Optimizing the programmatic deployment of the anti-malarials artemether-lumefantrine and dihydroartemisinin-piperaquine using pharmacological modelling

Deploying new anti-malarial drugs is a three-stage process. Firstly, new drugs are developed through a research and development (R&D) pipeline (preclinical phase). Secondly, clinical studies (Phases I to III) demonstrate that the new drugs are effective and safe under controlled clinical conditions. Thirdly, the drugs are deployed under programmatic or real-life circumstances (post-marketing, Phase IV). The current regulatory drug development process provides limited guidance on the programmatic deployment of anti-malarials in low-resource settings and lacks consensus on the evidence base required to optimize real-life drug delivery. Undoubtedly, clinical trials will always remain the gold standard for experimental validation of drug effectiveness and safety and no policy-maker would ever solely rely on model predictions, but, for ethical reasons, certain clinical trials cannot reasonably be conducted, e g, trials estimating the effect of known sub-therapeutic doses, leaving an uncomfortable gap in our knowledge that might be at least partly bridged by the output generated using modelling approaches.

Pharmacological drug treatment models can be constructed to assess dosing accuracy and impact at patient and population level and could constitute a strong support role in the policy decision-making process in regard to pharmacological aspects. Their potential has been highlighted both for the development of paediatric formulations for the ‘Essential Medicines List’ [1] and to analyse the likely effects of drugs on malaria throughout a global eradication campaign [2]. Accurate simulations can rapidly investigate the consequences of varied drug deployment strategies and help identify optimal dosage levels, frequency and duration. Moreover, they can be used to investigate real-life situations that cannot be field tested, such as anticipated sub- or supra-therapeutic dosing in patients around the cut-off points of dosing bands or the impact of poor patient adherence on treatment outcome, and the potential lessons for programmatic delivery strategies and the associated monitoring and evaluation. Similarly, they can be used to predict susceptibility to, and efficacy of, anti-malarials at a time of developing drug tolerance or resistance and its subsequent spread through the population [3]. Important factors that determine treatment success in programmatic settings are linked to drug exposure related to dosing regimens, treatment adherence and drug resistance. Others include drug quality, drug interactions, poor or erratic absorption and misdiagnosis [4].

Decades of work on malaria models have resulted in numerous models of its epidemiology, and the genetics of drug resistance, but fewer than a dozen published models specifically focus on anti-malarial drug treatment [3, 5‐13]. Drug treatment models for malaria are based on mathematical pharmacokinetic/pharmacodynamic (PK/PD) models describing the effect of antimicrobial drugs (recently reviewed by Czock & Keller [14]). In the case of malaria, these models use differential equations to track parasite growth (the parasite submodel), the effect of anti-malarial drugs (the anti-malarial submodel), and changing drug concentrations (the pharmacokinetic submodel) [14]. The differential equations are then used to describe the dynamics of a parasite population in the presence of anti-malarial drug treatment. Existing PK/PD models either investigate only monotherapy [5‐7, 9‐11], do not model the artemisinin-based combination therapy (ACT) drug components individually [8] or are not able to reliably replicate the results of clinical trials [12]. None of the PK/PD models specifically aim to simulate programmatic settings where, e g, (un-)intended alterations of intake dose or drug resistance can jeopardize drug effectiveness and safety. Models to investigate these real-life challenges are therefore required to address substantial gaps in our evidence base, and must be able to (i) allow investigation of the effectiveness of several drugs co-administered as ACT; (ii) allow changes in PK/PD parameters of individual ACT drug components (e g, increasing resistance, genetic variation in drug elimination); and, (iii) reliably reproduce data from clinical trials.

This study presents a novel PK/PD model that integrates two existing models to simulate the real-life population level effectiveness of artemether-lumefantrine (AM-LF) and dihydroartemisinin-piperaquine (DHA-PPQ) against background scenarios of varying age and weight-based dosing regimens and levels of drug adherence, some of the many challenges faced when deploying anti-malarials in programmatic settings.

