Statistical comparison of the slopes of two regression lines: A tutorial

Comparing the slopes of two regression lines is an almost daily task in analytical laboratories. The usual procedure is based on a Student’s t-test although literature differs in whether the standard errors of the slopes or the standard errors of the regressions should be employed to get a pooled standard error. In this work fundamental concepts on the use of the Student’s test were reviewed and Monte Carlo simulations were done to ascertain whether relevant differences arise when the two options are considered. It was concluded that for small sample sets (as it is usual in analytical laboratories) the Student’s t-test based on the standard error of regression models must be used and special attention must be paid on the equality of the models variances. Finally, alternative approaches were reviewed, with emphasis on a simple one based on the analysis of the covariance (ANCOVA).     

Variable selection in visible/near infrared spectra for linear and nonlinear calibrations: A case study to determine soluble solids content of beer

Three effective wavelength (EW) selection methods combined with visible/near infrared (Vis/NIR) spectroscopy were investigated to determine the soluble solids content (SSC) of beer, including successive projections algorithm (SPA), regression coefficient analysis (RCA) and independent component analysis (ICA). A total of 360 samples were prepared for the calibration (n = 180), validation (n = 90) and prediction (n = 90) sets. The performance of different preprocessing was compared. Three calibrations using EWs selected by SPA, RCA and ICA were developed, including linear regression of partial least squares analysis (PLS) and multiple linear regression (MLR), and nonlinear regression of least squares-support vector machine (LS-SVM). Ten EWs selected by SPA achieved the optimal linear SPA-MLR model compared with SPA-PLS, RCA-MLR, RCA-PLS, ICA-MLR and ICA-PLS. The correlation coefficient (r) and root mean square error of prediction (RMSEP) by SPA-MLR were 0.9762 and 0.1808, respectively. Moreover, the newly proposed SPA-LS-SVM model obtained almost the same excellent performance with RCA-LS-SVM and ICA-LS-SVM models, and the r value and RMSEP were 0.9818 and 0.1628, respectively. The nonlinear model SPA-LS-SVM outperformed SPA-MLR model. The overall results indicated that SPA was a powerful way for the selection of EWs, and Vis/NIR spectroscopy incorporated to SPA-LS-SVM was successful for the accurate determination of SSC of beer.     

Determination of calcium in wine using reconfigurable PSoC based spectrophotometer

This paper discusses the determination of calcium in wine samples using Programmable Systemon-Chip (PSoC) microcontroller. This embedded system uses a PSoC CY8C27443 integrated circuit (IC) spectrophotometer as core unit, high intensity orange LED as light source and photodiode as light detector having the relative spectral sensitivity above 93% in the range of 550–650 nm. This single-chip design reduces hardware complexity and increases the stability by miniaturizing the device. The instrument obeys Beer’s law up to the concentration of 160 mg/L. Coloring agent Methylthymol Blue (MTB) forms a complex with calcium in presence of alkali (pH ≈ 12); the complex exhibits maximum absorbance at 610 nm. The spectral range, concentration of MTB and pH of the solution at which the reaction is carried out are optimized. The results of the developed method are compared statistically with those obtained by a conventional method by applying Student’s t-test and F-test. The regression analysis reveals excellent correlation (R ² = 0.9998) and regression line equation obtained for that line Y = 0.29 + 0.99X with standard error of 0.62. It can be concluded that the obtained results are in good agreement with the reference method at 95% confidence level.     

Simultaneous Determination of Guaifenesin and Theophylline by Chemometrics Methods

In this study, simultaneous spectrophotometry determination of guaifenesin and theophylline in pharmaceuticals by chemometric approaches has been reported. Spectra of mixtures of these drugs were recorded and corresponding first derivatives were calculated. Partial least squares regression (PLS) alone and ant colony optimization (ACO) coupled with PLS were used in analysis of the data. Ant colony system (ACS) as an efficient ACO algorithm was used. In addition, ACS was combined to genetic algorithm (GA) to produce better results. The analytical performances of these chemometric methods were characterized by relative prediction errors. These methods were successfully applied to pharmaceutical formulation.     

