How Robust Are Malaria Parasite Clearance Rates as Indicators of Drug Effectiveness and Resistance?

Abstract

Artemisinin-based combination therapies (ACTs) are currently the first-line drugs for treating uncomplicated falciparum malaria, the most deadly of the human malarias. Malaria parasite clearance rates estimated from patients' blood following ACT treatment have been widely adopted as a measure of drug effectiveness and as surveillance tools for detecting the presence of potential artemisinin resistance. This metric has not been investigated in detail, nor have its properties or potential shortcomings been identified. Herein, the pharmacology of drug treatment, parasite biology, and human immunity are combined to investigate the dynamics of parasite clearance following ACT. This approach parsimoniously recovers the principal clinical features and dynamics of clearance. Human immunity is the primary determinant of clearance rates, unless or until artemisinin killing has fallen to near-ineffective levels. Clearance rates are therefore highly insensitive metrics for surveillance that may lead to overconfidence, as even quite substantial reductions in drug sensitivity may not be detected as lower clearance rates. Equally serious is the use of clearance rates to quantify the impact of ACT regimen changes, as this strategy will plausibly miss even very substantial increases in drug effectiveness. In particular, the malaria community may be missing the opportunity to dramatically increase ACT effectiveness through regimen changes, particularly through a switch to twice-daily regimens and/or increases in artemisinin dosing levels. The malaria community therefore appears overreliant on a single metric of drug effectiveness, the parasite clearance rate, that has significant and serious shortcomings.

INTRODUCTION

The timely provision of effective antimalarial drugs is a public health priority in most of the developing world (1). The current generation of antimalarial drugs centers on artemisinin-based combination therapies (ACTs), and recent reports that tolerance of and/or resistance to artemisinins is evolving (2–7) have caused considerable concern (8–12). ACTs remain largely effective in clearing malaria infections, but reduced parasite clearance rates (i.e., the rate at which parasitemia declines after treatment [13]) have been widely interpreted as indicating the presence of reduced parasite sensitivity to the artemisinin component and hence indicative of the early stages of resistance (2–12). Parasite clearance rates have also been used to evaluate the likely clinical impact of alterations in artemisinin or ACT dosing regimens (14) that may be able to increase ACT effectiveness and hence reduce the threat of resistance. It therefore seems reasonable to expect that parasite clearance rates are a well-validated, demonstrably robust measure of drug effectiveness and resistance. Unfortunately, this appears not to be the case, as reflected in concerns raised in recent commentaries (15–17). Herein, the pharmacology of drug action, parasite biology, and human immunity are combined to investigate the dynamics of parasite clearance following ACT. This reveals the basic properties of the metric and allows critical review of the use of the parasite clearance rate as an indicator of drug effectiveness and resistance.

The parasite clearance phenotype is as follows. The microscopically observed number of infected red blood cells (iRBCs) following ACT fluctuates for a brief period of around 6 to 20 h posttreatment (18–20). This initial fluctuation is usually explained by the imbalance between the introduction of new merozoites into the circulation from sequestered schizonts and the depletion of circulating iRBCs through sequestration. This is then followed by a sustained linear decline in log iRBC numbers over the next 40 to 60 h (18–20). The slope of this linear decline is the parasite clearance rate, and there are well-established protocols for its measurement (20, 21). One critical point to note is that artemisinins have a very short half-life of around 40 min in humans (22) and are present as short pulses of active concentrations for only 4 to 6 h posttreatment (23). This means that the initial artemisinin pulse has effectively been eliminated from the circulating blood by the time the linear clearance dynamics (which define parasite clearance rates) occur. The practical consequence is that iRBC clearance rates measured more than ∼6 h posttreatment cannot be a direct measure of the effectiveness of artemisinin in its first pulse (because the artemisinin is no longer present) but must be an indirect proxy measure. Importantly, the subsequent short pulses of artemisinin treatment in an ACT regimen, typically at 24 and 48 h after the first treatment, do not usually show as increased clearance rates at these points, again emphasizing the indirect nature of iRBC clearance as a measure of current drug killing.

The observed reductions in parasitemia following drug treatment are invariably referred to as “parasite” clearance rates. In reality, clinical observations consist of counts (actually the density) of iRBCs, which may contain live, dead, or dying malaria parasites (24). This was noted by Kremsner and Krishna (25), who discussed clearance times after drug treatment and concluded that “a circulating parasite might be alive, injured (fatally), or dead in these circumstances.” Similarly, Watkins et al. (26) stated that “the stained blood film, although it can be accurate and reproducible, provides only a total parasite count from which viable and nonviable counts cannot be differentiated.” The difference between parasite clearance and iRBC clearance is not merely semantic; the fact that iRBCs must be cleared (i.e., removed from the blood circulation by the spleen or other host mechanisms), rather than the parasite being cleared directly, is important. An iRBC presents a complex target to the human immune system, implying that immunity will play a large role in the dynamics of clearance. The impact of host immunity can therefore reduce both the sensitivity and the specificity of iRBC clearance as a diagnostic of drug effectiveness. The term “iRBC clearance rate” is used here in place of the more usual “parasite clearance rate” to emphasize what is actually being observed and measured. Readers will be aware that the terms are synonymous, but the former is more technically correct. The principal research questions addressed herein are to consider the likely relative contributions of drug effectiveness and host defense mechanisms to the iRBC clearance rates observed in patients after ACT and to evaluate the use and application of iRBC clearance rates as research and surveillance tools.

