The average steady state plasma concentration was calculated by dividing the AUC over one dosing interval by the time of the dosing
interval. An Emax model (Eq. (1)) was used to describe the relationship between Ku 0059436 plasma concentration and percent efficacy (the effect). The flea or tick count taken 24 h (flea) or 48 h (tick) after infestation was compared to the flea or tick count at the same time on control dogs that were not treated, and a percent difference from control was calculated as follows: 1 − [count (X h post-infestation) for dog i]/[geometric mean count for the control dogs at X h post-infestation] × 100, where count = the number of live fleas or ticks. The percent efficacy versus afoxolaner plasma concentration was input into the WinNonlin® software 3-MA order and fit to a Sigmoid Emax model (Eq. (1)). In the model the Effect is set to 0% when plasma concentrations
are 0. The maximal effect, Emax, is a parameter determined by the model and expected to be close to 100% and is a measure of maximal efficacy. The following equation was used to fit the data: equation(1) Effect(t)=Emax×C(t)GammaC(t)Gamma+EC50Gamma Emax Model EC50 is the plasma concentration corresponding to Emax/2 and is a measure of potency. C(t) is the measured afoxolaner plasma concentration at time t, and Gamma, a measure of the selectivity, is related to the steepness of the plasma concentration versus effect curve. The Nedler Mead algorithm was used without weighting to estimate the parameters of the model. The EC90, the afoxolaner plasma concentration estimated to provide 90% efficacy, was then
calculated using the following equation: EC90=EC50∗90100−901/Gamma Dose proportionality was assessed by calculating the strength of a linear relationship between AUC and dose or between C max and dose using the power method ( Hummel et al., 2009). Log dose versus log AUC0-Tlastlog AUC0-Tlast, AUC0-Inf or C max were fit using linear regression with reciprocal out dose weighting. The upper and lower 95% confidence and prediction intervals also were determined, and the residuals were tested for normality. The parameters (AUC0-TlastAUC0-Tlast, AUC0-Inf or Cmax) were considered to increase proportionally with dose if the slope of the Log dose versus Log parameter curve was completely within the 95% confidence interval of 0.8–1.25. To confirm that the pharmacokinetic processes were linear, afoxolaner plasma concentration versus time curves for each dog following multiple monthly dosing were simulated using parameters from the single dose two-compartment analysis and assuming linear kinetics. The extent of plasma protein binding was greater than 99.9% in dog plasma over the range of afoxolaner plasma concentrations tested (200–10,000 ng/mL).