

TABLE 2 Summary of the number of blood samples for parasitemia measurement, including the number of samples below the microscopic limit of detection (LOD), and baseline patient characteristics for each study

Characteristic	Data for research team:
Characteristic	Kremsner et al. 2012 (10)	Maude et al. 2009 (13)
No. of patients	80	14
No. male	44	11
No. of samples	463	87
No. below LOD^a	68	5
Median samples per patient (range)	6 (2–9)	11 (1–14)
Baseline patient characteristics^b
Median parasitemia (parasites/μl of blood)	214,824 [869–1,870,264)	92,630 (22,608–534,554)
Age (years)	3 (0.6–9.3)	37.5 (22–62)
Weight (kg)	12 (6–24)	60 (33–75)

LOD, limit of detection for microscopic blood film examination (50 parasites/μl of blood).

Median (range).

Assessment of model fit and parameter estimation.

A within-host PK-PD model was incorporated into a Bayesian hierarchical model and fitted to the observed parasitemia profiles (Materials and Methods and Text S1). Definitions for the nine model parameters are provided in Table 3.

TABLE 3

TABLE 3 Parameter definitions for the within-host pharmacokinetic-pharmacodynamic model

Parameter	Description
IPL	Initial parasite load of patient on admission
$μ_{IPL}^{*}$	Mean of the age distribution of the initial parasite load (hours) before truncation (normal)
μ_IPL	Mean of the age distribution of the initial parasite load (hours) after truncation (truncated normal)
$σ_{IPL}^{*}$	Standard deviation of the age distribution of the initial parasite load (hours) before truncation (normal)
σ_IPL	Standard deviation of the age distribution of the initial parasite load (hours) after truncation (truncated normal)
PMF	Parasite multiplication factor. Number of parasites released by a ruptured schizont at the end of the life cycle
K_max	Maximal killing rate of the drug (per hour)
EC₅₀	In vivo concentration when killing rate is 50% of K_max (ng/ml)
γ	Slope of in vivo concentration-effect curve
k_e0	Rate at which the drug moves from the central compartment (blood plasma) to a hypothetical effect site (intraerythrocytic compartment) (per hour)
δ_P	Rate of parasite removal due to processes other than drug (per hour). Patients are assumed to be immunologically naive

The posterior predictive check (Text S2) in Fig. 1a indicates that the within-host PK-PD model successfully captures the central trend and variability in the observed parasite count profiles.

FIG 1

The estimates of the population average parameters are presented in Table 4. The average age of the initial parasite load (μ_IPL) was 12.95 h, and the middle 50% of parasites (interquartile range) were aged between 6.16 and 18.17 h, indicating that on admission, infections consisted of parasites predominantly at the ring stage. The time delay before dihydroartemisinin (DHA) concentration levels in plasma reached the malaria parasite in red blood cells (reflected in a hypothetical intraerythrocytic effect compartment) was 3.3 h (log_e2/0.21). The 50% effective concentration (EC₅₀) in the hypothetical compartment was 20.35 ng/ml. Assuming patients are immunologically naive, the rate of parasite removal resulting from processes other than the drug (δ_P) was 0.06/h, that is 6% (100 × [1 – e^–0.06]) of parasites at each age will be removed every hour independent of treatment. DHA is assumed to kill parasites aged 6 to 44 h (referred to as DHA’s killing window). The maximal killing effect (k_max) of DHA was 0.53/hour. Thus, for every hour that DHA concentrations are much greater than the EC₅₀ concentration, the number of parasites within the killing window will be reduced by 41% (100 × [1 – e^–0.53]).

