Integrated Pharmacokinetic–Pharmacodynamic Model for Acetaminophen, Ibuprofen, and Placebo Antipyresis in Children

Abstract

A descriptive profile for antipyretic drug action has been documented for children. However, a linked pharmacokinetic–pharmacodynamic (PK/PD) model is central to the understanding of antipyretic drug action in febrile children. This was examined for previously reported data from 178 febrile children who received a single oral dose of acetaminophen (APAP) (12.5 mg/kg), ibuprofen (IBU) (5 or 10 mg/kg), or placebo. Rectal temperatures and plasma levels (μg/ml) of APAP and IBU were measured for up to 12 hr after drug administration. Nonlinear regression analyses were applied to these measurements and yielded simultaneous solutions of an integrated one-compartment PK, link, and SigmoidE_max effect model in 102/153 febrile children given APAP or IBU. The PK parameters (t_lag ,k_a , β,T₁ / _2β ,AUC_0–∞ ,V_d/F,andCl_p/F) were not different than those reported previously, except the APAPk_a was significantly lower. The link component yieldedk_eo s of 0.58±0.06 (X±SE), 0.70±0.11 and 0.57 ± 0.11 hr ^-1 for APAP, IBU05, and IBU10, respectively: the SigmoidE_max component yieldedEC₅₀ s (μg/ml) and sigmoidicity (γ) of 4.63±0.39 and 3.98±0.42 for APAP, 11.33±1.35 and 3.97±0.58 for IBU05 and 12.83±1.89 and 4.27±0.63 for IBU10. On visual inspection of the efficacy–time profiles of the febrile children, a number of them had an apparent linear function (slope; Δ°C/hr) and/or a sinusoidal cyclic function “confounding” standard approaches to PD analysis. Thus, the temperature profiles of 91/102 children given APAP or IBU required the addition of a slope (Δ°C/hr) and/or a sinusoidal cyclic function to the SigmoidE_max component to fit the data satisfactorily. All 22 children given a placebo also required a slope and/or a cyclic function in their PD model. The residual Δ°Cs (observed-predicted) of the placebo group were not significantly different from 0. Thus, no placebo antipyretic effect was observed. Dose dependency of IBUAUC_0–∞ was confirmed; doubling the dose from 5 to 10 mg/kg increased theAUC_0→∞ by only 1.5-fold. The confounding effect of initial temperature (Temp_i ) on antipyretic efficacy in all treatment groups except placebo was also confirmed to expose nonlinear pharmacodynamics. A significant (p=0.03) contribution ofTemp_i (but not age) on the value of the slope function was found. There was no consistent effect of age orTemp_i , on the cyclic component of the integrated model of antipyresis. In addition, a multiple linear relationship of age andTemp_i was observed with a large number of the PK, link, and PD variables in those who received IBU. Dose, age, andTemp_i interacted with β in a significant multiple linear relationship withAUC_0–∞ . The effects of IBU dose, age, andTemp_i are pervasive and cascade down the chain of events leading to the PD response. The etiology of pyresis may create the slope function, the magnitude of which may be partially due to the underlying disease. In some cases, the cyclic function may be explained by temperature regulation. Regardless of their cause, both confound analysis of drug action and make the simple, unmodified SigmoidE_Max effect model less than satisfactory for interpretation of antipyretic drug effects. The influence of Temp_i on the magnitude of antipyretic drug response is also a finding with major impact on PD investigations of antipyretic medications. In children receiving IBU, dose and age are also confounders, in addition toTemp_i . A multiplicity of covariables must be taken into account when developing appropriate dosing regimens for these antipyretics in febrile children.