Optimization of Pressurized Liquid Extraction and In Vitro Neuroprotective Evaluation of Ammodaucus leucotrichus. Untargeted Metabolomics Analysis by UHPLC-MS/MS

Ammodaucus leucotrichus is a spontaneous plant endemic of the North African region. An efficient selective pressurized liquid extraction (PLE) method was optimized to concentrate neuroprotective extracts from A. leucotrichus fruits. Green solvents were tested, namely ethanol and water, within a range of temperatures between 40 to 180 °C. Total carbohydrates and total phenolics were measured in extracts, as well as in vitro antioxidant capacity (DPPH radical scavenging), anticholinesterase (AChE) and anti-inflammatory (LOX) activities. Metabolite profiling was carried out by ultra-high-performance liquid chromatography coupled to quadrupole time-of-flight tandem mass spectrometry (UHPLC-ESI-q-TOF-MS/MS), identifying 94 compounds. Multivariate analysis was performed to correlate composition with bioactivity. A remarkable effect of the temperature using water was observed: the higher temperature, the higher extraction yield, the higher total phenolic content, as well as the higher total carbohydrates content. The water extract obtained at 180 °C, 10.34 MPa and 10 min showed meaningful anti-inflammatory (IC50_LOX = 39.4 µg/mL) and neuroprotective activities (IC50_AChE = 55.6 µg/mL). The Principal Components Analysis (PCA) and the cluster analysis correlated these activities with the presence of carbohydrates and phenolic compounds.     

The thermodynamic properties of 4-pentenoic acid

The enthalpy of formation of liquid 4-pentenoic acid was determined by combustion calorimetry. The vapor pressure and enthalpy of vaporization of the compound were measured by the transfer method over the temperature range 289–324 K. Conformational analysis was performed. The equilibrium structure, fundamental vibrations, moments of inertia, and total energy of the stablest acid conformers were calculated by the B3LYP/6-311G(d, p) and G3MP2 quantum-chemical methods. The experimental IR spectrum and calculated vibrational frequencies were used to assign IR bands. The thermodynamic properties of monomeric 4-pentenoic acid in the ideal gas state were calculated over the temperature range 0–1500 K. Additive and quantum-chemical methods were used to estimate the Δ_f H°(g) and Δ_vap H° values. Close agreement between the calculation results and experimental data was obtained. It was shown that additive and quantum-chemical methods could be used for estimating the enthalpies of formation and vaporization of nonconjugated alkenoic acids.     

Assessment of quality performance parameters for straight line calibration curves related to the spread of the abscissa values around their mean

In validation of quantitative analysis methods, knowledge of the response function is essential as it describes, within the range of application, the existing relationship between the response (the measurement signal) and the concentration or quantity of the analyte in the sample. The most common response function used is obtained by simple linear regression, estimating the regression parameters slope and intercept by the least squares method as general fitting method. The assumption in this fitting is that the response variance is a constant, whatever the concentrations within the range examined.The straight calibration line may perform unacceptably due to the presence of outliers or unexpected curvature of the line. Checking the suitability of calibration lines might be performed by calculation of a well-defined quality coefficient based on a constant standard deviation.The concentration value for a test sample calculated by interpolation from the least squares line is of little value unless it is accompanied by an estimate of its random variation expressed by a confidence interval. This confidence interval results from the uncertainty in the measurement signal, combined with the confidence interval for the regression line at that measurement signal and is characterized by a standard deviation s_x0 calculated by an approximate equation. This approximate equation is only valid when the mathematical function, calculating a characteristic value g from specific regression line parameters as the slope, the standard error of the estimate and the spread of the abscissa values around their mean, is below a critical value as described in literature.It is mathematically demonstrated that with respect to this critical limit value for g, the proposed value for the quality coefficient applied as a suitability check for the linear regression line as calibration function, depends only on the number of calibration points and the spread of the abscissa values around their mean.     

Towards standardisation of cell-free DNA measurement in plasma: controls for extraction efficiency,fragment size bias and quantification

Circulating cell-free DNA (cfDNA) is becoming an important clinical analyte for prenatal testing, cancer diagnosis and cancer monitoring. The extraction stage is critical in ensuring clinical sensitivity of analytical methods measuring minority nucleic acid fractions, such as foetal-derived sequences in predominantly maternal cfDNA. Consequently, quality controls are required for measurement of extraction efficiency, fragment size bias and yield for validation of cfDNA methods. We evaluated the utility of an external DNA spike for monitoring these parameters in a study comparing three specific cfDNA extraction methods [QIAamp® circulating nucleic acid (CNA) kit, NucleoSpin® Plasma XS (NS) kit and FitAmp? plasma/serum DNA isolation (FA) kit] with the commonly used QIAamp DNA blood mini (DBM) kit. We found that the extraction efficiencies of the kits ranked in the order CNA kit > DBM kit > NS kit > FA kit, and the CNA and NS kits gave a better representation of smaller DNA fragments in the extract than the DBM kit. We investigated means of improved reporting of cfDNA yield by comparing quantitative PCR measurements of seven different reference gene assays in plasma samples and validating these with digital PCR. We noted that the cfDNA quantities based on measurement of some target genes (e.g. TERT) were, on average, more than twofold higher than those of other assays (e.g. ERV3). We conclude that analysis and averaging of multiple reference genes using a GeNorm approach gives a more reliable estimate of total cfDNA quantity. Figure