TABLE 4

TABLE 4 Posterior summaries for the population mean pharmacodynamic (PD) parameters between subject variability (BSV), and study-specific residual errors calculated from 4,000 draws from the posterior distribution

Parameter	Bounds^a	Posterior median (95% credible interval)	ESS^b	R̂^c
Population average PD parameter^d
IPL (no. of parasites)	8.69 × 10⁹, 1.870264 × 10¹³	2.8 × 10¹¹ (1.9 × 10¹¹, 4 × 10¹¹)	668	1.01
$μ_{IPL}^{*} (h)$	1,48	5.41 (2.49, 11.39)	689	1
μ_IPL (h)	12.95 (11.53, 15.90)
$σ_{IPL}^{*} (h)$	4,14	12.74 (11.75, 13.46)	1,839	1
σ_IPL (h)	8.47 (7.73, 9.51)
PMF	5,20	11.39 (6.47, 17.75)	2,379	1
k_max (h^–1)	0.26,1	0.53 (0.47, 0.6)	342	1.01
EC₅₀ (ng/ml)	1.44,533	20.35 (7.97, 41.26)	756	1.01
γ	1,13	7.14 (2.74, 11.51)	2893	1
k_e0 (h^–1)	0.01,10	0.21 (0.11, 0.33)	728	1
δ_p (h^–1)	0.001,0.1	0.06 (0.02, 0.09)	744	1
Between subject variability (ω)^e
ω_IPL	1.51 (1.23, 1.86)	1,475	1
ω_{μ_IPL}	0.37 (0.02, 1.01)	1,022	1
ω_{σ_IPL}	1.76 (1.02, 2.78)	306	1.01
ω_PMF	0.63 (0.03, 2.14)	2,468	1
ω_{k_min}	1.09 (0.81, 1.45)	675	1.01
ω_EC50	0.58 (0.04, 1.25)	717	1
ω_γ	0.63 (0.03, 2.13)	3,498	1
ω_{k_e0}	0.4 (0.04, 1.01)	392	1.01
ω_{k_min}	0.42 (0.02, 1.81)	469	1
Study-specific residual error (σ)
σ₁	0.95 (0.86, 1.05)	1439	1
σ₂	0.69 (0.56, 0.89)	745	1.01

A justification for the bounds is provided in Table S1.

Effective sample size (ESS) is the number of independent draws of the parameter of interest from the posterior distribution (see Materials and Methods).

If all chains have converged to a common distribution, R̄ will be 1; otherwise, it will be greater than one (see Materials and Methods).

Prior to drug administration, the initial parasite load (IPL) of each patient is distributed among the 48 hourly age intervals of the P. falciparum life cycle according to a truncated normal distribution with location parameter

μ_{IPL}^{*}

hours, scale parameter

σ_{IPL}^{*}

hours, and truncation limits 1 to 48 h (Text S1, equation S1). μ_IPL and σ_IPL are the mean and standard deviation, respectively, of the truncated parasite age distribution. Definitions for the nine model parameters are provided in Table 3.

Between subject variability (BSV) is the population standard deviation of the individual PD parameters on the logistic transform scale (see Materials and Methods and equation 1). BSV was only included on

μ_{IPL}^{*}

and

σ_{IPL}^{*}

, not the resulting mean and standard deviation of the truncated age distribution.

The observed parasitemia profiles were not informative for estimation of the population average or the individual-specific parasite multiplication factor (PMF). Similarly, the profiles were not informative for estimation of the slope of the in vivo concentration-effect curve (γ). For these parameters, the prior and marginal posterior distributions were very similar (see Fig. S2). The prior distributions for PMF and γ were based on data and parameter estimates from clinical and in vitro studies (Table S1). Figure S3 shows how the between subject variability (ω) parameters influence the shape of the marginal densities of the multivariate logistic-normal distribution specified for individual PD parameters.

Parasitological outcome and dosing regimens.

The parasitological outcome measure selected for comparing the different i.v. artesunate regimens was clearance of 99% of a patient’s admission parasitemia within 24 h (PC24≥99%), a measure that was used previously in noninferiority clinical trials of parenteral artesunate (10, 11). The 95% credible interval for PC24≥99% simulated from the model contains the observed PC24≥99% of 82% (95% confidence interval [exact method], 70% to 90%) for children and 70% (95% confidence interval, 35% to 93%) for adults (Fig. 1b).

The following three dosing regimens were examined in this study: (i) 2.4 mg/kg of i.v. artesunate at 0, 12, 24, 48, and 72 hours (standard regimen), (ii) 4 mg/kg of i.v. artesunate at 0, 24, and 48 hours (simplified regimen), (iii) 3 mg/kg of i.v. artesunate for smaller children (<20 kg) and 2.4 mg/kg for adults and larger children (>20 kg) at 0, 12, and 24, 48, and 72 hours (revised regimen).