In order to predict drug effectiveness at the individual and population level and to investigate the effects of decreased parasite drug susceptibility to treatment and poor patient adherence an already existing, validated, in silico simulation of anti-malarial drug action (hereafter referred to as the ‘original model’) [3, 13] was extended. While the original model simulated treatment outcomes based on variation in individual patient PK/PD parameters it only assumed each patient received the ‘correct’ mg/kg dose. As one of the main interests of this study was the comparison of weight- and age-based dosing regional specific weight-for-age tables were integrated to assign realistic body weights across all ages of the population [15]. This allowed simulated patients to vary in age and weight so that patient dosages (in mg/kg) would vary according to proposed age-based and weight-based dosing regimens. The model was implemented in the statistical software package R version 3.0.1 [16]. A schematic representation of the model targeted at an audience with a rather non-modelling background is presented in Figure 1. The following sections are mainly directed at readers with particular interest in the mathematical and technical details of the drug treatment model, its calibration and validation.

Treatment outcome at 63 days was categorized as either (i) all parasites cleared (<1 parasite); (ii) parasites still present but below the microscopic limit of detection (LoD) of 10⁸ parasites and might subsequently either clear or recrudesce; (iii) drug failures, ‘recrudescences’ in the malaria jargon, above LoD; or, (iv) parasites never cleared, i e, above LoD during entire post-treatment period.

This work identified a PK/PD modelling tool that could support a more standardized approach towards optimizing the programmatic delivery of anti-malarials based on weight- or age-bands and exploring their population level performance in real-life settings. To illustrate this approach, treatment outcome for AM-LF and DHA-PPQ at population level was compared and the potential impact of programmatic factors, including regionally optimized age-based dosing regimens, poor patient adherence and drug resistance on treatment outcome were investigated. Predicted cure rates for both treatments were very high in fully adherent patients. The proportion of individuals that cleared all parasites after treatment with AM-LF was predicted to be more than 99% regardless of region or assessed dosing regimen provided that at least the first four of the six doses were taken. This is in line with a study using a four-dose regimen for AM-LF [21] that reported high cure rates in an area in the absence of multidrug-resistant parasites. DHA-PPQ cure rates in this study were around 97% for the weight-based dosing regimen in fully adherent patients. This is consistent with a pooled analysis that reported polymerase chain reaction (PCR)-corrected cure rates of 98.7% for DHA-PPQ [46]. Thus the basic model seems capable of reproducing what occurs in controlled settings typical of clinical studies, increasing confidence in the model’s ability to accurately predict the impact of important programmatic factors (such as poor compliance and the threat posed by drug resistance) that are more difficult to quantify and use for direct comparison in the validation process of the model. Interestingly, results suggest that the assessed optimized age-based dosing regimens would achieve similar average cure rates for an entire population compared to weight-based dosing regimens in the case of AM-LF but would incur unacceptably high failure rates of around 10% in the case for DHA-PPQ. These findings suggest that AM-LF is more robust than DHA-PPQ in this respect and that the ability of DHA-PPQ to clear infections is hampered by a suboptimal ratio of DHA:PPQ (1:8 mg) and associated low DHA dose. In comparison, the AM-LF ratio of 1:5 mg in the fixed-dose combination exceeds the optimal ratio based on the WHO recommended target dose of 1:7 mg [30]. A 1:4.5 mg DHA:PPQ ratio might be preferable as this is the ratio of the WHO recommended target intake doses for the two components, i e, 4 mg/kg of DHA and 18 mg/kg of PPQ [30]. However, the WHO artemisinin dose recommendation is based on studies of artesunate which has a higher molecular weight than DHA (384.4 versus 284.4 mg/mmol, respectively). Consequently, a target intake dose of 3 mg/kg DHA would be equivalent to 4 mg/kg artesunate, suggesting an alternative plausible 1:6 mg ratio to achieve 3 mg/kg of DHA and 18 mg/kg of PPQ. The narrow therapeutic dose range of PPQ compared to DHA (16–26 mg/kg versus 2–10 mg/kg per dose [30], i e, a therapeutic index (TI; the ratio of the maximum to minimum recommended therapeutic intake dose in mg/kg) of 1.6 versus 5.0, respectively) means PPQ drives the weight or age cut-offs in DHA-PPQ regimens, leaving DHA at a high risk of under-dosing. The average dose for DHA was 2.5 mg/kg and 19.7 mg/kg for PPQ (63 and 109% of the recommended target dose [30]) in 10,000 predicted individuals based on the global weight-for-age distribution. These results are similar to the findings from a pooled analysis by WWARN on DHA-PPQ where 19.6% of patients received a total dose of DHA over three days of less than 6 mg/kg (the lower limit for DHA recommended by the WHO [30]), 20.3% of patients received less than the WHO recommended lower limit of PPQ (48 mg/kg total dose over three days). The corresponding percentages in the simulation presented here were 19.89% for each drug. The WWARN analysis identified that children aged 1–5 years were at greatest risk of receiving a sub-therapeutic doses compared to all other age groups [39]. The simulations presented here also found children under the age of 5 years at particular high-risk, i e, 44.13% with sub-therapeutic doses. In the WWARN study the dose of DHA-PPQ was found to be a significant predictor of parasite positivity on Day 3, and the dose of PPQ was a significant predictor of recrudescence (Table 6 and Figure 4 in [39]). Individuals with low DHA-PPQ were, as expected, more likely to have detectable parasites (> 10⁸) at Day 42 (n = 182) and the results obtained here were extremely similar to those reported in the WWARN study (Figure 2D here versus Figure 4 in [39], noting that the difference in x-axis scale arises because Figure 2 here is dose per administration so has to be multiplied by three for total doses). The one difference is that predicted failure rates in the simulations became very low at high drug levels whereas the WWARN tended to plateau off at around 2% even at high drug dosages. Figure 2 was produced assuming full adherence so it is likely that some failures occurred in the WWARN meta-analysis even at high drug dosages due to poor adherence. Due to the low number of individuals with more than 10⁸ parasites at Day 3 (n = 44), no clear trend in dose and parasite positivity was found for Day 3.

