Explaining the acetaminophen-ibuprofen analgesic interaction using a response surface model

The value of acetaminophen-ibuprofen combination therapy over single therapy is uncertain in acute pediatric pain management. A model describing the interaction between these two drugs would be useful both for understanding current literature and for future study design.

Published pooled time-effect profiles in adults given combination or single therapy after dental extraction were used to construct an interaction model. Pain was measured using pain intensity differences (PRID, 0-10) from zero to eight hours postoperatively. Pharmacodynamic parameter estimates were assumed the same in adults as children. Pediatric pharmacokinetic estimates were scaled using allometric theory. Curve fitting was performed using nonlinear mixed effects models.

Pooled data were available in adults given eight single and multiple dose combinations as well as placebo. The ibuprofen dose range was 100-400 mg, and acetaminophen dose range was 500-1000 mg. Pharmacodynamic parameter estimates, expressed using the Hill equation, were maximum effect (E(MAX) ) 4.06 (95% CI: 3.24, 5.51), the concentration of acetaminophen associated with 50% of the maximal drug effect (EC(50,ACET) ) 11.9 (95% CI: 6.0, 49.5) mg·l(-1) , the ibuprofen EC(50) (EC(50,IBU) ) 5.07 (95% CI: 3.50, 8.26) mg·l(-1), and Hill coefficient 2 (95% CI: 1.3, 2.8). An interaction term was fixed at zero (additive interaction). Simulation showed that the addition of acetaminophen to ibuprofen when less than 5 mg·kg(-1) was effective; acetaminophen had minimal effect when given with ibuprofen at doses greater than 5 mg·kg(-1) in the immediate postoperative period. A more sustained analgesic effect was noted at 4-8 h after combination dosing.

This drug interaction modeling example is useful to explain combination therapy nuances and impacts on study design. Differences in effect between single drug therapy and combination therapy should be sought at lower doses and beyond the immediate postoperative period. Combination therapy may prolong the duration of analgesia. The maximum effect (E(MAX) ) limits the early additional analgesic gain from combination therapy beyond commonly used doses.