Before 2015, the standard regimen was recommended by the WHO. In 2012, the simplified regimen was examined in a randomized controlled trial (RCT) as an alternative to the standard regimen in resource-poor settings in Africa. In 2015, the standard regimen for children was revised based on pharmacometric modeling (14, 15). The dose for smaller children was increased in the revised regimen to provide comparable drug exposure to adults and larger children. The PC24≥99% only evaluates the efficacy of the dose(s) administered in the first 24 h after treatment.

Comparison of dosing regimens.

Medians (black dots) and 95% credible intervals (error bars) were used to compare the distribution of PC24≥99% derived from 100 data sets consisting of different hypothetical patient populations, 100 adults, 100 larger children, and 100 smaller children (Fig. 2). Simulation of hypothetical patients with either artemisinin-sensitive or reduced ring stage artemisinin sensitivity infections was performed. Decreased ring stage artemisinin sensitivity was modeled by shortening the DHA killing window from 6 to 44 h to 12 to 44 h to mimic a partial (i.e., 6 h) loss of ring stage activity. The concentration-effect relationship for parasites remaining in the killing window was assumed to be the same as that inferred for artemisinin-sensitive infections.

FIG 2

The DHA concentration profiles for hypothetical adults and larger and smaller children given each dosing regimen are presented in Fig. S4. An example of the corresponding parasitemia profiles is presented in Fig. S5.

Artemisinin-sensitive infections.

The simplified 4 mg/kg i.v. artesunate dose group in Kremsner et al. (10) was used for external validation of the model prediction. External validation focused on whether the model could reproduce the PC24≥99% for the simplified regimen reported in Kremsner et al. (10); the parasitemia profiles from the standard regimen from this study were used for model fitting.

Kremsner et al. (10) reported that 78% (95% confidence interval, 69% to 87%) of patients that received the simplified regimen achieved PC24≥99%, and 85% (95% confidence interval, 77% to 93%) of patients that received the standard regimen achieved PC24 ≥ 99%. A treatment difference of –7.2% was observed between the PC24≥99% for the simplified and standard regimens. The corresponding 95% confidence interval ranged from –18.9% to 4.4% and did not include the prespecified noninferiority margin of –20%.

The median (95% credible interval) for the PC24≥99% for hypothetical patients with sensitive infections administered the standard regimen was 86% (75.5% to 93.5%) for adults, 83% (72.5% to 90.5%) for larger children, and 80% (72% to 88%) for smaller children (Fig. 2, top panel). These 95% credible intervals for hypothetical larger children treated with the standard regimen and for hypothetical smaller children treated with either the standard or revised regimen contain the observed percentage and 95% confidence interval reported in Kremsner et al. (10) for the standard regimen.

For the simplified regimen, the median and 95% credible interval derived from the hypothetical children (63.5% [44.5% to 80%] for larger children and 58.5% [41% to 74%] for smaller children) underestimated the observed PC24≥99% for the children that received the simplified regimen in Kremsner et al. (10) (i.e., data set for external validation; Fig. 2, top panel).

Decreased ring stage sensitivity to artemisinin.

For infections where the killing window was shortened to 12 to 44 h to reduce ring stage activity, rapid clearance of such infections appears to be compromised compared to sensitive infections for both the standard (two doses of 2.4 mg/kg of i.v. artesunate at 0 and 12 h) and simplified (single dose of 4 mg/kg at 0 h) regimens. The median values (95% credible intervals) for standard and simplified regimens were 65% (52.5% to 74.5%) versus 44% (25% to 61.5%) for adults, 62% (51.5% to 74.5%) versus 39% (20.5% to 58.5%) for larger children (≥20 kg), and 60% (48.5% to 70%) versus 36% (20% to 53.5%) for younger children (<20 kg) (Fig. 2, bottom panel).

