Interspecies Allometric Scaling of Antimalarial Drugs and Potential Application to Pediatric Dosing

Abstract

Pharmacopeial recommendations for administration of antimalarial drugs are the same weight-based (mg/kg of body weight) doses for children and adults. However, linear calculations are known to underestimate pediatric doses; therefore, interspecies allometric scaling data may have a role in predicting doses in children. We investigated the allometric scaling relationships of antimalarial drugs using data from pharmacokinetic studies in mammalian species. Simple allometry (Y = a × W^b) was utilized and compared to maximum life span potential (MLP) correction. All drugs showed a strong correlation with clearance (CL) in healthy controls. Insufficient data from malaria-infected species other than humans were available for allometric scaling. The allometric exponents (b) for CL of artesunate, dihydroartemisinin (from intravenous artesunate), artemether, artemisinin, clindamycin, piperaquine, mefloquine, and quinine were 0.71, 0.85, 0.66, 0.83, 0.62, 0.96, 0.52, and 0.40, respectively. Clearance was significantly lower in malaria infection than in healthy (adult) humans for quinine (0.07 versus 0.17 liter/h/kg; P = 0.0002) and dihydroartemisinin (0.81 versus 1.11 liters/h/kg; P = 0.04; power = 0.6). Interpolation of simple allometry provided better estimates of CL for children than MLP correction, which generally underestimated CL values. Pediatric dose calculations based on simple allometric exponents were 10 to 70% higher than pharmacopeial (mg/kg) recommendations. Interpolation of interspecies allometric scaling could provide better estimates than linear scaling of adult to pediatric doses of antimalarial drugs; however, the use of a fixed exponent for CL was not supported in the present study. The variability in allometric exponents for antimalarial drugs also has implications for scaling of fixed-dose combinations.

INTRODUCTION

The World Health Organization and standard pharmacopeial sources recommend that antimalarial drugs be administered at the same weight-based (mg/kg of body weight) or linear dose for children and adults (1). However, this linear method of dosage calculation is known to underestimate the optimum pediatric dose of many drugs (2–5). Recent clinical reports indicate that higher doses of sulfadoxine-pyrimethamine (6, 7), chloroquine (6, 8, 9), quinine (10), piperaquine (11–14), and artesunate (15, 16) are required for effective antimalarial therapy in children.

Allometric scaling is a well-established technique for relating physiological or pharmacokinetic parameters to body weight (17–22), and allometric relationships have been demonstrated for a wide range of drugs, including antimicrobial agents (23–27). The conventional applications of interspecies allometric scaling include prediction of human doses by extrapolation from preclinical animal studies and dose estimates for other mammalian species in veterinary medicine (18, 23, 26, 28). Increasing interest has been shown in the application of interspecies allometric scaling data to predict pharmacokinetic parameters or drug doses in children (27, 29, 30). Despite a paucity of reports on antimalarial drugs (31, 32), interpolation of allometric scaling of chloroquine supports recommendations from clinical studies for higher chloroquine doses in children (8, 9, 33).

The rationale for using scaling techniques to estimate pharmacokinetic parameters in children is that relatively few pediatric pharmacokinetic investigations are conducted, compared to adult studies, and sparse sampling is normally required because there are practical and ethical limitations to obtaining rich pharmacokinetic data sets from pediatric subjects (34). One alternative to conventional interspecies scaling is fixed-exponent scaling from human adult pharmacokinetic data (2–5, 34–37). The principle of scaling with a fixed exponent (e.g., 2/3 or 3/4) may provide some consistency and practical advantages; however, the validity of a universal exponent in pharmacokinetics is subject to conflicting evidence and debate (3, 5, 27, 34–40). Regardless of the scaling method that is used, caution is required for recommendations for very young children, due to immature clearance mechanisms, and for disease states for which there are limited data available or evidence that clearance may be altered in compromised patients (30, 35, 36).

We sought to investigate the allometric scaling relationships of antimalarial drugs using data from pharmacokinetic studies of healthy and malaria-infected mammalian species. Our hypothesis was that linear scaling (i.e., exponent of 1.0) would not apply and that interpolation of interspecies allometric scaling would be suitable for estimating pediatric doses of antimalarial drugs.

MATERIALS AND METHODS

Data collection.