In practice, full adherence to anti-malarial drug regimens can be less than 50% in ‘real life’ situations [47]. Reasons for non-adherence to anti-malarials are manifold, including adverse events (AEs) [48], rapid clinical recovery [42, 48‐52], misunderstanding of instructions [50, 52] and, especially in children, difficulties in administration [48, 50‐52] and fear from over-dosing (‘too many tablets’) [50, 52]. Fixed-dose combinations, user-friendly packaging and paediatric formulations adopted for newly developed anti-malarials may help improve adherence, but a certain level of non-adherence is inevitable and programmatic deployment policies need to mitigate its impact. Simulations suggested that delaying a dose did not alter treatment outcome or time of recrudescence (Tables 5, 6, 7 and 8) suggesting that this form of non-adherence does not threaten drug effectiveness when only a single parasite population is present. Generally, when the right mg/kg dose is taken, delaying one dose of the regimen did not lead to significant levels of failures, whereas decreasing the total dose did. These results might change in a more complex model of several parasite populations with different levels of sensitivity to the drug.

A recent study in Papua New Guinea [53] reported low effectiveness of AM-LF. While this could be explained by a number of different factors, this study investigated whether this observation could be simply due to poor bio-availability of LF if it is not taken with fatty food. Cure rates for AM-LF remained above 99% even when the bio-availability of LF was decreased by around 50%. In this case, the presented model may be a helpful tool in testing hypotheses on low effectiveness in clinical trials as it suggests lack of fatty food may not the reason.

Drug resistance is a long-term concern for all anti-malarials because it can drastically shorten the anti-malarials’ therapeutic life-span. While rarely taken into account, the robustness of a drug and its dosing regimen against increasing drug tolerance of the parasites should be considered when deploying new treatment regimens. The presented modelling tool allows exploring the potential threat posed by drug resistance on treatment outcome of different drug regimens by simply altering IC₅₀ value of the parasite population. Previous work used the PK/PD model and allowed patients to acquire new infections during the course of follow-up (Appendix of [54]). The model described in this paper could easily be extended to describe emergence of resistance during therapy by incorporating multiple parasite clones that would then be selected depending on selection pressure posed by the drug treatment.