DISCUSSION

Our within-host PK-PD model captures the key features of malaria parasite clearance following the start of antimalarial treatment. The modeled profiles show central trends (lag and decline) and variability in the observed parasitemia profiles similar to those observed in African children and Southeast Asian adults who received the 2.4 mg/kg i.v. artesunate dosing regimen in the studies reported by Kremsner et al. 2012 (10) and Maude et al. (13), respectively (Fig. 1). Simulated parasitological outcomes from the model PD parameters reproduced the percentage PC24≥99% observed for the standard 5-dose regimen (i.e., data used for model fitting). In an external validation of the simplified 3-dose i.v. artesunate regimen, based on findings reported in Kremsner et al. (10), our model underestimated the observed percentage PC24≥99%.

The patient data used for our model predictions were from a setting prior to the decline in efficacy of artemisinin-based therapies being detected in Southeast Asia; consequently, inferences based on posterior summaries for the PD parameters are only appropriate for infections with artemisinin-sensitive parasites. In this study, decreased sensitivity to artemisinin derivatives was modeled by shortening the DHA killing window, i.e., reduced ring stage activity which conforms to the in vitro observations of reduced ring stage killing.

A delayed drug killing effect has been observed in in vitro (16, 17) and clinical studies for artemisinin derivatives (18, 19). The time delay before DHA plasma concentration had an apparent effect was 3.3 h in this study, shorter than the 9-h delay estimated for Cambodian and Thai adults (18) and the 5.6-h delay estimated for adults in southern Myanmar (19) after treatment with oral artesunate monotherapy. In addition, artemisinin-induced growth retardation (20 –22) and/or altering of growth patterns (23) were not modeled.

The within-host PK-PD model described in this study assumed patients were immunologically naive. This assumption was considered reasonable, as the adult patients were from Southeast Asia (a low-transmission setting) and a large proportion of the African children were under 5 years old (80%). Assuming the patients were immunologically naive may cause the killing rate of the drug (k_max) to be overestimated, as parasite clearance is attributed to drug only, and any contribution from the immune response is ignored.

The model included a parameter to capture drug-independent removal of parasites (δ_P) under the assumption that patients were immunologically naive (i.e., due to host-specific processes, such as the finite life span of red blood cells) (20, 24). In this study of Southeast Asian adults and predominantly African children, drug-independent removal assuming patients were immunologically naive was inferred to be 6% of parasites every hour.

The meta-analysis reported by Zaloumis et al. (15) found similar PK parameters for Southeast Asian adults and Africa children. The PK-PD analysis presented in this study assumed that the decline in parasitemia after treatment was driven by a patient’s PK profile, and hence the PD analysis was not stratified by adult and child patients. Figure S6 illustrates that simulated profiles generated from individual PD parameters derived from the analysis of the pooled PD profiles (i.e., both adults and children) can capture the central trend and variability in the separate adult and child profiles.

The estimation of our model parameters was based on data from only 94 patients and focused on the decline in parasitemia, and not on clinical outcomes, in the initial 24 h after treatment with intravenous artesunate. Although our model predicts a slower decline in parasitemia for infections with decreased ring stage sensitivity to artemisinin derivatives in the first 24 h, this may not translate to poorer clinical outcomes (25). To determine the consequences of delayed parasite clearance on clinical outcomes in severe falciparum malaria patients, studies should also focus on parasitological and clinical outcomes beyond the first 24 h of treatment.

In silico modeling of artemisinin-resistant severe malaria infections was also investigated in Jones et al. (12) by assuming early ring stage parasites were insensitive to artesunate. The conclusions in Jones et al. (12) regarding the efficacy of the standard i.m. dosing regimen for treating resistant infections where the killing window of DHA has been reduced are consistent with ours for i.v. artesunate and suggest that the standard regimen has reduced efficacy against these infections compared to sensitive infections. Our modeling approach differs in the following ways from that adopted in Jones et al. (12): Bayesian inference was used for parameter estimation, the posterior predictive distribution was used to simulate the parasitological outcome, and the efficacy of the simplified regimen against artemisinin-resistant infections was examined.