A comprehensive literature search was conducted via PubMed, OvidSP, Google Scholar, and citation records, using relevant key words, including the specific antimalarial drugs and mammalian species. The initial target list of antimalarial drugs was determined from WHO treatment guidelines (1): artemisinin, artesunate, artemether, dihydroartemisinin, mefloquine, amodiaquine, piperaquine, chloroquine, quinine, primaquine, lumefantrine, sulfadoxine-pyrimethamine, atovaquone, proguanil, tetracycline, doxycycline, and clindamycin. Exclusions comprised fixed-dose combinations where data for individual drugs were not readily available (sulfadoxine-pyrimethamine, artemether-lumefantrine, atovaquone-proguanil), drugs for which pharmacokinetic data were available from fewer than three mammalian species (amodiaquine and lumefantrine), and drugs that are contraindicated in children (tetracycline and doxycycline). Chloroquine (33) and doxycycline (41) had been studied previously and were excluded.

The pharmacokinetic studies were screened for suitability of the data, with a focus on uniformity of biological matrix (especially for quinolines with high blood-plasma ratio), period over which blood and plasma samples were collected for the pharmacokinetic study (preferably >3 half-lives), route of administration, and use of validated analytical methods. Although pharmacokinetic parameters from studies with intravenous (or parenteral) drug administration are preferred for allometric scaling, other routes of administration were more appropriate for some antimalarials, such as those which are available only as oral formulations. The final list of drugs (and routes of administration) was as follows: artemisinin (intravenous [IV], intraperitoneal, and oral), artesunate (IV) and the active artemisinin metabolite dihydroartemisinin (from IV artesunate), artemether (IV and intramuscular), mefloquine (oral), piperaquine (oral), quinine (IV), and clindamycin (IV).

Pharmacokinetic parameters.

Clearance (CL), volume of distribution during terminal phase (V_z), and half-life (t_1/2) data were collated or determined from the available data using model-independent equations (CL = k × V; V_z = CL/k). Comprehensive pharmacokinetic data (e.g., mean residence time [MRT] and steady-state volume of distribution [V_ss]) were reported in a limited range of studies and therefore were not included in the present analysis. In studies where different doses were administered to the same subjects and there was no evidence of dose-dependent variability, the mean value of the pharmacokinetic parameter was used. However, if separate groups were given different doses within a study, the data were treated independently except when the results were reported as group data. In human studies where body weight was not reported, 60 kg was used for Asian and African subjects, whereas 70 kg was used for Caucasian subjects, based on standard references and other reports used in the present study. The body weight of animals was not provided in some nonhuman studies; hence, published standard body weights of the respective species were used for the allometric scaling (17, 25, 28, 42).

Allometric scaling.

Simple allometry was the principal method of interspecies scaling, using the equation

$$Y=a\times W^b$$ (1)

where Y is the pharmacokinetic parameter (e.g., CL or V_z), W is the body weight of the species, a is the coefficient, and b is the allometric exponent (19, 24, 38).

The pharmacokinetic parameter data were plotted against body weight on a log-log scale (SigmaPlot version 12.5; Systat Software, Inc., Chicago, IL) to determine the allometric coefficient and exponent by regression analysis.

Data from healthy control subjects were used for the allometric scaling, as there were insufficient pharmacokinetic studies in malaria-infected nonhuman species for each antimalarial drug that was investigated. However, pharmacokinetic parameters from human (adults) studies of malaria infection were compared to the healthy-control data, as a guide to the application of allometric interpolation to decisions on pediatric doses.

Maximum life span potential (MLP) correction.

Several alternative methods of scaling and use of correction factors have been proposed and reviewed (17–19, 26, 43, 44), although the physiological relevance and application of some methods were not applicable in the present study. The most relevant and best-studied method for our consideration was MLP correction, which is an integral feature of the “rule of exponents” approach (26, 44). According to the rule of exponents, simple allometry is the best predictor for exponents in the range from 0.50 to 0.70, whereas CL × MLP provides the best prediction method when the range is 0.71 to 0.99 (44). As the CL exponent from simple allometry was <1 for all antimalarial drugs, we compared MLP correction to simple allometry.

The maximum life span potential (MLP) was calculated from the equation (17)

$$\text{MLP}=10.839\times {\text{BW}}^{0.636}\times {\text{B}}^{-0.225}$$ (2)

where BW is brain weight in grams and B is body weight in grams (the coefficient 10.839 is replaced with 185.5 if the brain and body weights are in kg [44]). Brain and body weight data for mammalian species are well established (17, 42, 45).

