□ 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.