In conclusion, our study suggests that in view of the declining efficacy, including recent reports of de novo emergence of Pfkelch13-mediated delayed parasite clearance in sub-Saharan Africa (26), the previous excellent therapeutic response to intravenous artesunate may be compromised in patients with severe falciparum malaria. In these areas, the clearance of parasites for both the standard and simplified parenteral regimens may be significantly slower. So far, in uncomplicated malaria, these delayed parasite clearance phenotypes have not compromised cures with artemisinin-containing combinations when the partner drug retains efficacy. Prospective trials of the clinical efficacy of different parenteral artesunate regimens are warranted in patients with severe falciparum malaria in areas with delayed parasite clearance, using clinically relevant endpoints. These trials should be guided by modeling of available data (11). New parenteral antimalarial drugs with ring stage activity are needed in the immediate future.

MATERIALS AND METHODS

Study population, study design, dosing, and blood sampling.

The site, study population, design, i.v. artesunate dosing, and blood sampling for the determination of DHA concentration and parasitemia (parasites/μl of blood) for both studies included in the pooled data set are provided in Table 1.

Within-host pharmacokinetic-pharmacodynamic model.

The within-host pharmacokinetic-pharmacodynamic (PK-PD) model was previously published in references 27 and 28 and describes the blood stage of a malaria infection and its response to treatment. In brief, prior to drug administration, the initial parasite load (IPL) of each patient is distributed among the 48 hourly age intervals of the P. falciparum life cycle according to a truncated normal distribution with location parameter

μ_{IPL}^{*}

hours, scale parameter

σ_{IPL}^{*}

hours, and truncation limits 1 to 48 h (Text S1, equation S1). μ_IPL and σ_IPL are the mean and standard deviation, respectively, of the truncated parasite age distribution (Text S1, equation S2 and Fig. S7). Every hour after treatment, the parasites aged 1 to 47 h are shifted to the right and become the number of parasites aged 2 to 48 h. The parasites aged 48 h are then multiplied by the parasite multiplication factor (PMF; Table 3). This process was repeated for a follow-up time of 48 h.

The proportion of parasites that survive an hour of treatment with i.v. artesunate is determined by the delayed concentration-effect sigmoid-E_max model described in reference 18 that links the DHA concentration in the central compartment (blood plasma) to a hypothetical effect-site (intraerythrocytic) compartment (Text S1, equation S6). The model assumes patients are immunologically naive. The rate of parasite removal due to processes other than drug in patients assumed to be immunologically naive, δ_P, is included in the model (e.g., host-specific processes, such as the life span of red blood cells). The PMF is corrected to account for δ_P (Text S1, equation S4).

After removal of parasites due to drug and drug-independent processes, the sum of the simulated number of parasites aged 1 to 26 h was used to predict the circulating parasitemia at time points of interest. DHA, the active metabolite of artesunate, was assumed to kill parasites aged 6 to 44 h (29). The model does not have an explicit compartment from which parasites “damaged” by drug can either be cleared or recover and be returned to the blood circulation (30). Full details of the model are provided in the Text S1.

Statistical analysis.

The within-host model (Text S1) was incorporated into a Bayesian hierarchical model (Text S3) which allows the dynamics to vary across patients and, consequently, the variation in the observed parasitemia profiles to be modeled. Parasitemia measurements were natural log (log_e) transformed and assumed to follow a normal distribution where the residual standard deviation varied by observed study. Data below the microscopy limit of detection (50 parasites/μl of blood) were modeled as censored data using the M3 method (31). The prior distribution for the individual-specific PD parameters was assumed to be multivariate normal (MVN) after logistic transformation (32), i.e.,

ϕ_{i} = lo g_{e} (\frac{θ_{i} - a}{b - θ_{i}}) \sim MVN (ϕ, Ω)

(1)

where ϕ_i and θ_i denote 9-dimensional vectors of individual-specific PD parameters after and before logistic transformation for the ith individual, and a and b are 9-dimensional vectors containing the lower and upper bounds for each PD parameter provided in Table 4 and in Table S1 along with a justification for their selection. The mean vector (ϕ) of the MVN distribution in equation 1 is the logistic transform of a 9-dimensional vector of population average PD parameters (θ), i.e.,

ϕ = lo g_{e} (\frac{θ - a}{b - θ})

. The covariance matrix (Ω) was decomposed into a vector of standard deviation parameters and a correlation matrix (see equation S10 in Text S3). The hyperprior distributions for the elements of the mean vector ϕ, standard deviation parameters, correlation matrix, and study-specific residual error were normal(0, 1), half-normal(0, 1), Cholesky LKJ correlation distribution (33, 34) with shape parameter equal to 2, and half-Cauchy(0, 5), respectively.