The CL × MLP data were plotted against body weight on a log-log scale (SigmaPlot) to determine the coefficient and exponent by regression analysis. Clearance exponents from simple allometry and MLP correction were used to determine interpolated CL for children and compared to available clinical study data.

Pediatric doses.

A standard allometric model for pediatric dosing is to use one of the following equations:

$${\text{dose}}_{\text{child}}={\text{dose}}_{\text{adult}}\times {({\text{weight}}_{\text{child}}/{\text{weight}}_{\text{adult}})}^b$$ (3)

$${\text{CL}}_{\text{child}}={\text{CL}}_{\text{adult}}\times {({\text{weight}}_{\text{child}}/{\text{weight}}_{\text{adult}})}^b$$ (4)

where dose_child is the total dose for a child at the specified weight (weight_child), dose_adult is the standard total dose for an adult at the specified weight (weight_adult), and CL_child and CL_adult are the total CL of the drug.

The exponent derived by allometric scaling (equation 1) was applied in the present study (equation 3) to compare calculated doses to pharmacopeial or reference doses for arbitrary weights of 15 kg and 25 kg (children approximately 4 and 8 years of age, respectively). Dose estimates for children less than 2 years were not considered, due to the known physiological and pharmacokinetic differences between very young infants and adults (35, 36).

Statistical analyses.

Data analysis and representation were performed with SigmaPlot version 12.5 (Systat Software, Inc., Chicago, IL). Data are means ± standard deviations (SD) unless otherwise indicated. The 95% confidence interval (CI) was determined for the allometric exponent [95% CI = mean ± (1.96 × standard error)]. The Student t test was used for two-sample comparison as appropriate, with significance at a P value of <0.05.

RESULTS

Simple allometry.

Simple allometric scaling data for CL and V_z are shown in Tables 1 and 2 respectively. A strong correlation was found for both CL and V_z for all antimalarials except V_z for the prodrug artesunate (Tables 1 and 2). Artemether (Fig. 1) is normally administered by intramuscular injection, but the inclusion of IV data from a rodent and rabbit study did not significantly alter the allometric parameters. Artemisinin was given parenterally in the studies of mice and rats, but as oral administration was used in human studies, CL data were corrected for oral bioavailability to facilitate scaling (Table 1). Due to the mixed sources of data, artemisinin was excluded from subsequent analyses.

TABLE 1.

Simple allometric scaling data for clearance (CL) of antimalarial drugs in healthy mammals

Drug	Route of administrationa	No. of speciesb	r2	Allometric exponent (95% CI)	Allometric coefficient	References
Artesunate	IV	4 (r, d, p, h)	0.92	0.71 (0.53–0.88)	7.0	55, 58–62
Dihydroartemisinin (from IV artesunate)	IV	4 (r, d, p, h)	0.94	0.85 (0.68–1.03)	3.3	55, 58–63
Artemether	IM	3 (r, d, h)	0.98	0.66 (0.38–0.93)	3.3	59, 64–66
Artemether	IM or IV	4 (r, rb, d, h)	0.99	0.66 (0.56–0.75)	3.3	59, 64–67
Artemisinin	IV, IP, oral×Fc	3 (m, r, h)	0.92	0.83 (0.69–0.96)	4.2	68–79
Clindamycin	IV	3 (d, r, h)	0.98	0.62 (0.55–0.69)	1.4	80–87
Piperaquine	Oral	3 (m, r, h)	0.99	0.96 (0.86–1.05)	1.6	88–92
Mefloquine	Oral	3 (m, r, h)	0.90	0.52 (0.43–0.61)	0.2	93–110
Quinine	IV	3 (r, d, h)	0.89	0.40 (0.33–0.47)	1.9	111–123

^aIV, intravenous; IM, intramuscular; IP, intraperitoneal.

^bSpecies: m, mouse; r, rat; d, dog; p, pig; rb, rabbit; h, human.

^cArtemisinin dose was corrected for relative oral bioavailability (oral:intramuscular); F = 0.32 (78).

TABLE 2.

