Assessing the utility of an anti-malarial pharmacokinetic-pharmacodynamic model for aiding drug clinical development

Table 4 Statistical distributions selected for each pharmacodynamic parameter

Parameter	Drug	Distribution^b	Additional details
μ _IPL ^a	DU(4, 16)
σ _IPL ^a	DU(2, 8)
*PMF* ^a	TRI(8, 12, 10)
k _max	ARS/DHA	TRI(0.26, 0.47, 0.37)^c	PRR = 10^5.28; KZ = 38
	ART	TRI(0.12, 0.33, 0.22)^c	PRR = 10^2.9; KZ = 38
	LF	TRI(0.18, 0.54, 0.36)^c	PRR = 10³; KZ = 22
	MQ	TRI(0.11, 0.46, 0.28)^c	PRR = 10^2.25; KZ = 22
	PQ	TRI(0.33, 0.65, 0.49)^c	PRR = 10^4.6; KZ = 24
γ	ARS/DHA	lnN(1.31, 0.65)
	ART	lnN(1.53, 0.31)
	LF	lnN (0.81, 0.58)
	MQ	lnN (0.97, 0.54)
	PQ	lnN (1.35, 0.66)
EC₅₀ (ng/mL)	ARS/DHA	U(1.44, 532.05)	a = $I C 50$ (adjusted)(ng/mL)^b,d; b = 0.5×C_max (ng/mL)^b,d
	ART	U(4.38, 46.20)
	LF	U(1.75, 2331.60)
	MQ	U(20.48, 1087.22)
	PQ	U(11.56, 94.19)

ARS – artesunate, ART – artemether, DHA – dihydroartemisinin, LF – lumefantrine, MQ – mefloquine, PQ – piperaquine.
^aDrug independent parameters.
^bDU – Discrete-uniform (DU (a, b); a < b; a and b positive integers); TRI – Triangular (TRI (a, b, c); a < c < b; a, b and c real numbers); ln N – Log-normal (lnN (μ _ln, σ _ln); μ _ln and σ _ln positive real numbers); and U – Continuous-uniform: (U (a, b); a < b; a and b real numbers).
^cThe mode of the triangular distribution for $k max$ (c) was calculated from the following expression: $k max = 1 / K Z × ln P R R + 1 / 48 × ln P M F$ , where PRR is the parasite reduction ratio for the drug in the corresponding row; KZ is the length of the killing zone in hours for each drug in the corresponding row; PMF in this expression equals 10 parasites / 48 h. The lower /upper limit of the triangular distribution for $k max$ (a/b) is calculated by evaluating the latter expression $k max$ at a PRR decreased/increased by 50-fold (KZ remains unchanged).
^d $I C 50$ (adjusted) = $I C 50$ × (100 – BM / 100) × (100 / 100 - HPPB) × HWB;
BM – binding media; HPPB – human plasma protein binding; HWB – human whole blood to plasma ratio. IC50 (adjusted) values for each drug are given in Table 5 and C_max is the peak plasma concentration of a drug after administration.