MATERIALS AND METHODS

Failure rates of ACTs are currently very low (1), so it is not statistically feasible to compare in vivo iRBC clearance rates in patients whose drug treatment was successful with those in patients whose treatment was unsuccessful (for example, Ashley et al. (7) reported a cure rate of 98% in their study of 1,241 patients in Southeast Asia). Even if such a comparison were possible, immunity is likely to affect both therapeutic outcomes and iRBC clearance rates, causing a correlation that could be mistaken for causality (as explained later). These circumstances dictate that pharmacological modeling be used to simulate ACT and to investigate the properties of iRBC clearance rates when used as an indicator of drug effectiveness.

Pharmacological model.

A pharmacological model of artemisinin drug treatment incorporating drug stage specificity was constructed on the basis of the standard model first implemented by Hoshen et al. (27) and used by several subsequent authors (23, 28). Its construction and calibration are detailed in Part S1 of the supplemental material. Briefly, the parasite population is split into 48 developmental “age bins” corresponding to each hour of the Plasmodium falciparum 48-h life cycle. At each hour posttreatment, the drug kills some of the parasites in each age bin (if the drug is present and active against that developmental age bin) and surviving parasites are then moved into the next development stage. Parasites in the 48th age bin rupture to release new parasites (default of 10 per schizont), and the latter are moved into the 1st age bin. This enables the number of parasites in each age bin to be tracked each hour posttreatment.

Drug killing rates are expressed in units per hour and are obtained from the more familiar parasite reduction ratio at 48 h (PRR₄₈), which is the ratio of the number of parasites present at the start of treatment divided by the number remaining 48 h later, for the methodological reasons explained in the text around Equation S1.1 in the supplemental material. As a reference to interpret these killing rates on an hourly scale, killing rates of 0.19, 0.14, and 0.096 are equivalent to PRR₄₈ values of 10⁻⁴ (because e^{−48 × 0.19} = 10⁻⁴), 10⁻³, and 10⁻², respectively, assuming that all parasite stages are equally sensitive. In fact, not all stages are equally sensitive, which is why the killing rates for the sensitive stages have to be increased to compensate for the lack of killing in the nonsensitive stages to maintain the same PRR₄₈ values (see the supplemental material for details).

Previous work (27, 28) typically did not track the fate of parasites once they were dead within iRBCs, as the studies focused on drug effectiveness, and the clearance dynamics of dead parasites were of no interest. A simple extension was added to this basic methodology; rather than assuming that killed parasites are instantaneously removed from the circulation, those killed while inside circulating iRBCs are moved into a “dead-but-circulating” population of iRBCs that is cleared by the host at a clearance rate determined by host factors. Parasites killed while in sequestered iRBCs are assumed to die in situ and do not re-enter the circulation (see the discussion in Part S1 of the supplemental material). The same strategy has been used previously by other authors. Hietala and colleagues (29), following Gordi et al. (30), fitted a “spleen clearance” compartment to their pharmacokinetic/pharmacodynamic (PK/PD) analyses of patients treated with the ACT artemether-lumefantrine. They found that inclusion of a spleen clearance rate of 0.26/h (equivalent to a half-life of 2.7 h), as reported by Gordi et al. (30), provided a better fit to the data. The term “spleen clearance rate” will be used here to quantify the rate at which iRBCs containing dead or dying parasites are removed from the circulation by host defenses. It is synonymous with the “spleen and macrophage clearance rate” used previously by Hietala, Gordi, and colleagues (29, 30). The use of spleen clearance rate is for clarity and to avoid any ambiguity with iRBC clearance, but readers will realize that iRBC clearance is a complex drug-dependent process that also depends on immunity, the spleen, and possibly other host factors (in fact, patients without spleens can still clear their infections) and that spleen clearance rate is simply a convenient term covering all of these factors; a more detailed discussion of host defenses and access to the primary literature can be found elsewhere (18). We also assume that all circulating iRBCs are counted to obtain the clearance rate, as guidelines for microscopy in research settings do not distinguish between live and dead parasites (31). There are variants of this procedure. Parasites may be scored as dead or alive on the basis of their morphology (although this is particularly difficult in vivo, where circulating parasites are predominantly early ring stages) and clearance rates would subsequently be based on the reduction of “live” parasites (20). Alternatively, direct counts may be replaced with molecular surrogates such as quantitative PCR and clearance may be quantified as the reduction in the quantitative PCR signal (32).