Simple allometric scaling data for volume of distribution (V_z) of antimalarial drugs in healthy mammals

Drug	Route of administrationa	No. of speciesb	r2	Allometric exponent (95% CI)	Allometric coefficient	References
Artesunate	IV	4 (r, d, p, h)	0.69	0.54 (0.22–0.85)	3.2	55, 58–62
Dihydroartemisinin (from IV artesunate)	IV	4 (r, d, p, h)	0.99	0.86 (0.78–0.94)	4.2	55, 58–63
Artemether	IM	3 (r, d, h)	0.99	0.93 (0.82–1.05)	12.4	59, 64–66
Artemether	IM or IV	4 (r, rb, d, h)	0.96	1.06 (0.75–1.38)	6.7	59, 64–67
Clindamycin	IV	3 (d, r, h)	0.98	0.81 (0.72–0.91)	2.5	80–86
Piperaquine	Oral	3 (m, r, h)	0.94	1.16 (0.87–1.45)	280	88–92
Mefloquine	Oral	3 (m, r, h)	0.91	0.78 (0.66–0.90)	39.8	93–110
Quinine	IV	4 (r, rb, d, h)	0.92	0.88 (0.74–1.01)	4.61	111–124

^aIV, intravenous; IM, intramuscular.

^bSpecies: m, mouse; r, rat; d, dog; p, pig; rb, rabbit; h, human.

FIG 1.

Simple allometric scaling relationship with 95% confidence interval (---) for CL of artemether and quinine. Artemether scaling (top) comprised data from 5 studies (▲). The scaled estimate of CL for a 10-kg child (△) was 1.5 liters/h/kg. By comparison, the mean adult CL is 0.88 liter/h/kg (Table 3), the estimated CL based on a fixed exponent of 3/4 is 1.4 liters/h/kg, and the CL from one clinical study in children (9.5 kg) was 1.5 liters/h/kg (150). Quinine scaling (bottom) comprised data from 12 studies (●). The scaled estimate of CL for a 15-kg child (○) was 0.37 liter/h/kg. By comparison, the mean adult CL is 0.17 liter/h/kg (Table 3), the estimated CL based on a fixed exponent of 3/4 is 0.25 liter/h/kg, and the CL from one clinical study in children (15 kg) was 0.24 liter/h/kg (118).

The 95% CI for CL of piperaquine, mefloquine, and quinine did not encompass 2/3 or 3/4, hence the application of these fixed exponents could not be supported by the present data (Table 1, Fig. 1). Linear dosing of piperaquine could be supported, based on the 95% CI for CL in the present analysis (Table 1).

The 95% CI for V_z encompassed unity for three of the seven drugs: artemether, piperaquine, and quinine (Table 2). Volume of distribution is normally used in calculations of loading dose and in pharmacokinetic modeling; therefore, no further analysis of V_z was undertaken for the purposes of the present study.

Control versus malaria.

In the absence of pharmacokinetic data from malaria-infected nonhuman species for each antimalarial drug, a direct comparison of pharmacokinetic parameters from human (adult) healthy controls and malaria-infected patients was performed (Table 3). Artesunate could be excluded on the basis that dose predictions according to the active metabolite dihydroartemisinin may be more appropriate. Apart from quinine and dihydroartemisinin, which showed significantly lower CL in malaria infection than in healthy controls, the P values were >0.1 and the power of the analyses were <30% for the other antimalarial drugs. Despite limited data, it was also apparent that CL of quinine in malaria infected children is likely to be significantly lower than CL in healthy controls (Table 3). The power of the analysis for dihydroartemisinin CL was <80%; hence, a type I error cannot be excluded in the present study.

TABLE 3.

Clearance of antimalarial drugs in malaria-infected patients compared to healthy adults

Drug	Route of administrationa	CL (liters/h/kg) (no.of groupsb)		Healthy vs. malaria		Referencesb
		Healthy	Malaria	P value	Power
Artesunate	IV	1.9 ± 0.6 (3)	2.9 ± 0.8 (8)	0.09	0.4	55, 60, 62, 125–130
Dihydroartemisinin (from IV artesunate)	IV	1.11 ± 0.16 (3)	0.81 ± 0.2 (8)	0.04	0.56	55, 60, 62, 125–131
Artemether	IM	0.88 ± 0.35 (2)	1.8 ± 0.9 (2)	0.32	0.13	64, 65, 132, 133
Piperaquinec	Oral	0.86 ± 0.65 (6)	1.55 ± 0.73 (4)	0.15	0.28	56, 88, 90, 91, 134–137, 154
Mefloquine	Oral	0.030 ± 0.014 (17)	0.039 ± 0.014 (5)	0.24	0.21	94–109, 138, 139
Quinine	IV	0.17 ± 0.05 (6)	0.07 ± 0.03 (9)	0.0002	0.99	112, 114–117, 122, 140–145
Quinine (children)	IV	0.24 (1)	0.064 ± 0.014 (5)	NAd	NA	118, 146, 147

^aIV, intravenous; IM, intramuscular.

