2.2 Linear regression modeling of sublingual absorption
Concentration-time data were extracted from dose-escalation23,26 and dose-linearity28 studies (training data) using WebPlotDigitizer (v4.5, Ankit Rohatgi, Pacifica, CA). Area under the curve (AUC; i.e. , AUC0– ∞ and AUC0–τ for single and multiple dose studies, respectively) and peak concentration (Cmax) following sublingual tablet or solution administration were determined through Bayesian estimation by fitting the buprenorphine population PK model reported by Moore et al .46 to these extracted concentration-time profiles using MWPharm++ (v2.0.4; Mediware Incorporated, Prague, Czech Republic). Subsequently, the proportion of the dose to be sublingually absorbed in the PBPK model to exactly recover the AUC and Cmax observed in the clinical trial (i.e. , ideal proportion) was determined by reviewing PBPK model-based predicted geometric mean AUC and Cmax under various degrees of sublingual absorption. The relationship between AUC- and Cmax-optimized ideal proportion and dose was explored for sublingual tablets and solution separately through linear regression modeling using the stats package (v4.1.2, R Core Team) for R (v4.1.2, R Foundation for Statistical Computing, Vienna, Austria). The following bivariate linear model was used (Equation 1):
Proportioni = α + β × Dose
where Proportioni is the AUC- or Cmax-optimized ideal proportion (%) for clinical studyi , α is the intercept, β is the slope, and Dose is the sublingual tablet or solution dose in milligrams. Visual inspection of the data indicated a linear or inverse exponential relationship between ideal proportion and dose. Therefore, four varieties of the linear model were explored, i.e. , either untransformed or with Dose, Proportioni , or both logarithmically transformed using a decimal logarithm of base 10. Thus, in total, 16 linear regression analyses were performed, namely, four linear model varieties explaining four individual relationships (i.e. , AUC- and Cmax-optimized ideal proportions vs . sublingual tablet and solution doses). The linear model achieving the highest mean coefficient of determination (R 2) across the four individual relationships was selected. AUC- and Cmax‑optimized linear models were subsequently averaged, thereby obtaining two final linear models (one for sublingual tablets and one for sublingual solution) describing the relationship between ideal proportion and dose.