Sensitivity analysis of iRBC clearance rates and drug effectiveness.

The parameterization of the methodology is described in Part S1 of the supplemental material. Individual parameter values were varied systematically within calibrations to isolate the effect of changing single parameters (see the discussion of Fig. 1 below). A sensitivity analysis was then performed by simulating 5,000 patients treated with either dihydroartemisinin-piperaquine (DHA-PPQ) or artesunate-mefloquine (AS-MQ). Each patient had an initial parasite number of 10¹², which may be uniformly distributed across all age bins or may be predominantly in early ring stages. Note that the initial parasite number has no effect on the subsequent shape of dynamics in the model output except to alter the time until circulating parasites become undetectable. The following four factors were varied during the sensitivity analysis: the artemisinin killing rate, the duration of artemisinin killing after treatment (specified as an integer, i.e., number of hours), the partner drug killing rate, and the spleen clearance rate (see the text surrounding Equation S1.2 in the supplemental material for the technical details of drug killing). The correlations among these four factors, drug effectiveness, and iRBC clearance rates were measured. Drug effectiveness was quantified by using the conventional metric of the PRR₄₈. More effective treatments will kill more parasites and consequently will result in a higher PRR₄₈.

FIG 1.

The lack of sensitivity of clearance rates to changes in artemisinin killing. Changes in artemisinin killing may arise in two ways. First, the duration of killing posttreatment will alter if parasites evolve resistance (measured as a reduced concentration at which drug killing is half its maximum value) or if the intake dose given to patients is changed. The left column shows the effect of varying the duration of artemisinin killing from 1 to 8 h after each dose (the default value being 6 h). Panel A shows the impact on the observed iRBC clearance rate. Panel B shows the impact on drug effectiveness quantified as the PRR₄₈. Second, the artemisinin killing rate may changes as parasites evolve resistance. The right column shows the effect of varying the artemisinin killing rate from 10 to 120% of the default value. Panel C shows the impact on the observed iRBC clearance rate. Panel D shows the impact on drug effectiveness quantified as the PRR₄₈. The two drugs investigated were AS-MQ and DHA-PPQ. Parasite sensitivity to AS and DHA follows “isosensitivity” or “hypersensitivity” PD profiles, respectively, and the dosing was either once or twice daily. All simulations had spleen clearance rates set to 0.231/h (equivalent to a clearance half-life of 3 h). See Part S1 of the supplemental material for technical details. Note that the red and green dotted lines are superimposed on panels B and D, as are the blue and black dotted lines. Note also that PRR₄₈ does not fall to zero, as partner drug killing alone would achieve a PRR₄₈ of around 10³.

Impact of dosing regimen and increasing parasite cell cycle time on iRBC clearance rates.

Concerns over the future effectiveness of ACTs and the lack of readily available alternatives have driven attempts to increase clinical effectiveness through changes in deployment regimens. One such strategy is to increase the dosage given. This is predicted to result in an increased duration of drug killing after treatment (33; see the discussion of Fig. 1 below). Another strategy is to split the dosage regimen. The specific example of splitting the standard 3-day regimen of DHA-PPQ into twice-daily dosing was then investigated (see Part S1 of the supplemental material for details). Theory and intuition suggest that the main impact will be on artemisinin, rather than partner drug, killing (33; see our companion paper in this issue [34]), so simulations were run with and without PPQ killing, the latter to remove the complicating factors of PPQ drug action.

There has been speculation (35) that mutations in the P. falciparum kelch13 (K13) propeller domain may be associated with increased cell cycle duration. The K13 mutations appear to have reduced drug sensitivity during the hypersensitive early ring stages (36). The likely impact of a simple increase in cell cycle time on iRBC clearance rates was investigated by increasing the cell cycle time from 48 to 57.6 h (a 20% increase) or to 72 h (a 50% increase). The impact of simultaneously increasing the cell cycle time and reducing drug sensitivity was investigated by modifying the hypersensitive profile (see Part S1 of the supplemental material) so that malaria parasites became insensitive to artemisinin during their hypersensitive early ring age bins.

RESULTS

The model recovered the main features of iRBC clearance dynamics that occur after artemisinin treatment; i.e., the characteristic linear decline in the number of circulating iRBCs following artemisinin treatment was routinely observed. Moreover, this linearity was not affected by additional killing periods due to subsequent doses of artemisinins (e.g., see Fig. 2).

FIG 2.