The authors are not dogmatic about the exact PK/PD method used to predict cure and note there are variations on the in silico method; for example, users may want to use one-hour time steps to track stage specificity, reparameterize the models according to their own local PK/PD estimates or investigate different putative regimens. Notably, the model does not include acquired host immunity at present. While this can be incorporated (e g, [13]) it was omitted at this stage as its calibration relies on arbitrary parameters. Drugs must be able to reliably cure patients irrespective of their immune status, so the absence of assumptions on level of immunity will result in the most conservative recommendations. Similarly, further fine-tuning of this method could involve the inclusion of differences in PK parameters in specific subgroups of the population, such as children and pregnant women, if available.

In essence, a methodology is described that provides a more probabilistic approach to optimizing dosing based on PK/PD modelling to estimate treatment outcome according to proposed deployment policies. This tool can support the development process for ACT with low TIs (e g, PPQ or mefloquine), where dosing all patients within the narrow therapeutic dose range will not be feasible using age-based dosing or weight-based dosing regimens that only use four dose categories (e g, avoiding use of complex regimens with tablet fractions). In these cases, deployment decisions on appropriate banding of dosing regimens will be a compromise between optimal dosing accuracy and programmatic feasibility. This study used simple PK/PD modelling and the primary intention is to demonstrate a methodological ‘road map’ capable of addressing important deployment issues. For example, while the lower therapeutic dose for PPQ is defined as 16 mg/kg, this does not mean that those receiving less than 16 mg/kg will inevitably fail treatment and those receiving 16 mg/kg or above will always be cured. Someone receiving 15.9 mg/kg is less likely to fail treatment as someone receiving 10 mg/kg. In reality many factors determine whether or not a patient fails treatment and many ‘under-dosed’ individuals will still be cured because they have relatively drug-sensitive parasites or they metabolize drugs slower and maintain high drug concentrations for longer. The method simply aims to define and capture this complexity to support the (so far unregulated) decision-making process to translate the regulatory mg/kg dosing recommendation to programmatic dosing based on weight or age bands.

The obvious next step is to get similar nuanced, probabilistic measures for the risk of toxicity at higher dose exposure. Some AEs are dose-independent and would occur at a constant rate irrespective of the used dosing regimen, e g, in a pooled analysis of individual patient data vomiting or diarrhoea were not correlated with the mg/kg dose of PPQ [39]. Others are dose-dependent and correlated with PK factors, such as the total AUC and the maximum concentration reached (c_max), e g, the length of the corrected interval between the Q and T wave in the heart’s electrical cycle is positively correlated with halofantrine exposure [55], glucose-6-phosphate dehydrogenase (G6PD) deficiency mediates dose-related toxicity in primaquine [56] and pruritus in sensitive individuals is linked to chloroquine levels [57]. It is of note that the between-subject variability in human PK parameters is typically 30–50% [58]. The PK component of the model estimates factors such as c_max and AUC for each patient, allowing replacing the arbitrary upper therapeutic threshold in mg/kg with a more nuanced prediction based on patients’ individual PK. In practice, this is hampered by the lack of reliable, standardized safety data from preclinical and clinical studies. Toxicity data from preclinical studies is mostly unpublished and only accessible to the manufacturer and regulatory authorities. Furthermore, outside clinical trial settings, the relationship between dose and individual AEs is rarely known, reports on accidental over-dosing are scarce, there are no standardized tools to collect or report safety data, and the association to dose or dose exposure levels are rarely reported [59]. If these data were available the methodology would be able to output the proportion of patients in a group receiving toxic doses and the likely degree of their toxicity. For example, this would allow to estimate that x% of patients had ‘mild’ toxicity (perhaps defined as <10% above a critical c_max). This would allow policy makers to review and balance the risks of toxicity versus drug failure based on PK/PD prediction, particularly for anti-malarials with a narrow TI, where it is unavoidable that a substantial proportion of patients will receive a dose outside the established therapeutic dose range.

This PK/PD modelling approach is a major methodological advance in the rational design of programmatic drug deployment, complementary to the data generated from clinical trials.