The No U-Turn (NUTS) sampler implemented in the open-source software packages RStan 2.18.2 (35) and R 3.4.2 (36) was used to sample the population average PD, individual-specific PD, between subject variability (BSV) parameter values, and study-specific residual errors from the posterior distribution. For each model parameter, four Markov chains were initialized using random numbers generated by RStan. The first 1,000 parameter values sampled for each chain were discarded as burn-in, and an additional 1,000 parameter values were sampled and combined, resulting in 4,000 samples per parameter for calculation of posterior summaries. The posterior summaries calculated were the median of the 4,000 samples for each parameter (posterior median) and 95% credible interval, which is calculated from the 2.5th and 97.5th percentiles of the 4,000 samples for each parameter. The credible interval can be interpreted as an interval in which the probability that the unknown parameter lies within is 0.95.

Trace plots were examined to assess whether the 1,000 parameter draws from each chain had converged to a common distribution (Fig. S8). Convergence was also monitored using the R̄ statistic, which is the ratio of the mean of the variances of the samples within each chain to the variance of the pooled samples across chains (34). If all chains have converged to a common distribution, R̄ will be 1. The effective sample size (ESS) is an estimate of the number of independent draws of the parameter of interest from the posterior distribution (34). The draws within a Markov chain are not independent, and if there is high autocorrelation between the draws for a parameter, the ESS will be much smaller than the total sample size (i.e., the 4,000 draws retained after burn-in for each parameter). To gauge the degree to which the observed data update the prior information, a comparison of the prior distribution and marginal posterior distribution for the population average PD parameters, between-subject variability, and individual-specific PD parameters for an individual are provided in Fig. S2. Additional details concerning model building and selection are provided in Text S4.

Simulation of PC24≥99% under standard and simplified dosing regimens.

PK parameters (clearance [CL] and volume of distribution [V]) were simulated for different hypothetical patient populations (100 adults, 100 larger [≥20 kg] children and 100 smaller [<20 kg] children) from the population PK model for patients that received i.v. artesunate at baseline described in reference 15. Simulation of individual-specific PK parameters from this model requires age, weight, hemoglobin, and body temperature values for each hypothetical patient. There was little correlation between these variables for the 14 adults in the pooled study (all Pearson’s correlations below 0.4), so values of these variables for the 100 hypothetical adults were sampled from uniform distributions with limits set to the observed range for each variable as follows: age, 21 to 62 years; weight, 33 to 75 kg; hemoglobin, 2.9 to 11.5 g/dl; and temperature, 34 to 39°C.

For the 80 children in the pooled study, age was correlated with both weight and hemoglobin, but temperature was not strongly correlated with any variable. A total of 500 age and temperature values were sampled from uniform distributions with limits set to the observed range for the 80 children as follows: age, 0.5 to 9.2 years; temperature, 35 to –40°C. The sampled age values were used to simulate 500 corresponding weight and hemoglobin values using the coefficient estimates from the linear regressions of age and weight (estimated intercept, age coefficient, and residual standard error were 7.02, 1.76, and 2.01, respectively) and age and hemoglobin (estimated intercept, age coefficient, and residual standard error were 5.79, 0.59, and 2.01, respectively) for the 80 children in the study. The age, hemoglobin, and temperature values for the first 100 weight values ≥20 kg (<20 kg) were retained and used to simulate PK parameters for larger (smaller) children.

Then, for each dosing regimen, the simulated weights and PK parameters for each hypothetical patient were used to calculate the i.v. artesunate dose in μg and to simulate the DHA plasma concentration (ng/ml) from the intravenous-bolus one-compartment PK model described in reference 15, respectively.