An example of the lack of sensitivity of parasite clearance rates to changes in drug effectiveness caused by regimen changes. Blue lines are “parasite clearance rates,” i.e., the number of circulating iRBCs containing either live or dead parasites. Green lines are the number of circulating iRBCs containing live parasites. Black lines are total parasitemia, i.e., the total number of live parasites in both circulating and sequestered iRBCs. Red horizontal bars indicate when DHA is present at active concentrations, and the gray horizontal band indicates the parasite detection limit below which circulating parasites cannot be realistically detected or counted by routine microscopy. The drug simulated is DHA alone (top row) and in combination with PPQ (bottom row). The left column is the drug(s) given once per day over 3 days, and the right column is an alternative regimen in which the same total amount of drug(s) is given but split into twice-daily doses given over 3 days. The spleen clearance rate of iRBCs containing dead parasites is assumed to be 0.26/h, as estimated by Gordi et al. (30), equivalent to a spleen clearance half-life of 2.7 h. The drug sensitivity profiles follow the hypersensitivity model, i.e., where early ring stages are hypersensitive to DHA. The infection at the start of treatment was primarily in early ring stages (mean, 10.5 h; standard deviation, 5 h). For the modeling details, see Part S1 of the supplemental material.

The results from the sensitivity analysis of PRR₄₈ and iRBC clearance rates are shown on Table 1. The correlations among the artemisinin killing rate, the partner drug killing rate, the duration of artemisinin killing, and overall drug effectiveness measured as the PRR₄₈ are high. However, negligible correlations were observed between these factors and iRBC clearance rates (recall that the PRR₄₈ is the change in the total number of living parasites, both circulating and sequestered, whereas iRBC clearance is the change in the number of circulating iRBCs that may contain either living or dead parasites). The main correlation of iRBC clearance rates is with the spleen clearance rate, indicating that the latter is the dominant force determining iRBC clearance rates and almost entirely obscures any impact of the artemisinin killing rate, the partner drug killing rate, the duration of artemisinin killing, or the PRR₄₈ on iRBC clearance rates. Drug effectiveness, measured as the PRR₄₈, is essentially invisible; the largest correlation between the PRR₄₈ and iRBC clearance is 0.04 in the simulated data sets, whereas the correlation between the spleen clearance rate and iRBC clearance is >0.93 in all simulations and generally very close to 1. These are correlation coefficients, and squaring their values quantifies the proportion of the variability in iRBC clearance rates that may be explained by the differing factors. Drug effectiveness parameters therefore explain a maximum of 0.16² = 2.5% of the variation in the iRBC clearance rates (Table 1), while spleen clearance rates explain between 0.93² = 86% and 1² = 100% of the variability.

TABLE 1.

Sensitivity analysis showing coefficients of correlation between drug effectiveness (measured as PRR₄₈) or iRBC clearance rates and underlying drug and host parameters^a

Drug and parameter	Isosensitivity				Hypersensitivity
	Uniformb		Early ringb		Uniformb		Early ringb
	PRR48	iRBCcr	PRR48	iRBCcr	PRR48	iRBCcr	PRR48	iRBCcr
DHA-PPQ
Artemisinin duration (h)	0.18	0.05	0.17	0.02	0.18	0.08	0.21	0.08
Artemisinin killing rate (h−1)	0.19	0.05	0.18	0.08	0.19	0.10	0.22	0.15
Partner killing rate (h−1)	0.14	0.03	0.14	0.02	0.15	0.04	0.14	0.09
PRR48		−0.01		0.00		0.04		0.03
Spleen clearance rate (h−1)		0.99		0.99		0.99		0.93
AS-MQ
Artemisinin duration (h)	0.19	0.02	0.20	0.01	0.19	0.01	0.19	0.07
Artemisinin killing rate (h−1)	0.21	0.04	0.22	0.05	0.20	0.06	0.21	0.16
Partner killing rate (h−1)	0.14	0.00	0.15	0.02	0.13	0.01	0.14	0.11
PRR48		0.01		0.00		0.01		0.04
Spleen clearance rate (h−1)		1.00		0.99		0.99		0.93

^aThe model parameters investigated were the duration of artemisinin killing after dosing (Artemisinin duration), the magnitude of the artemisinin killing rate, the magnitude of the partner drug killing rate, and the spleen clearance rate of circulating iRBCs containing dead parasites. The drugs investigated were DHA-PPQ and AS-MQ. Two artemisinin sensitivity profiles were investigated (the iso- and hypersensitivity profiles), and the starting stage distribution of parasites may be either uniform or early ring stage. See Part S1 of the supplemental material for more explanation and technical details. iRBCcr, iRBC clearance rate.

^bParasite distribution at time of treatment.

