Pediatric MDD patients treated by sertraline from Xuzhou Oriental Hospital Affiliated to Xuzhou Medical University (Ethical approval number: 20220725011) between September 2021 and January 2024 were collected, retrospectively. Sertraline concentrations of pediatric MDD patients were obtained from therapeutic drug monitoring (TDM) database.

We chose population pharmacokinetics (PPK) as the MIPD model, which was built via the non-linear mixed effect modeling (NONMEM) software (Edition 7.4.1, ICON Development Solutions, Ellicott City, MD, United States). Given trough concentrations, we researched the absorption phase with a one-compartment model. Sparse trough concentrations monitored by TDM could provide insufficient information, and a lag time of absorption and bioavailability (F) could not be evaluated. Therefore, our pharmacokinetic parameters mainly included apparent oral clearance (CL/F), volume of distribution (V/F), and Ka, the absorption rate constant of the model. Furtherly, we attempted to estimate Ka at 0.01/h, 0.4/h, 0.5/h, 0.6/h, 1.0/h, and 2.0/h.

Formula 1 was used to assess the inter-individual variability: A i = TV A × exp η i (1) A_i was individual parameter. TV (A) was typical individual parameter. η_i was the inter-individual variability and represented symmetrical distribution, which was random term with zero mean and variance omega^∧2 (ω²).

Formula 2 was used to assess the random residual variability: B i = C i + C i * ε 1 + ε 2 (2) B_i was observed concentration. C_i was individual predicted concentration. ε₁ was the proportional residual variability and ε₂ was the additive residual variability. ε₁ and ε₂ represented symmetrical distribution, which were random term with zero mean and variance sigma^∧2 (σ²).

Formula 3 was used to assess the relationship of pharmacokinetic parameters with weight: D i = D std × E i / E std F (3) D_i was i-th individual parameter. E_i was i-th individual weight. E_std was standard weight of 70 kg and D_std was typical individual parameter, whose weight was E_std. F was the allometric coefficient: 0.75 for the CL/F and 1 for the V/F (Anderson and Holford, 2008).

Formulas 4, 5 were used to assess the pharmacokinetic parameters between continuous covariates or categorical covariates, respectively: G i = TV G × Cov i   / Cov m θ (4) G i = TV G × 1 + θ × Cov i (5) G_i was individual parameter. TV (G) was typical individual parameter. θ was parameter to be estimated. Cov_i was covariate of the i-th individual. Cov_m was population median for the covariate.

The covariate model of PPK was carried out by a stepwise way, where the objective function value (OFV) changes were selected as the covariate inclusion criteria. The decrease of OFV > 3.84 (P < 0.05) was deemed to the inclusion standard and increase of OFV > 6.63 (P < 0.01) was deemed to the exclusion standard.

The final model was validated using visualization and the median and 2.5–97.5 th percentiles of bootstrap (n = 1,000) were used for comparing with final model parameters.

Monte Carlo simulation was used for forecasting sertraline initial dosage optimization, where the recommended therapeutic window for sertraline in pediatric MDD patients was 10–150 ng/mL (Poweleit et al., 2023). We thoroughly investigated the possible interactions with other drugs that the patients might be using, included alprazolam tablet, aripiprazole tablet, benzoxol hydrochloride tablet, buspirone hydrochloride tablet, clonazepam tablet, diazepam injection, haloperidol injection, levetiracetam tablet, lithium carbonate extended-release tablet, lorazepam tablet, olanzapine tablet, oxazepam tablet, perphenazine tablet, piropilone hydrochloride tablet, pregabalin capsule, propranolol hydrochloride tablet, quetiapine fumarate tablet, sodium valproate sustained-release tablet, sodium valproate tablet, zopiclone tablet. Furtherly, the influential covariates from the PPK model were include in the simulations.

A total of 111 pediatric MDD patients treated with sertraline were included for analysis, where 23 boys and 88 girls, whose ages were from 11.04–16.00 years old, weights were from 35.00–117.00 kg. Demographic data of pediatric MDD patients and drug combination were shown in Tables 1, 2, respectively.

Through evaluation we found that when Ka were at 0.01/h, 0.4/h, 0.5/h, 0.6/h, 1.0/h, and 2.0/h, the OFV were 1,138.021, 1,104.104, 1,104.200, 1,104.208, 1,104.129, 1,104.020, respectively. Combined with the fact that Ka was fixed at 0.5/h in previous literature (Poweleit et al., 2023), we finally fixed Ka at 0.5 in our study. Weight was fixed via allometric exponent (Anderson and Holford, 2008). In addition, it was found that only zopiclone was included in the final model and had significant interaction with sertraline, as shown in Supplementary Table S1 for the research process. Thus, weight and zopiclone co-administration influenced sertraline clearance in pediatric MDD patients. The final PPK model of sertraline in pediatric MDD patients were as follow, which were shown in Formulas 6, 7: CL / F = 74 × weight / 70 0.75 × 1 − 0.547 × ZOP (6) V / F = 874 × weight  / 70 (7) CL/F was apparent oral clearance and V/F was apparent volume of distribution. ZOP was zopiclone, when pediatric MDD patients took zopiclone, ZOP was 1, otherwise ZOP was 0.

Visual evaluation index and VPC of model were shown in Figures 1A–G, respectively, showing the sertraline concentrations were well predicted by the final PPK model. Figure 1H showed that with the same weight, the sertraline clearance rates were 54.7% lower in patients taking zopiclone than those not taking zopiclone. Individual plots were shown in Figure 2, showing the final model may predict the sertraline concentrations of pediatric MDD patients well at the individual level. Table 3 showed the parameter estimates of the final model and bootstrap validation, whose biases were all less than ±3%, showing the final model was accurate and reliable.