Comparison of single and multiple reference gene normalisation for quantification of plasma cell free DNA     

Quantitative determination of Malathion in pesticide by modified attenuated total reflectance-Fourier transform infrared spectrometry applying genetic algorithm wavelength selection method

A simple and environment friendly method was developed for determination of Malathion content of analytical and commercial insecticide samples with no special preparation. Attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectra were characterized and 1000-2000 cm⁻¹ region was selected for quantitative analysis utilizing partial least square (PLS) and two wavelength selection methods: (a) principal component regression (PCR) and (b) genetic algorithm (GA). Relative error of prediction (REP) was calculated in PLS, PCR-PLS and GA-PLS methods and was 3.536, 1.656 and 0.188, respectively. Proposed method is successfully applicable for quantification of Malathion in commercial grade samples and reliable results in comparison with known methods, confirms this idea.     

Significance of Non-isothermal Kinetic Data. A statistical study

Arrhenius parameters values, in non-isothermal kinetic vaporisation processes for a series of compounds with related structures, have been calculated. This was made using a method of calculation that allows to find the most probable vaporisation mechanisms. According to this method DTG curves were compared with some theoretical ones reported in literature, whose shape results to be only a function of the mechanisms. In this way the choice of the mathematical functions which can be inserted in the kinetic equations, was influenced by the shape of the DTG plots and other thermal analysis signals thus allowing to choose the most probable mechanisms. The kinetic parameters derived from these mechanisms were compared, using statistical analysis, with those obtained from another method of calculation based on ‘a priori’ vaporisation mechanism chosen for the investigated liquid–gas transition. The standard deviations of the slope and of the intercept, together with the standard deviation and the square correlation coefficient (r ²) of the linear regression equations related to the mechanisms of the two methods were calculated. Student t-test, Fisher F-test, confidence intervals (c.i.) and residuals valueswere also given. Statistical analysis shows that the mechanisms obtained with the former method (diffusive and geometrical models) and the related Arrhenius parameters result to be more significant (in terms of probability) than the corresponding quantities of the latter for which a first-order model was chosen. This revised version was published online in August 2006 with corrections to the Cover Date.     

Cellulose I crystallinity determination using FT–Raman spectroscopy: univariate and multivariate methods

Two new methods based on FT–Raman spectroscopy, one simple, based on band intensity ratio, and the other using a partial least squares (PLS) regression model, are proposed to determine cellulose I crystallinity. In the simple method, crystallinity in cellulose I samples was determined based on univariate regression that was first developed using the Raman band intensity ratio of the 380 and 1,096 cm^?1 bands. For calibration purposes, 80.5% crystalline and 120-min milled (0% crystalline) Whatman CC31 and six cellulose mixtures produced with crystallinities in the range 10.9–64% were used. When intensity ratios were plotted against crystallinities of the calibration set samples, the plot showed a linear correlation (coefficient of determination R ² = 0.992). Average standard error calculated from replicate Raman acquisitions indicated that the cellulose Raman crystallinity model was reliable. Crystallinities of the cellulose mixtures samples were also calculated from X-ray diffractograms using the amorphous contribution subtraction (Segal) method and it was found that the Raman model was better. Additionally, using both Raman and X-ray techniques, sample crystallinities were determined from partially crystalline cellulose samples that were generated by grinding Whatman CC31 in a vibratory mill. The two techniques showed significant differences. In the second approach, successful Raman PLS regression models for crystallinity, covering the 0–80.5% range, were generated from the ten calibration set Raman spectra. Both univariate-Raman and WAXS determined crystallinities were used as references. The calibration models had strong relationships between determined and predicted crystallinity values (R ² = 0.998 and 0.984, for univariate-Raman and WAXS referenced models, respectively). Compared to WAXS, univariate-Raman referenced model was found to be better (root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP) values of 6.1 and 7.9% vs. 1.8 and 3.3%, respectively). It was concluded that either of the two Raman methods could be used for cellulose I crystallinity determination in cellulose samples.     