Mutations that affect the intrinsic drug susceptibility of malaria parasites were found to act in two main ways (we later discuss the possible impact of changes in cell cycle duration). First, such changes may alter the duration of artemisinin killing after treatment (33), although this will have little impact on iRBC clearance rates unless the duration of killing falls to less that around 2 h (Fig. 1A), despite the large impact of a reduced duration of killing on drug effectiveness (Fig. 1B). This clearly shows that iRBC counts by microscopy are highly insensitive to changes in artemisinin drug effectiveness and can detect changes only once parasite susceptibility to artemisinin has fallen to very low levels. Even a reduction in the duration of killing by 83% from 6 h to 1 h posttreatment was predicted to reduce iRBC clearance rates by only around 10% (i.e., from around 0.22 to 0.20) despite drug killing (PRR₄₈) falling by factors of up to 10¹⁰.

The second way in which the impact of a mutation(s) on the parasite's intrinsic susceptibility to artemisinin may be manifested is in reductions in killing rates. In the model, reduced artemisinin killing rates were found to exhibit little impact on the iRBC clearance rate until they reached very low levels. A mutation(s) that reduces artemisinin killing rates below around 20% of wild-type levels may become detectable as reduced iRBC clearance rates, although, as might be expected intuitively, the magnitude of this reduced iRBC clearance depends on the stage distribution of parasites at the time of treatment (Fig. 1C). Once again, this low sensitivity occurs despite the huge impact that changing artemisinin killing rate has on drug effectiveness (Fig. 1D).

One common method of increasing a drug's effectiveness in the face of resistance is to increase the amount of the drug given to patients (within the limit of toxicity). Pharmacologically, this increases the duration of artemisinin killing after treatment, and its predicted impact has already been shown in Fig. 1; dose increases that extend the duration of killing for more than around 2 or 3 h posttreatment are unlikely to be detected when using iRBC clearance rates (Fig. 1A), despite the huge changes in drug effectiveness that arise from such dose increases (Fig. 1B). This suggests that iRBC clearance rates have low sensitivity for monitoring the impact of drug regimen changes based on dose escalation.

An alternative method to increase drug efficacy that does not involve increasing the total dose is to change the dosing regimen. The consequences of splitting the dose of DHA-PPQ into a twice-daily dosing regimen are shown in detail in Fig. 2. As predicted (34), drug effectiveness varied substantially (by a factor of 10⁸), with the PRR₄₈ values being 1.7 × 10⁴, 9.8 × 10⁷, 1.8 × 10⁸, and 1.0 × 10¹² for Fig. 2A to D, respectively. Despite these differences in ACT effectiveness, the clearance rates are identical in each panel of Fig. 2, suggesting that clearance rates are unable to detect even huge changes in drug effectiveness. The impact of the additional doses of artemisinin on total parasitemia are quite clear (Fig. 2B versus A and D versus C), but the effects of spleen clearance rates and the constant background killing of PPQ obscure these differences to the extent that observed iRBC clearance rates (blue lines) are not sufficiently sensitive to detect even the substantial impact on total drug killing that occurs as the dosage is split and given twice daily. In this case, the slope of the observed iRBC clearance (blue line) measured in its linear portion between 18 and 48 h was 0.26/h in all cases despite the large differences in artemisinin killing rates (black lines).

The impact of extending the parasite's cell cycle time from 48 to 57.6 h (a 20% increase) or to 72 h (a 50% increases) are shown on Table S1 in the supplemental material. Changes in iRBC clearance rates are small and occur only when spleen clearance rates are relatively high, i.e., with half-lives in the region of 2 h. Moreover, the impact is unpredictable, sometimes lowering clearance rates and sometimes increasing them. The largest alteration was of the latter, i.e., clearance rates increasing from 0.34/h to 0.43/h when the cycle time was extended from 48 to 72 h (see Table S1 in the supplemental material, i.e., the example of DHA-PPQ with an isosensitive profile used to treat an early ring stage infection in a patent whose endogenous clearance rate was 0.35/h). It therefore seems unlikely that small-to-moderate increases in cell cycle time could explain the increasing clearance rates currently being observed in Southeast Asia. Note that this is only a small pilot exploration designed to reveal whether extending the cell cycle time has a consistently large impact. It was assumed that the increase in cell cycle length affected all age bins equally, while a more nuanced analysis would investigate more complex patterns where the increase in cell cycle length was due to changes in the amounts of time spent in specific age bins (such as early rings) (35).

DISCUSSION

The results presented here have such wide-ranging implications that the discussion will be split into four distinct sections to maintain focus and to enable readers to navigate through the separate strands of the discussion.

Consistency with previous results.

