·To explore the application of nonlinear mixed effects model based on the allometric equation on up-and-down data to determine the half effective dose (ED₅₀) in pediatric patients.

·Twenty-two pediatric patients aged 2 to 12 years with obstructive sleep apnea (OSA) who were undergoing drug-induced sleep endoscopy (DISE) were enrolled. All patients received intravenous bolus S⁺-ketamine 0.5 mg/kg. At the same time, a predetermined bolus dose of dexmedetomidine was infused continuously over 10 min for anesthesia induction. The bolus dose of dexmedetomidine was calculated according to the Dixon up-and-down method with initial dose 1.0 μg/kg and step size 1.2 times. DISE was conducted 10 min after dexmedetomidine infusion, and the response of the patients to the procedure was recorded. Dixon-Massey formula and nonlinear mixed effects model fitting are used to calculate ED₅₀.

·There were 9 and 13 children with successful and failed sedation. The value of dexmedetomidine ED₅₀, 1.9 μg/kg, calculated by Dixon-Massey formula was similar to the fitting value, 2.0 μg/kg, of nonlinear mixed effects model. The introduction of allometric equation significantly improved the model (P<0.05). After normalizing adults' body weight to 70 kg, the ED₅₀ and ED₉₅ were 5.76×(body weight/70) μg/kg and 11.5×(body weight/70) μg/kg, and the slope (γ) of the dose-response relationship of dexmedetomidine is 4.25.

·The experimental data from the up-and-down method can be fitted with a nonlinear mixed effects model based on the allometric equation. Compared with the Massey formula, the advantage is that the ED₅₀, ED₉₅ and γ can be determined at the same time, and this method helps to determine the possible effect of covariates.