*2.6. Model Development*

PPK analysis was conducted with a non-linear mixed effects model (NLME) approach through the Phoenix NLME (8.1 version, Pharsight, Certara Inc., Princeton, NJ, USA) program. In addition, PPK model development was performed in the first order conditional estimates method with extended least squares (FOCE-ELS) estimation (with ŋ–ε interaction).

As the first step of PPK modeling, data were fitted to two or one compartment disposition models with first order elimination and absorption kinetics without or with absorption lag-time for determining the structural base model (without covariates). In addition, a multiple transit model with a compartment added to the absorption phase was evaluated to establish the structural base model. The final selection of structural base model was performed by the statistical significance between models using goodness-of-fit (GOF) plots, twice the negative log likelihood (-2LL), and Akaike's information criterion (AIC). The initial values for the parameters used in this process were obtained and referenced using NCA and classic compartment models. As a result, the basic PK parameters were as follows: clearance for the central compartment (CL), absorption lag time (Tlag), volume of distribution for the central compartment (V), first oral absorption rate constant (Ka1), and second oral absorption rate constant (Ka2).

The residual variability was determined to additive error model in log transformed (plasma concentration) data, as shown in the following equation: Cobs,ij = Cpred,ij·exp(εij), where εij is the intra-subject variability (including model misspecification and assay error) with mean 0 and variance σ 2 , and Cpred,ij and Cobs,ij are the jth predicted and observed plasma concentrations in the ith subject, respectively.

The inter-individual variability (IIV) in PK parameters of tiropramide was evaluated by using an exponential error model, as shown in the following equation: P<sup>i</sup> = Ptv·exp(ŋ<sup>i</sup> ), where ŋ<sup>i</sup> is the random variable for the ith individual, which was normally distributed with mean 0 and variance ω<sup>2</sup> ; P<sup>i</sup> is the parameter value of the ith individual, and Ptv is the typical value of the population parameter.

As a second step of PPK modeling, candidate covariates (including demographic and genetic information) screened during this study were considered in reflecting the structural base model to account for PK diversity of tiropramide in the population. Height, body weight, age, BMI, BSA, creatinine, albumin, AST, ALT, ALP, creatinine clearance, and total protein were used as demographic candidate covariates. Here, BMI was determined by using the metric unit system [13]. BSA was determined on the basis of the Mosteller equation [14]. Creatinine clearance was determined on the basis of the Cockcroft–Gault equation [15]. There were also *ABCB1* 1236C>T, *ABCB1* 2677G>T/A, *ABCB1* 3435C>T, *CYP2D6* (\*1 and \*10), *OCT2* 808G>T, and *PEPT1* 1287G>C as genetic candidate covariates. To confirm the correlation between covariates and PK parameters, these potential covariates were plotted against individual post hoc parameters. In addition, the covariates were divided into categorical and continuous types in order to reflect the identified (correlation with PK parameters) candidate covariates in the PK parameters of the model. Continuous covariates (mainly demographic candidate covariates) were normalized by median values (of observed values). On the other hand, categorical covariates (mainly genetic candidate covariates) were reflected as index variables in the model. The effects of each covariate were confirmed using exponential, power, or additive options. By stepwise backward elimination and forward addition procedure, the covariates were included or eliminated. By change in the objective function value (OFV), the inclusion of covariates was determined. Covariates corresponding to a decrease in the OFV value greater than 3.84 (*p* < 0.05) were included in the base model (in the forward addition procedure). In addition, covariates corresponding to the case where the decrease in OFV value was greater than 6.63 (*p* < 0.01) through the backward elimination process were not removed from the model and were included.
