Prediction of Unbound Ceftriaxone Concentration in Children: Simple Bioanalysis Method and Basic Mathematical...

The pharmacological activity of ceftriaxone depends on the unbound concentration. However, direct measurement of unbound concentrations is obstructive, and high individual variability of the unbound fraction of ceftriaxone was shown in children. We aim to evaluate and validate a method to predict unbound ceftriaxone concentrations in pediatric patients. Ninety-five pairs of concentrations (total and unbound) from 92 patients were measured by the bioanalysis method that we developed. The predictive performance of the three equations (empirical in vivo equation, disease-adapted equation, and multiple linear regression equation) was assessed by the mean absolute prediction error (MAPE), the mean prediction error (MPE), the proportions of the prediction error within ±30% (P₃₀) and ±50% (P₅₀), and linear regression of predicted versus actual unbound levels (R²). The average total and unbound ceftriaxone concentrations were 126.18 ± 81.46 μg/ml and 18.82 ± 21.75 μg/ml, and the unbound fraction varied greatly from 4.75% to 39.97%. The MPE, MAPE, P₃₀, P₅₀, and R² of the empirical in vivo equation, disease equation, and multiple linear equation were 0.17 versus 0.00 versus 0.06, 0.24 versus 0.15 versus 0.27, 63.2% versus 89.5% versus 74.7%, 96.8% versus 97.9% versus 86.3%, and 0.8730 versus 0.9342 versus 0.9315, respectively. The disease-adapted equation showed the best predictive performance. We have developed and validated a bioanalysis method with one-step extraction pretreatment for the determination of total ceftriaxone concentrations, and a prediction equation of the unbound concentration is recommended. The proposed method can facilitate clinical practice and research on unbound ceftriaxone in children. (This study has been registered at ClinicalTrials.gov under identifier NCT03113344.).