^bData are means ± SD. Some studies comprised several groups.

^cPiperaquine studies included piperaquine alone and piperaquine-dihydroartemisinin data for healthy volunteers, but only piperaquine-dihydroartemisinin data for patients with malaria. Our data and a previous report (148) indicate that there is no significant difference in piperaquine clearance when administered alone or in combination with dihydroartemisinin.

^dNA, not applicable.

MLP correction.

The MLPs for mice, rats, rabbits, dogs, pigs, human adults, 15-kg children, and 25-kg children were 2.7, 4.8, 8.7, 20, 16, 93, 109, and 106 years, respectively. The effect of MLP correction is therefore to multiply CL 3- to 5-fold in rodents, 16- to 20-fold in dogs, pigs, sheep, and cows (17), 35-fold in horses, 93-fold in adult humans, and >100-fold in human children. The result was that scaling extended over four orders of magnitude (Fig. 2). Compared to simple allometry (Table 1), the r² for MLP-corrected scaling of CL for dihydroartemisinin (0.99), mefloquine (0.96), and quinine (0.98) improved, but the r² for artemether (0.98), clindamycin (0.96), and piperaquine (0.99) was similar or slightly lower.

FIG 2.

Allometric scaling relationship for clearance of dihydroartemisinin. (Top) Simple allometric scaling of data from 7 studies (▲). The scaled estimate of CL for a 15-kg child (△) was 2.2 liters/h/kg. By comparison, the mean adult CL is 1.1 liters/h/kg (Table 3), the estimated CL based on a fixed exponent of 3/4 is 1.6 liters/h/kg, and the CL from one clinical study in children (13 kg) was 2.2 liters/h/kg (149). (Bottom) CL × MLP correction (y axis) for the same 7 studies (●). The scaled estimate of CL for a 15-kg child (○) is 0.53 liter/h/kg.

The effect of MLP correction on interpolated prediction of CL in children, compared to simple allometry, is shown in Table 4. Results for interpolation of simple allometry for artemether and quinine are illustrated in Fig. 1, with interpolation at 10 kg and 15 kg, respectively, to facilitate comparison with clinical study data (Table 4). Dihydroartemisinin scaling by both simple allometry and MLP correction is provided in Fig. 2. Predictions based on simple allometry were close to the results from clinical studies of dihydroartemisinin and artemether, albeit in children with malaria infection (Table 4). In contrast, simple allometry showed an overestimation of CL for mefloquine and quinine. It was observed that MLP correction routinely underestimated CL (Table 4).

TABLE 4.

Antimalarial drug clearance from clinical studies in children compared to interpolated CL from simple allometry and MLP correction

Drug	Allometric exponenta		Interpolated CL (liters/h/kg)a		Clinical studyb
	Simple allometry	MLP correction	Simple allometry	MLP correction	CL (liters/h/kg)	Wt (kg)	Reference
Dihydroartemisinin	0.85	1.31	2.21	0.48	2.16	13	149
Artemether	0.66	1.18	1.52	0.35	1.5	9.5	150
Piperaquine	0.96	1.46	1.40	0.50	1.85c	16	56
Piperaquine	0.96	1.46	1.39	0.57	0.85c	19.1	57
Mefloquine	0.52	1.0	0.068	0.023	0.046d	9.5e	151
Mefloquine	0.52	1.0	0.068	0.023	0.048d	9.5e	152
Mefloquine	0.52	1.0	0.045	0.024	0.026d	23	153
Quininef	0.40	0.93	0.37	0.13	0.24	15.4	118

^aAllometry was conducted in healthy controls; CL/F was determined for piperaquine and mefloquine.

^bData from studies in malaria-infected children; CL/F was determined for piperaquine and mefloquine.

