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.