It is widely recognized that immunity affects the iRBC clearance rate, since high immunity is associated with faster clearance. A review by White (18) specifically noted that “As immunity increases … parasite clearance is accelerated so the slopes of parasite clearance curves become steeper.” Commentators are also aware of this effect. Uhlemann and Fidock (9), for example, stated that “The shift in parasite clearance rates with time could have various causes, including waning immunity as interventions reduced exposure of patients to parasites.” It has long been known that increasing failure rates of other drugs can be due to decreased immunity rather than increased resistance. For example, Greenhouse and colleagues (37) concluded that the increasing drug failure rates in their longitudinal study were due to decreasing levels of immunity rather than changes in parasites drug resistance levels. Similarly, Lopera-Mesa et al. (38) reported that clearance rates at their study sites most likely reflected differences in patients' immune status. The results presented above show that immunity, which clearly contributes to spleen clearance rates, is most likely the dominant factor determining iRBC clearance rates.

Clearance rates have been used to quantify drug effectiveness and in surveillance programs designed to detect drug resistance (2–4, 6, 7, 39, 40; see references 15 to 17 for critical appraisals of these usages). The theoretical underpinning of their use in this context follows this simple logic. The presence of detectable parasites in a patient 3 days after treatment is known to be a risk factor for drug failure (41). The iRBC clearance rates partially determine whether or not parasites are detectable at day 3 (initial parasitemia also plays a role). Consequently, lower parasite clearance rates must be associated with an increased risk of day 3 positivity and therefore be associated with increased failure rates. This logic appears robust, but note the last step, i.e., that lower clearance rates are associated with increased failures but do not necessarily cause failures. It is a basic tenet of data analysis that association does not imply causation. It is highly plausible that this association arises from a common factor, human immunity (42), which affects both the iRBC clearance rate and the eventual probability of treatment failure, and that interpreting this association as causation is logically unsound. Another complicating factor is that malaria infections, especially in high-transmission areas, are genetically heterogeneous and clearance rate of the majority of iRBC may not reflect the ultimate fate of the infection (treatment success or failure), as the latter may depend on the presence or absence of low-density resistance genotypes present as minority clones in the infections (43).

Our simulations allow a detailed consideration of the dynamics of iRBC clearance. This suggests the underlying reason why host immunity is the main determinant of iRBC clearance rates. Artemisinins are present at active concentrations for around 4 to 6 h posttreatment. The proportion of circulating parasites killed by artemisinin during this period will be called the initial kill burst (IKB). Clearance measures are typically delayed for 6 to 20 h after treatment to allow the log-linear decline in the iRBC count to become established and measurable (21). This delay is therefore likely to largely exclude the factor we are really interested in measuring, the extent of artemisinin killing in the IKB; artemisinin killing occurs before iRBC clearance rates are estimated, so it makes no contribution to the subsequent iRBC clearance rate. The subsequent rate of decline of circulating iRBCs then most likely measures how rapidly host clearance mechanisms remove iRBCs containing dead or dying parasites killed during the IKB.

This interpretation also explains the clinical observation that subsequent doses of artemisinin (indicated by horizontal red lines in Fig. 2) have no further impact on clearance rates. The dynamics can be understood as the interactions among the three factors that determine iRBC clearance dynamics, i.e., spleen clearance rates, sequestration rates, and new merozoite release rates. These rates differ substantially. Spleen clearance rates have half-lives in the region of 2 to 5 h. Sequestration rates depend on the number and developmental stages of circulating parasites, but half have been sequestered by age bin 14, so half-lives may be approximated as 14 h (although this is more for illustration, as it forces an exponential decline onto a very complex sequestration regimen; see Part S1 of the supplemental material). Finally, sequestered parasites have a half-life of around (48 − 14)/2 = 17 h before their schizonts release new merozoites into the circulation. Sequestration and new merozoite release rates are therefore both substantially lower than spleen clearance rates, but these rates must be scaled by the number of parasites in each group. The dynamics can therefore be understood as follows. The first few hours of nonlinearity occur because the IKB has to establish a sufficient number of iRBC with dead parasites such that the spleen clearance rates completely dominate the other two factors and hence dominate the overall dynamics of iRBC clearance. Subsequent doses of artemisinin may kill a large proportion of the remaining viable circulating parasites, but this will be invisible because, as noted above, it is impossible to distinguish circulating iRBC with live, dead, or dying parasites (26). This interpretation is supported by clinical data from Wootton and colleagues (44), who estimated the proportion of viable parasites among circulating iRBCs to be <0.5% following treatment with 2 or 4 mg/kg of AS, a clear demonstration that treatment with ACTs results in a huge pool of dead iRBCs awaiting spleen clearance.

Implications for assessment of drug effectiveness.

One of the main opportunities to increase drug effectiveness is by regimen changes, typically increasing the total dosage given to patients and/or changing dosing patterns. This is particularly important given current concerns that artemisinin resistance may be spreading and threating the therapeutic effectiveness of ACTs.