^cPiperaquine CL/F was determined from studies of piperaquine-dihydroartemisinin in malaria-infected children. There is no significant difference in piperaquine clearance when piperaquine is administered alone or in combination with dihydroartemisinin (148). One recent study reported a CL/F of 0.57 liter/h/kg; however, the data were pooled from a previous study of piperaquine-dihydroartemisinin (57) and an investigation of piperaquine-artemisinin (12). A report of a piperaquine CL/F of 0.42 liter/h/kg from capillary blood samples could not be compared directly to investigations using venous plasma samples for determination of piperaquine pharmacokinetic parameters (13).

^dMefloquine CL/F was determined from studies of mefloquine-sulfadoxine-pyrimethamine in malaria-infected children. Mefloquine clearance may be lower when mefloquine is administered in combination with sulfadoxine and pyrimethamine (101).

^eMalaria-infected children were all <2 years of age in these studies; the mean age was 1.6 years.

^fAll quinine data are from studies in healthy controls.

Pediatric doses.

Pediatric dose calculations were based on pharmacopoeial (mg/kg) recommendations (1) and were 10 to 70% higher, according to allometric predictions (Table 5). Mefloquine and quinine had the lowest exponent, which led to predictions 1.6- to 2.5-fold higher than reference doses.

TABLE 5.

Allometric interpolation of antimalarial doses in comparison to current pharmacopeial recommendations

Drug	Route of administration	Standard regimena	Dose (mg) for:
			15-kg child		25-kg child
			Referenceb	Allometryc	Referenceb	Allometryc
Dihydroartemisinin (as IV artesunate)	IV	Dose at 0, 12, 24 h, then once/day (2.4 mg/kg/dose)	35	45	60	70
Artemetherd	Oral	Twice/day for 3 days	40	30	60	40
Clindamycin	Oral	Twice/day for 7 days (10 mg/kg/dose)	150	260	250	360
Piperaquine	Oral	Once/day for 3 days (18 mg/kg/day)	270	290	450	470
Mefloquine	Oral	2/3 total dose day 1; 1/3 total dose day 2 (25-mg/kg total dose)	375	790	625	1,025
Quinine	IV	Three times per day for 5–7 days (10 mg/kg/dose)	150	370	250	460

^aAs reported by the World Health Organization (1) and confirmed by reference to the British National Formulary.

^bBased on mg/kg doses and practical recommendations.

^cBased on reference doses and equation 3, where adult dose was according to a 70-kg body weight and the allometric exponent was from Table 1. Doses were mostly rounded to a 10-mg increment rather than the nearest practical dose.

^dCurrent artemether dose recommendation is for body weight range (1, 2, 3, and 4 20-mg tablets for patients weighing 5 to 14 kg, 15 to 24 kg, 25 to 34 kg, and >34 kg, respectively). The adult (70 kg) dose is therefore the same as that for a child of 34 kg (80 mg), which equates to 1.1 mg/kg for adults and 2.3 mg/kg for the 34-kg child. Hence, current practical dose recommendations are higher (mg/kg) for children and vary within the weight ranges.

Although quinine CL is significantly lower in malaria infection than in healthy controls and data presented in Table 3 suggest that quinine CL is lower in malaria-infected children than in adults (contrary to allometric principles), the allometric exponent for quinine CL (Table 1) was used in the present analysis. Cautious interpretation of the result for quinine is therefore required. However, increased doses for dihydroartemisinin (as IV artesunate), clindamycin, and mefloquine appear to be warranted (a piperaquine dose increase would likely not be clinically relevant or practical).

DISCUSSION

The present study has demonstrated that interpolation of interspecies allometric scaling could be a useful strategy to include in development and refinement of pediatric doses for antimalarial drugs. We found strong allometric relationships for seven drugs (dihydroartemisinin, artemether, artemisinin, clindamycin, piperaquine, mefloquine, and quinine) and showed that linear scaling of clearance is not applicable, although the 95% confidence intervals spanned unity for dihydroartemisinin and piperaquine (Table 1). In contrast, linear scaling of the volume of distribution appeared to be valid for some drugs, notably artemether and piperaquine (Table 2).

Allometric scaling is founded on sound theoretical principles and evidence of a power law relationship between biological parameters and body weight; however, there are conflicting reports on the application of fixed exponents and correction factors (20, 35, 36, 38–40, 46, 47). Historical research on basal metabolic rate established a 2/3 power scaling of body mass and is supported by the concept of scaling surface area to volume of 3-dimensional objects (20, 39). The “1/4 power law” is based on seminal studies that scaled the metabolic rate of animals using an exponent of 3/4 and is reported to be consistent with structure and function observations in biology (20, 21, 38, 39). This power law has been translated to the use of an exponent of 3/4 for drug clearance, 1/4 for elimination half-life, and 1 for volume of distribution (21, 22, 35, 36, 38, 39). It has recently been argued that the small numerical difference between 2/3 and 3/4 powers is of little clinical relevance in pharmacokinetics (36).