On the basis of whether zopiclone was used in combination, and a once-daily or a twice-daily sertraline administration, we simulated four different situations: (1) Once-daily sertraline administration dosage without zopiclone, (2) Twice-daily sertraline administration dosage without zopiclone, (3) Once-daily sertraline administration dosage with zopiclone, (4) Twice-daily sertraline administration dosages with zopiclone, where each situation included 1,000 virtual pediatric MDD patients, six dosages (0.5, 1.0, 2.0, 3.0, 4.0, 5.0 mg/kg/day) for six weight groups (30, 40, 50, 60, 70, 80 kg), respectively. The twice-daily sertraline administration dosage was split evenly into two dosages a day. The evaluation criterion was the probability to achieve target concentrations.

Simulated sertraline concentrations from once-daily sertraline administration dosage without zopiclone, twice-daily sertraline administration dosage without zopiclone, once-daily sertraline administration dosage with zopiclone, twice-daily sertraline administration dosages with zopiclone were shown in Figures 3–6, respectively. The probabilities to achieve the target concentrations were shown in Figure 7, where Figures 7A–D were once-daily sertraline administration dosage without zopiclone, twice-daily sertraline administration dosage without zopiclone, once-daily sertraline administration dosage with zopiclone, twice-daily sertraline administration dosages with zopiclone, respectively. The recommended optimal sertraline initial dosage in pediatric MDD patients were shown in Table 4.

For example, Figures 3A–F were simulated sertraline concentrations from once-daily sertraline administration dosage without zopiclone in pediatric MDD patients with 30 kg, 40 kg, 50 kg, 60 kg, 70 kg and 80 kg, respectively. In Figure 3A, different color “weight boxes” represented concentrations at different simulated dosages, among which the part between the two red dashed lines represented the concentration points reaching the therapeutic window. The evaluation criterion was the probability to achieve target concentrations. In this way, in pediatric MDD patients with 30 kg, simulated 0.5 mg/kg, 1.0 mg/kg, 2.0 mg/kg, 3.0 mg/kg, 4.0 mg/kg, 5.0 mg/kg sertraline dosages corresponded to six probability values of reaching the treatment window, respectively. By analogy, in pediatric MDD patients with 40 kg, 50 kg, 60 kg, 70 kg and 80 kg, simulated 0.5 mg/kg, 1.0 mg/kg, 2.0 mg/kg, 3.0 mg/kg, 4.0 mg/kg, 5.0 mg/kg sertraline dosages, the simulated dosages would correspond to its own probability values of reaching the treatment window. Finally, when the simulated sertraline dosage was 0.5 mg/kg, pediatric MDD patients with 30 kg, 40 kg, 50 kg, 60 kg, 70 kg and 80 kg each has a probability value of reaching the treatment window. Furtherly, we made probability figure, the dark blue line with slanted square was determined by simulated 0.5 mg/kg sertraline dosage, weight as horizontal coordinate and probability value as vertical coordinate. In a similar way, the probability lines of 1.0 mg/kg, 2.0 mg/kg, 3.0 mg/kg, 4.0 mg/kg, 5.0 mg/kg sertraline dosages were done. The simulated dosage with the highest probability in the same body weight range was the optimized dosage, which was shown in Figure 7A, the dosages of 4.0, and 3.0 mg/kg/day were optimization for pediatric MDD patients with body weight of 30–38.5, and 38.5–80 kg, respectively. Similarly, Figures 7B–D were the exploration way of optimized dosage for twice-daily sertraline administration dosage without zopiclone, once-daily sertraline administration dosage with zopiclone, twice-daily sertraline administration dosages with zopiclone, respectively.

In a word, without zopiclone, for once-daily sertraline scheme, the dosages of 4.0, and 3.0 mg/kg/day were suggested for pediatric MDD patients with body weight of 30–38.5, and 38.5–80 kg, respectively, and simultaneously, the probabilities to achieve the target concentrations for the dosages of 4.0, 3.0 mg/kg/day were 84.9%–86.3%, 86.3%–89.7%, respectively; for twice-daily sertraline scheme, the dosage of 2.0 mg/kg/day was suggested for pediatric MDD patients with body weight of 30–80 kg, and simultaneously, the probability to achieve the target concentrations for the dosage of 2.0 mg/kg/day was 97.4%–98.2%. With zopiclone, for once-daily sertraline scheme, the dosage of 1.0 mg/kg/day was suggested for pediatric MDD patients with body weight of 30–80 kg, and simultaneously, the probability to achieve the target concentrations for the dosage of 1.0 mg/kg/day was 96.7%–98.3%; for twice-daily sertraline scheme, the dosage of 0.5 mg/kg/day was suggested for pediatric MDD patients with body weight of 30–80 kg, and simultaneously, the probability to achieve the target concentrations for the dosage of 0.5 mg/kg/day was 98.5%–99.6%.

In other words, how the findings can be applied in real-world settings? When pediatric MDD patients do not take zopiclone at the same time, and if the once-daily sertraline scheme is clinically intended to be adopted, pediatric MDD patients with body weight of 30–38.5, and 38.5–80 kg will be recommended to take 4.0, and 3.0 mg/kg/day sertraline, respectively; If the twice-daily sertraline scheme is clinically intended to be adopted, pediatric MDD patients with body weight of 30–80 kg will be recommended to take 2.0 mg/kg/day sertraline. On the other hand, when pediatric MDD patients take zopiclone at the same time, and if the once-daily sertraline scheme is clinically intended to be adopted, pediatric MDD patients with body weight of 30–80 kg will be recommended to take 1.0 mg/kg/day sertraline; If the twice-daily sertraline scheme is clinically intended to be adopted, pediatric MDD patients with body weight of 30–80 kg will be recommended to take 0.5 mg/kg/day sertraline.