The first option to increase drug effectiveness is to increase the artemisinin dose; this essentially increases the duration of killing after treatment (33). Figure 1A and B suggest that iRBC clearance rates will be unable to detect even substantial increases in artemisinin killing that occur above a duration of killing threshold of around 2 to 3 h posttreatment. It is possible to convert this threshold into one based on drug intake doses. We investigated what DHA intake dosages would result in 2 or 3 h of parasite killing by using standard PK/PD modeling with our default DHA parameters (see Table 1 of reference 45). An intake DHA dose of ∼0.2 mg/kg resulted in a duration of artemisinin killing after treatment of around 2 h, while an intake dose of ∼0.5 mg/kg resulted in a duration of killing of around 3 h for reference, the currently recommended DHA dosage is 4 mg/kg, giving a duration of killing of around 5 to 6 h (see Fig. 3 in reference 34). Hence, the threshold of 2 to 3 h in Fig. 1A equates to a DHA intake dose of around 0.2 to 0.5 mg/kg. In practice, this threshold will be higher because there is substantial PK/PD variation in nature and so a considerable proportion of patients treated with 0.5 mg/kg of DHA would have durations of killing much shorter than 3 h. Using a rule of thumb of 3-fold variation in PK/PD (45, 46) suggests that the threshold of detection, above which additional artemisinin killing will not be detected by iRBC clearance rates (Fig. 1A), will probably lie somewhere in the region of 3 × 0.5 = 1.5 mg/kg. Angus et al. (47) concluded that no further increase in iRBC clearance rates occurs above doses of around 2 mg/kg. They administered AS, which has a higher molecular weight than DHA (384 versus 284 g/mol, respectively), meaning their 2 mg/kg of AS was equivalent to a DHA dose of 2 × 284/384 = 1.5 mg/kg. Their results are therefore highly consistent with the threshold identified in our model, although visual inspection of their raw data (Fig. 2 and 3 of reference 47) suggests that this threshold for the detection of increased AS killing by iRBC clearance rates may plausibly be lower than 2 mg/kg. Similarly, Saunders and colleagues (48) reported no difference in iRBC clearance times or rates when dosing with AS at 2, 4, or 6 mg/kg; again, these results are highly consistent with our model prediction that all three doses would lie above the detection threshold. Angus et al. (47) asserted that no further increase in iRBC clearance rates occurred above 2 mg/kg because higher doses had no further impact on drug killing. A clear alternative interpretation is that their metric, the iRBC clearance rate, simply lacks the sensitivity required to detect further increases in parasites killing (Fig. 1A). If the latter interpretation is true, it clearly indicates an opportunity to increase ACT drug effectiveness through the relatively simple expedient of increasing the artemisinin dose, at least within the levels restrained by toxicity.

Another strategy to improve drug effectiveness is to split the standard dose and give it more frequently. In ACT, this essentially means switching from a single daily dose to twice-daily dosing (as is currently done for artemether-lumefantrine (AM-LF), noting that the need for twice-daily dosing is driven by the LF rather than the AM component). The total dose remains unchanged, so the twice-daily dose has half the drug content of the once-daily dose. Pharmacological modeling of clinical data suggested that this could increase drug effectiveness (28). Our more recent quantitative PK/PD modeling (34) identified its mechanistic basis (it arises from the law of diminishing returns in antimalarial drug dosing [33]) and showed that split dosing is a far more effective strategy for improving artemisinin's effectiveness than simply increasing the total amount of artemisinin given. Figure 2 illustrates the comparative dynamics of daily and twice-daily dosing in more detail on the basis of current DHA-PPQ regimens and separates out the effect of artemisinin alone (top row) with the effect of including the partner drug PPQ (bottom row). The clear conclusion is that the split-dose strategy will result in increased drug effectiveness but that iRBC clearance rates primarily reflect patient immune status and so were similar in all cases and unable to detect the changes in drug effectiveness. Note that this is robust over a range of calibrations and partner drugs; the latter have such long half-lives that our model output suggests that the impact of split dosing is immaterial for partner drugs, it is the artemisinin killing that increases so dramatically with split-dose regimens.

Unfortunately, attempts to implement ACT split-dose regimen changes are currently hindered by a trial (14) that evaluated twice-daily regimen changes by using iRBC clearance rates as an indicator of drug effectiveness and reported no difference in clearance rates. A key operational question is therefore to decide whether this is a valid measure of drug efficacy or whether it reflects an inherent lack of sensitivity in the metric being used to estimate effectiveness. We therefore suggest an alternative interpretation of the results of Das et al. (14); no differences in clearance rates occurred between different regimens because the overwhelming impact of immunity on clearance rates would have obscured differences in drug killing between the regimens. The huge costs of developing a new drug and the potential risks to human subjects as drugs enter clinical development make it operationally and ethically essential to use well-validated clinical indicators of likely efficacy. It seems essential that the malaria community now reconsiders drug regimen changes as a means to offset, or even prevent, the early stages of resistance (34).

