□ Population pharmacokinetic analysis
The population pharmacokinetic analysis was performed using Monolix 2019R2 (Lixoft SAS, Antony, France), which incorporates the stochastic approximation expectation-maximization (SAEM) algorithm. The model was parameterized in terms of volumes (Vn), elimination clearance (CL) and distribution clearances (Qn). Between subject variability (BSV) of the parameters was assumed to be log-normally distributed. The individual parameter estimate values (\(\theta_{i}\)) are modeled according to Equation 1.
\(\theta_{i}=\theta_{\text{pop}}\cdot e^{\eta_{\theta,i}}\) (1)
Where \(\theta_{\text{pop}}\) is the typical population parameter mean and \(\eta_{\theta,i}\) is assumed to be the random individual deviation from \(\theta_{\text{pop}}\). The random effects are log-normally distributed with zero as a mean and a variance of \(\omega^{2}\). Residual error was described by a proportional error model. For the\(j\)th observed concentration of the \(i\)th individual, the relation for observation \(Y_{\text{ij}}\) is described by Equation 2.
log(\(Y_{\text{ij}})={\log(c}_{\text{pred},\ \text{ij}})+b\cdot{log(c}_{\text{pred},\ \text{ij}})\cdot\epsilon_{\text{ij}}\)(2)
Where \(c_{\text{pred},\ ij}\) is the predicted propofol concentration for the \(j\)th concentration of the \(i\)th individual, \(b\) is the proportional error term and \(\epsilon_{\text{ij}}\) is assumed to be a standardized Gaussian random variables representing residual error the for the \(j\)th concentration of the \(i\)th individual, with zero as a mean and a variance of \(\sigma^{2}\). Covariate modeling was performed by successive inclusion starting from the base structural model, guided by a priori physiological plausibility and plots of covariates vs. empirical Bayesian parameter estimates. Inclusion of covariates and selection of the modeled covariate structure was judged based on decrease in objective function values (OFV), expressed as minus two times log likelihood (-2LL), the Akaike information criterion (AIC), the Bayesian-Schwartz information criterion (BIC) and visual inspection of diagnostic plots. Diagnostic plots to evaluate model fit included visual predictive checks (VPC), goodness of fit (GOF) plots of both population and individual estimates and distributions of the random effects. All diagnostic plots were stratified by study. Additionally, the standard errors of the parameter estimates were also evaluated to compare competing models.