Next, 100 data sets, each consisting of 100 hypothetical adults, larger children, or smaller children with parasitemia measurements simulated at 6 hourly intervals for 7 days follow-up, after treatment with each i.v. artesunate dosing regimen, were simulated. The 100 hypothetical data sets were generated from the last 100 of the 4,000 draws of ϕ and Ω as defined in equation 1. For each patient population, 100 vectors of ϕ_i were then sampled from this distribution at each of the 100 draws of ϕ and Ω. The inverse logistic transform, (a × [1 – logit^–1 (ϕ_i)]) + b × logit^–1 (ϕ_i), where logit^–1 (×) = 1/(1 + e^–x), and a and b are the lower and upper bounds, respectively, for the PD parameters in Table 4 and Table S1, was then applied to each of the ϕ_i vectors to obtain individual-specific PD parameters on the original scale and within their biologically plausible bounds. These vectors were then used to simulate parasitemia profiles from the within-host PK-PD model for each hypothetical patient (Fig. S5).

For each dosing regimen examined, the simulated DHA concentration profiles (Fig. S4) do not vary between data sets. The individual-specific PD parameters for the hypothetical patients vary between data sets, but not between dosing regimens. Details concerning the calculation of PC24≥99% for hypothetical patients are provided in Text S5. The simulation of parasitemia profiles for infections with reduced ring stage sensitivity to artemisinin derivatives required shortening the DHA killing window from 6 to 44 h, where the drug is known to have an effect, to 12 to 44 h in Equation S5. The process outlined above is then repeated for the within-host PK-PD model with shortened DHA killing window.

ACKNOWLEDGMENTS

We thank staff and patients at Chittagong Medical College Hospital in Bangladesh, Centre de Recherches Médicales de Lambaréné and Université des Sciences de la Santé in Gabon, and Queen Elizabeth Central Hospital in Malawi, where the data were collected.

S.G.Z. and J.A.S. wrote the first draft of the manuscript; J.A.S. designed the research with input from R.N.P. and N.J.W.; P.K., S.K., A.D., N.J.W., and R.J.M. contributed the data; S.G.Z., J.M.W., and J.A.S. performed the statistical analysis with guidance from J.M.M, J.T., M.T.W., P.C., S.D., and F.J.I.F. All authors critically reviewed and approved the final version of the manuscript.

We declare no competing interests for this work.

The work was supported by the National Health and Medical Research Centre (NHMRC) of Australia project grant 1025319 and supported in part by the Australian Centre for Research Excellence on Malaria Elimination, funded by the NHMRC (1134989). S.G.Z. is funded by an Australian Research Council (ARC) Discovery Early Career Researcher Award (170100785), J.A.S. is supported by an NHMRC Senior Research Fellowship (1104975), F.J.I.F. is supported by an NHMRC Career Development Fellowship (1166753), R.N.P. is a Wellcome Trust senior research fellow in clinical science (200909), and N.J.W. is a Principal Wellcome Trust fellow. J.T., R.J.M., and A.D. are supported by the Wellcome Trust as part of the Wellcome Trust–Mahidol University–Oxford Tropical Medicine Research Program. J.T. and R.J.M. are partly funded from the Bill & Melinda Gates Foundation. J.M.M., P.C., and J.A.S. are supported by an Australian Research Council Discovery Project (170103076).

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REFERENCES

WHO. 2019. World malaria report 2019. WHO, Geneva, Switzerland.

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ABSTRACT

INTRODUCTION

RESULTS

Assessment of model fit and parameter estimation.

Parasitological outcome and dosing regimens.

Comparison of dosing regimens.

Artemisinin-sensitive infections.

Decreased ring stage sensitivity to artemisinin.

DISCUSSION

MATERIALS AND METHODS

Study population, study design, dosing, and blood sampling.

Within-host pharmacokinetic-pharmacodynamic model.

Statistical analysis.

Simulation of PC24≥99% under standard and simplified dosing regimens.

ACKNOWLEDGMENTS

Supplemental Material

REFERENCES

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