The physiological origins of interspecies relationships provide some context for the limitations of allometric scaling in pharmacokinetics, which have been the subject of detailed review (39, 48–50). One limitation of scaling pharmacokinetic parameters that we encountered was a small range of mammalian species and low number of subjects in each study (typically 6 to 16 in human studies and 6 to 8 in other species). We were able to obtain data from only two or three nonhuman species, a finding that is consistent with similar previous investigations (24, 31, 33). However, some pharmacokinetic studies, especially veterinary reports, were compiled with data from at least 8 species (17, 19, 23, 51), and interspecies scaling of physiological parameters, such as basal metabolic rate, comprises data from over 20 species (21). A larger range of animal studies would therefore enhance the quality of allometric scaling data in future studies.

Further limitations may occur if there are species differences in the pharmacokinetic properties of drugs that lead to unpredictable and weak allometric scaling outcomes (39, 49, 50). Highly protein-bound drugs (>98% in humans), such as mefloquine (52) and piperaquine (53), may have inconsistent scaling if binding is substantially lower in other species. Bioavailability and renal or hepatic clearance mechanisms also may have species differences which could be relevant for antimalarial drugs that are subject to hepatic metabolism and commonly administered as oral formulations. However, there is generally a paucity of relevant data to address these potential limitations in the scaling of pharmacokinetic parameters (49, 50).

Notwithstanding the limitations of interspecies scaling and the power law relationship debate, allometric scaling data indicate that fixed exponents of 2/3 or 3/4 may not be universally applicable in pharmacokinetics (24, 28, 29, 31, 33, 38, 44, 47). Our analyses showed that the 95% CI encompassed both 2/3 and 3/4 for CL of artemether and artemisinin, whereas the upper limit of the 95% CIs for mefloquine, quinine, and chloroquine (0.63, based on reanalysis of a previous study [33]) were all <0.65 (Table 1). In contrast, the allometric exponents for dihydroartemisinin and piperaquine CL were 0.85 and 0.96, respectively, and the 95% CI of the exponent spanned unity. Hence, the use of a fixed exponent for CL of antimalarial drugs is not supported by the present study.

The influence of allometric exponents on interpolated dose predictions can be substantial and varies according to body weight. For example, if the recommended adult dose of a drug is 10 mg/kg (for a 70-kg adult), arbitrary exponents of 0.6 and 0.75 would lead to predicted doses of 18.5 mg/kg and 14.7 mg/kg, respectively, for a 15-kg child and of 15.1 mg/kg and 12.9 mg/kg, respectively, for a 25-kg child. The differential between adult and child doses will decrease for children with higher body weights and will also decrease as the exponent approaches unity. The potential effect of these inverse relationships on dose predictions demonstrates the importance of high-quality data for allometric scaling.

It was evident from our detailed literature search that an extensive range of interspecies scaling for antimalarial drugs was precluded by several factors. In particular, the target list of antimalarials was limited by a paucity of data for individual drugs within some common, fixed-dose combinations, and we could not obtain pharmacokinetic data from a minimum of three mammalian species for amodiaquine and lumefantrine. Studies with intravenous (or parenteral) drug administration would have been optimal, but inclusion of other routes of administration was necessary for artemisinin, artemether, mefloquine, and piperaquine. An important issue was the small body of pharmacokinetic research in malaria-infected nonhuman species for the antimalarial drugs, and this limitation was addressed by comparing drug clearance from studies in malaria-infected human adults with that reported for healthy controls (Table 3). Consistent with previous reports, only quinine was shown conclusively to have significantly different clearance in malaria infection (54). Our data indicate that dihydroartemisinin clearance was higher in healthy controls than patients with malaria infection (Table 3); however, the power of the analysis was inconclusive. The apparent clearance (CL/F) of piperaquine and mefloquine could be higher in malaria infection than in healthy controls (Table 3) and may be a function of altered bioavailability, as has been reported for dihydroartemisinin (55).