Comparative study of spectroscopic techniques for the estimation of iron in apple and vegetables

Iron has been determined in apple and vegetables spectrophotometrically, by complexing it with xylenol orange. 1:1 complex formed in a highly acidic medium is measured for its absorbance at its λ_max of 585 nm. The results have been compared by employing atomic absorption technique. Apples and vegetable samples were collected from local markets of Pakistan. Statistical manipulations, t-test and F-test, were performed and it was found that the results from the two techniques have an excellent agreement.     

Die bivalente Fehlersch?tzung in der R?ntgenspektrometrie

Summary Usually the standard deviation S _e of the calibration is calculated according to Eq. (1) and then considered as convenient estimation of the principally unknown analytical error X. It was shown in this paper that this method is only allowable for the simple linear regression. For all other evaluations it is necessary to calculate a standard deviation S _x by the aid of the bivalent procedure described in this paper. In that way a satisfactory approach to X is reached being confirmed by use of the F-test.     

Fluorescent quantification of terazosin hydrochloride content in human plasma and tablets using second-order calibration based on both parallel factor analysis and alternating penalty trilinear decomposition

Two second-order calibration methods based on the parallel factor analysis (PARAFAC) and the alternating penalty trilinear decomposition (APTLD) method, have been utilized for the direct determination of terazosin hydrochloride (THD) in human plasma samples, coupled with the excitation-emission matrix fluorescence spectroscopy. Meanwhile, the two algorithms combing with the standard addition procedures have been applied for the determination of terazosin hydrochloride in tablets and the results were validated by the high-performance liquid chromatography with fluorescence detection. These second-order calibrations all adequately exploited the second-order advantages. For human plasma samples, the average recoveries by the PARAFAC and APTLD algorithms with the factor number of 2 (N = 2) were 100.4 ± 2.7% and 99.2 ± 2.4%, respectively. The accuracy of two algorithms was also evaluated through elliptical joint confidence region (EJCR) tests and t-test. It was found that both algorithms could give accurate results, and only the performance of APTLD was slightly better than that of PARAFAC. Figures of merit, such as sensitivity (SEN), selectivity (SEL) and limit of detection (LOD) were also calculated to compare the performances of the two strategies. For tablets, the average concentrations of THD in tablet were 63.5 and 63.2 ng mL⁻¹ by using the PARAFAC and APTLD algorithms, respectively. The accuracy was evaluated by t-test and both algorithms could give accurate results, too.     

Multivariate methods on the excitation emission matrix fluorescence spectroscopic data of diesel-kerosene mixtures: a comparative study

Quantitative determination of kerosene fraction present in diesel has been carried out based on excitation emission matrix fluorescence (EEMF) along with parallel factor analysis (PARAFAC) and N-way partial least squares regression (N-PLS). EEMF is a simple, sensitive and nondestructive method suitable for the analysis of multifluorophoric mixtures. Calibration models consisting of varying compositions of diesel and kerosene were constructed and their validation was carried out using leave-one-out cross validation method. The accuracy of the model was evaluated through the root mean square error of prediction (RMSEP) for the PARAFAC, N-PLS and unfold PLS methods. N-PLS was found to be a better method compared to PARAFAC and unfold PLS method because of its low RMSEP values.     

Development and validation of novel LC–MS/MS method for determination of Lusutrombopag in rat plasma and its application to pharmacokinetic studies

A novel, simple and sensitive method for the determination of Lusutrombopag in rat plasma using liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) was developed and validated. The determination was performed on an API4000 triple quadrupole mass spectrometry in the multiple reaction monitoring mode using the respective [M+H]⁺ ions m/z 593.1 → 272.3 for Lusutrombopag. The limit of detection was 0.5 ng/mL, and the lower limit of quantification was 2.0 ng/mL in rat plasma. Good linearity was obtained over the range of 2.0–150.0 ng/mL and the correlation coefficient was found to be 0.9998. The intra and inter-day precisions were found to be 3.8–6.9% and 6.8–10.5%, respectively. The intra and inter-day accuracy derived from QC samples was found to be 2.5–4.9% and 5.5–7.2%, respectively. The analyte was stable under various conditions (at room temperature, during freeze-thaw, in the autosampler and under deep-freeze conditions). The F-test and t-test at 95% confidence level were subjected on data for statistical analysis. The developed method was successfully applied to the pharmacokinetic study in rats.