Reliability and uncertainty in the estimation of pK a by least squares nonlinear regression analysis of multiwavelength spectrophotometric pH titration data

Abstract

When drugs are poorly soluble then, instead of the potentiometric determination of dissociation constants, pH-spectrophotometric titration can be used along with nonlinear regression of the absorbance response surface data. Generally, regression models are extremely useful for extracting the essential features from a multiwavelength set of data. Regression diagnostics represent procedures for examining the regression triplet (data, model, method) in order to check (a) the data quality for a proposed model; (b) the model quality for a given set of data; and (c) that all of the assumptions used for least squares hold. In the interactive, PC-assisted diagnosis of data, models and estimation methods, the examination of data quality involves the detection of influential points, outliers and high leverages, that cause many problems when regression fitting the absorbance response hyperplane. All graphically oriented techniques are suitable for the rapid estimation of influential points. The reliability of the dissociation constants for the acid drug silybin may be proven with goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data. The uncertainty in the measurement of the pK (a) of a weak acid obtained by the least squares nonlinear regression analysis of absorption spectra is calculated. The procedure takes into account the drift in pH measurement, the drift in spectral measurement, and all of the drifts in analytical operations, as well as the relative importance of each source of uncertainty. The most important source of uncertainty in the experimental set-up for the example is the uncertainty in the pH measurement. The influences of various sources of uncertainty on the accuracy and precision are discussed using the example of the mixed dissociation constants of silybin, obtained using the SQUAD(84) and SPECFIT/32 regression programs.

The Thermodynamic Dissociation Constants of Clotrimazole, Terbinafine HCL, Acetylsalicylic Acid, Salicylic Acid, and Galanthamine by the Nonlinear Regression of Multiwavelength Spectrophotometric pH-Titration Data

“…Lachema Brno) were not further purified. The preparation of other solutions from analytical reagent-grade chemicals has been described previously [37][38][39][40].…”

“…The apparatus used and the pH-spectrophotometric titration procedure described in [37][38][39][40] were applied. The microscale pH-titrimetric method generally decreases the amount of drug sample required but the duration of experiment is as long as that of a conventional titration.…”

“…The computation scheme for the determination of the protonation constants of the multicomponent system is taken from Meloun et al, cf. [1, page 226] and the five steps are described elsewhere [37][38][39][40][44][45][46][47][48]: (1) instrumental error of absorbance measurements, s inst (A), (2) experimental design, (3) number of light-absorbing species with a factor analysis, (4) choice of computational strategy of the nonlinear regression, (5) diagnostics indicating a correct chemical (protonation) model: when a minimization process terminates, some curve-fitting diagnostics are examined to determine whether the results should be accepted: the physical meaning of parametric estimates, the physical meaning of the species concentrations, the goodness-offit test of spectra calculated, and the deconvolution of the experimental spectra set.…”

“…The procedure for the determination of the mixed protonation/dissociation constants has been described previously [37][38][39][40]. The details of the computer data treatment are collected in the Supporting Information.…”

“…, m, may be examined by a goodness-of-fit test, cf. a previous tutorial [37][38][39][40]. Repeatability and reproducibility (R&R) are critical factors closely related to precision and accuracy.…”