Our investigation of the relevance of correction factors for allometric scaling was to ascertain if the more sophisticated approaches to interpolation of interspecies scaling would be beneficial for antimalarial drugs. Some of the techniques require raw concentration-time data (17, 18, 43), which were not available in most reports, and we therefore confined our analysis to maximum life span potential (MLP). This correction method has been incorporated in the rule of exponents, whereby simple allometry is used for exponents in the range from 0.50 to 0.77 and scaling CL × MLP against body weight is recommended when the exponent from simple allometry is in the range from 0.71 to 0.99 (44).

Our study showed that MLP correction led to substantially lower interpolated CL estimates, compared to simple allometry and data from clinical reports, except for one group of children treated with mefloquine (Table 4). We conclude that the application of MLP correction for antimalarial drugs is not supported by the present study. By comparison, simple allometry overestimated the CL/F of mefloquine in children with uncomplicated falciparum malaria, which could lead to excessive dose predictions, and therefore, this requires more detailed, contemporary clinical investigations. Conversely, interpolation from simple allometry provided good estimates of CL for dihydroartemisinin and artemether (Table 4). The piperaquine data appear to be conflicting; however, there were several clinical differences between the two populations and no conclusive explanation for the findings (56, 57). Two recent reports of piperaquine pharmacokinetics showed lower CL/F values, suggesting that the rule of exponents may be applicable to piperaquine, but as noted in Table 4, these data could not be included in the present study due to the use of pooled results from different partner drugs (12) and use of capillary blood analysis to determine the pharmacokinetic parameters (13).

Quinine predictions are problematic, due to the difference in CL (and V_z) between healthy subjects and patients with malaria, and the reported lower CL in children than adults (Table 3). Therefore, cautious interpretation of allometric scaling results are required for quinine, due to the complex and multifactorial effects of malaria infection on the pharmacokinetic properties of this drug.

The final component of our study was to translate the allometric scaling results to dose estimates (Table 5). The recommendations for dihydroartemisinin (as IV artesunate) and clindamycin would be modest increases that can be achieved in the clinical setting, whereas the small predicted increase in piperaquine dose would not be practical. It is notable that recent clinical studies have recommended higher doses for piperaquine (11, 13, 14) and artesunate in children (15). Indeed, the doses proposed in the latter study closely match the allometric predictions of 3 mg/kg (15-kg child) and 2.8 mg/kg (25-kg child), based on scaling for dihydroartemisinin in the present study.

The recommended mefloquine doses were 1.6- to 2-fold higher than reference doses for adults (mg/kg), which could be viewed as excessive and to the best of our knowledge have not been proposed in any clinical studies. However, recent allometric scaling of chloroquine indicated that pediatric doses 1.6-fold higher than those for adults (mg/kg) were potentially appropriate, and these doses were exceeded by clinical studies where 2-fold-higher doses were used in children (8, 9, 33). Complementary data are available for quinine, notwithstanding our cautious interpretation of the allometric scaling. Indeed, our results from simple allometry of quinine suggest that 18 to 24 mg/kg could be more appropriate than 10 mg/kg (Table 5), and a recent study supports earlier recommendations in adults that 20 mg/kg quinine should be used as a loading dose in children (10).

An important consideration from our allometric exponent data is that disproportionate dose increases appear to apply to antimalarial drugs, and the implications for rational pediatric dosing of combination regimens are therefore significant. For example, an adult dose of a dihydroartemisinin-piperaquine (120/960 mg; approximately 2/16 mg/kg for a 60-kg patient) oral fixed-dose combination is reduced by linear calculations to 30/240 mg for a 15-kg child. However, based on our allometric interpolation, this would result in an appropriate scaled dose of piperaquine and a dihydroartemisinin dose that is 20% lower than optimum. Allometric scaling of fixed-dose combinations will be valid only if the same exponent applies to both drugs (or a default-to-fixed-exponent scaling is used); however, our data indicate this is unlikely to be appropriate for artemisinin-based combination therapies, due to mismatch of the allometric exponents (Table 1).

We conclude that interpolation of interspecies allometric scaling is plausible for estimation of pediatric doses of antimalarial drugs and would be valuable in designing clinical pharmacokinetic or efficacy studies. The limitations of allometric scaling are well documented; however, the ongoing use of linear scaling of adult to pediatric doses (mg/kg) is recognized as flawed (36) and should be the subject of further investigation in antimalarial chemotherapy.