The data used in the present study were obtained from clinical routine diagnostic examinations and treatments of shock patients treated between January 2016 and August 2018 at the Zhongda Hospital affiliated to Southeast University (Nanjing, China). The clinical information available from the database was retrospectively reviewed. The retrospective inclusion criteria were as follows: Subjects (patients without shock, septic shock, hemorrhagic shock, neurogenic shock and cardiogenic shock) treated with linezolid (600 mg linezolid every 12 h, intravenously). Regarding the different types of shock, the patients were treated with different therapeutic regimens. In order to avoid the influence of drug interactions from different therapeutic schemes on linezolid pharmacokinetics, the following exclusion criteria were set: Combined use of drugs, which may have affected the pharmacokinetics of linezolid. Blood concentrations were obtained from the records of therapeutic drug monitoring. The associated clinical data were from medical log information. Prior to the present study, the data (blood parameters and medical log information) were already available, no organized collection or biological detection was required, and the information was retrospectively collated and analyzed. Using the already recorded and available blood concentrations and medical log information, the PPK model was built. The present study was approved by the Research Ethics Committee of the Zhongda Hospital affiliated to the Southeast University (Nanjing, China). The present study is a retrospective study and the analysis was approved by the affiliated ethics committee without any requirement for written informed consent.

The medical information included the following parameters: Sex, age, albumin (ALB), globulin (GLB), ALB/GLB (A/G), alanine transaminase (ALT), aspartate transaminase (AST), serum creatinine (SCR), urea, total protein (TP), total bile acid (TBA), total bilibrubin (TBIL), hematocrit (HCT), hemoglobin (HGB), mean corpuscular hemoglobin (MCH) and mean corpuscular hemoglobin concentration (MCHC). In addition, the platelet count (PLT) was measured. Furthermore, the patient status (patients without shock, septic shock, hemorrhagic shock, neurogenic shock and cardiogenic shock) was also recorded.

The data were analysed using the non-linear mixed-effects model (NONMEM) computer program (version VII; ICON Development Solutions). A one-compartment model with clearance (CL) and volumes of distribution (V) was used to describe the pharmacokinetic parameters of linezolid in the population of the present study.

The inter-individual variabilities were evaluated by the exponential error model, according to the following equation:

P_i=T(P) × exp (η_i) (a), where P_i is the individual parameter value, T(P) is the typical individual parameter value and η_i is the symmetrical distribution, which includes zero-mean chance variables with a variance.

The variabilities of the residual error variability were estimated as follows:

OB=IP × (1+ε₁) (b), where OB is the observation and IP represents the individual predicted concentration. ε₁ represents the symmetrical distribution, which includes zero-mean chance variables with a variance.

The following two equations describe the correlation of the parameters between continuous and categorical covariates, respectively.

P_i=T(P) × (Cov_i/Cov_constant)^θ (c) P_i=T(P) × (1 + θ × Cov_i) (d), where P_i is the individual parameter value and T(P) is the typical individual parameter value. θ is the estimated parameter and Cov_i is the covariate of the i-th individual. Cov_constant was fixed at a value similar to the population median of the covariate.

The potential covariates were sex, age, ALB, GLB, A/G, ALT, AST, SCR, UREA, TP, TBA, TBIL, PLT, HCT, HGB, MCH and MCHC levels, as well as the different types of shock. The stepwise-way set-up covariate model and likelihood ratio were used to compare the hierarchical models. The alterations in the objective function values (OFV) were produced by covariate inclusions and a decrease of OFV to >3.84 (P<0.05) was deemed as the inclusion standard of the covariates into the basic model (18,19). Following the establishment of a full regression model, the assessment was performed by deleting covariates from each parameter one by one in order to obtain the final model. An increase in OFV to >6.64 (P<0.01) was considered as a standard for significant associations in the final model (18,19).

The final model was evaluated using bootstrap, an internal validation method, which was generated by repeated random sampling with replacement from the raw database. The process was performed by the software Wings for NONMEM, which performed 1,000 repetitions with different random sampling. The medians and percentiles (2.5–97.5) from bootstrap consequences were used for comparison of these values with those derived from the final model. Visual inspection of routine diagnostic plots included observations vs. individual predictions and absolute value of weighted residuals (iWRES) vs. individual predictions. The prediction-corrected visual predictive check (VPC) plots were used to assess the predictive performance of the final model.

The data of 37 Chinese patients treated with linezolid were analyzed, and their demographic and laboratory data are provided in Table I. The pharmacokinetic profiles of linezolid in patients with different types of shock are provided in Fig. 1A-E. The results revealed that the concentration-time relation from patients with different types of shock or patients without shock demonstrated certain differences. However, whether the differences were a result of patient status or other potential influencing factors requires further study in future research. The population included 18 patients without shock, 11 septic shock patients, 1 hemorrhagic shock patient, 4 neurogenic shock patients and 3 cardiogenic shock patients (Fig. 1F).

All potential covariates were analysed in the present study, and only the PLT on CL covariate exhibited statistical significance. The changes in the OFV are presented in Table II and the final model was constructed as follows:

CL=θ_CL × (PLT/200)^θ_PLT × ω_CL (e) V=θ_V × ω_V (f), where CL, V, θ_CL, θ_V, θ_PLT, ω_CL and ω_V are the clearance, volume of distribution, typical value of CL, typical value of V, the coefficient of the platelet, inter-individual variability of CL and inter-individual variability of V, respectively. The platelet count was included in the covariates and the clearance rate of linezolid was increased in parallel with an increase in the platelet count.

The routine diagnostic plots that were visually inspected are provided in Fig. 2. They included the following comparison of the variables: Observations vs. individual predictions and iWRES vs. individual predictions. The parameter estimates in the final model and internal validation are provided in Table III. From 1,000 bootstrap runs, 992 runs were minimised with a successful covariance step and were included in the bootstrap analysis. The bootstrap median values were approximate to the estimate values in the final model, and the absolute value of all bias was <6%, indicating that the final model was dependent on specific parameters. The VPC plots for the final model are presented in Fig. 3, revealing that the most frequently observed concentration data were included in the 95% prediction intervals produced by the simulation data. Overall, the data suggested that the final model was able to predict drug concentrations with optimal efficiency.