Implications for monitoring for drug resistance.

The most widespread application of clearance rates has occurred in surveys of ACTs in Southeast Asia, where reduced iRBC clearance rates have been routinely interpreted as indicating reduced drug effectiveness due to the onset of artemisinin “resistance” (see reference 49 for a review of the recent literature and Part S2 of the supplemental material for a discussion of the genetic analysis of iRBC clearance rates). The studies have used both artemisinin monotherapy (7, 39, 40) and artemisinins within ACTs (3, 50); the much higher potency of the artemisinin component against circulating stages (compared to its partner drugs within ACTs) means that artemisinins are the main determinants of clearance rates within ACTs, so the two types of studies, monotherapies and ACTs, can be viewed as equivalent in terms of their clearance phenotypes (18, 34). The results presented above show that iRBC clearance rates are a highly insensitive surveillance tool for resistance detection, as they can only detect resistance if it is sufficiently strong (or immunogenic [see below]) that virtually all of the parasites within circulating iRBCs survive the treatment. This is presumably the case with the newly identified K13 mutations (51), which appear to virtually remove parasite hypersensitivity in the early ring stages, allowing its detection through increased iRBC clearance rates. Note also that it is possible that some partner drugs may kill some circulating parasites, which would produce a pool of dead parasites within iRBCs that could partially obscure the effects of changing artemisinin sensitivity on iRBC clearance rates (see the discussion of the three iRBC clearance factors above). Consequently, it could be that artemisinin resistance may be detected as increased clearance time in ACTs whose partner drugs do not kill circulating parasites, while no such increase in clearance may be noted in ACTs whose partner drugs do kill some circulating iRBCs. Hence, a strategy of using artemisinin monotherapy to measure iRBC clearance rates (prior to the partner drug being administered) is a preferable strategy.

iRBC clearance rates also have potentially very low specificity, as other factors, notably, falling patient immunity, may cause slower clearance and be erroneously interpreted as indicating “resistance.” At least three reviews (15–17) have pointed out that declining levels of immunity may have contributed to the decreased clearance rates observed in Southeast Asia and have been confused with changes in drug sensitivity levels (see also references 52 and 53 for examples of the subsequent discussion). Given the concerns over the impact of possible artemisinin resistance (8–12), it seems imperative to properly design a surveillance strategy and recognize the dangers of overreliance on iRBC clearance rates as the sole surveillance tool. The properties of the K13 mutations, principally, their resistance to artemisinins while in circulating early ring forms (54) combined with possible changes in progression through early (but not later) stages of the parasite's nominal 48-h cycle (35), seem ready made to allow their detection through reduced iRBC clearance rates. However, there is no guarantee that other artemisinin resistance mutations will be so obliging, and indeed, it is possible that they may already be present but remain undetected; for example, mutations in the ap2-mu gene have been shown to modulate artemisinin sensitivity in both the murine and human forms of malaria (55, 56). Plowe (57), for example, noted that the K13 gene need not be the only artemisinin “resistance” gene and we require a surveillance method to detect other mutations. As stressed here, iRBC clearance rates are unlikely to be sufficiently sensitive to detect all manifestations of artemisinin resistance, and other surveillance tools, such as screening for genetic sweeps (58, 59) and in vitro sensitivity assays, need to be more widely recognized and used in surveillance for resistance.

Conclusions.

It is widely recognized that immunity makes a potentially substantial contribution to iRBC clearance rates and that fitting a “dead-awaiting clearance” class of iRBCs improves the model fit to clinical data (29, 30). It therefore seems extraordinary that there has been no objective investigation of the impact of host immunity on the use of iRBC clearance rates as surveillance tools for drug resistance and as efficacy tools for evaluating drug regimen changes. This was the impetus for the work presented here. Our model output suggests that host clearance processes such as immunity completely dominate the iRBC clearance phenotype unless artemisinin effectiveness is extremely low. This makes iRBC clearance rates highly insensitive to changes in underlying parasite drug sensitivity and to drug effectiveness cause by regimen changes.

The purpose of this study had been to open a more objective debate about the use of iRBC clearance rates posttreatment as proxy measures of drug effectiveness and resistance. It is possible, perhaps even likely, that iRBC clearance rates reflect the level of an individual patient's acquired immunity to malaria (38), with the degree of parasite resistance or drug effectiveness being effectively invisible against this background. The World Health Organization set up an action plan to contain artemisinin resistance in 2011 (60). It was laudable to act on this initial evidence, but no serious attempts appear to have been made in the subsequent few years to validate the use of the parasite clearance rate as a good metric of parasite resistance (15–17). The use of iRBC clearance rates as measures of drug effectiveness is particularly worrying, with the likely consequence that regimen changes capable of increasing drug effectiveness may be ignored, as they have little impact on iRBC clearance rates (34) (Fig. 2).