Multivariate data analysis in pharmaceutics: a tutorial review

We provide an overview of latent variable methods used in pharmaceutics and integrated with advanced characterization techniques such as vibrational spectroscopy. The basics of the most common latent variable methods, principal component analysis (PCA), principal component regression (PCR) and partial least-squares (PLS) regression, are presented. Multiple linear regression (MLR) and methods for improved interpretation, variable selection, classification and validation are also briefly discussed. Extensive use of the methods is demonstrated by compilation of the recent literature.     

Multivariate cluster analysis of pharmaceutical formulation data using Andrews plots

A multivariate clustering technique known as the Andrews Plot was applied to a set of previously published data describing a series of pharmaceutical tablet formulations. Dependent variable data were subjected to a trigonometric transform algorithm and unique sinusoidal patterns were obtained for each of 18 formulations characterized by a total of 12 granulation and tablet parameters. Three main formulation clusters were observed in close agreement with a previously published analysis of the same data set using principal components methodology. Interpretation of cluster behavior lead to conclusions closely aligned to those of the original investigators, although some alternate hypotheses also arise. Limitations of the Andrews plotting technique were explored. The method appears to have value in the analysis of complex data sets derived from pharmaceutical formulation characterizations.     

Multivariate data analysis as a fast tool in evaluation of solid state phenomena

A thorough understanding of solid state properties is of growing importance. It is often necessary to apply multiple techniques offering complementary information to fully understand the solid state behavior of a given compound and the relations between various polymorphic forms. The vast amount of information generated can be overwhelming and the need for more effective data analysis tools is well recognized. The aim of this study was to investigate the use of multivariate data analysis, in particular principal component analysis (PCA), for fast analysis of solid state information. The data sets analyzed covered dehydration phenomena of a set of hydrates followed by variable temperature X-ray powder diffractometry and Raman spectroscopy and the crystallization of amorphous lactose monitored by Raman spectroscopy. Identification of different transitional states upon the dehydration enabled the molecular level interpretation of the structural changes related to the loss of water, as well as interpretation of the phenomena related to the crystallization. The critical temperatures or critical time points were identified easily using the principal component analysis. The variables (diffraction angles or wavenumbers) that changed could be identified by the careful interpretation of the loadings plots. The PCA approach provides an effective tool for fast screening of solid state information.     

Multivariate statistical interpretation of laboratory clinical data

Laboratory aids are extensively used in the diagnosis of diseases, in preventive medicine, and as management tools. Reference values of clinically healthy people serve as a guide to the clinician in evaluating biochemical parameters. Determination of 21 biochemical parameters of healthy persons using standard methods of analysis. Cluster analysis and principal components analysis were applied on the above 21 biochemical parameters data. The application of a typical classification approach as cluster analysis proved that four major groups of similarity between all 21 clinical parameters are formed, which correspond to the authors assumption of the existence of several summarizing pattern of clinical parameters such as “enzyme,” “major component excretion”, “general health state,” and “blood specific” pattern. These patterns appear also in the subsets obtained by separation of the general dataset into “male”, “female”, “young”, and “adult” healthy groups. The results obtained from principal components analysis have additionally proved the validity of a similar assumption. The intelligent data analysis on the clinical parameter dataset has shown that when a complex system is considered as a multivariate one, the information about the system substantially increases. All these results support an idea that probably a general health indicator could be constructed taking into account the existing classification groups in the list of clinical parameters.     

Multivariate analysis of integrated and full-resolution 1H-NMR spectral data from complex pharmaceutical preparations: St. John's wort

Commercial herbal preparations are typically very complex mixtures and the relationship between content of various constituents and pharmacological action of the formulation is usually unclear. Such formulations are nevertheless standardized using a single marker constituent or a group of closely related constituents, which provides no information about other abundant constituents present in the extract. In this study, principal component analysis of 600 MHz 1H-NMR spectra of extracts of commercial formulations of St. John's wort (Hypericum perforatum), acquired in methanol-d4 and DMSO-d6, was shown to be able to discriminate between various preparations according to their global composition, including differentiation between various batches from the same supplier, while no clustering into classes of tablets and capsules was observed. This suggests that the plant extract variability rather than the manufacturing process accounts for the data clustering. Major variations in the content of flavonoids, recently linked to the antidepressant activity of St. John's wort extracts, were detected. Use of two NMR solvents provided complementary data sets, allowing assessment of various aspects of sample composition from separate PCA models. Both integrated (about 200 variables) and full-resolution NMR data (about 30,000 variables) have been used. The latter approach, applied for the first time in analysis of a herbal preparation, provided via loading plots more precise information about constituents responsible for data clustering, and may be generally preferable for PCA analysis of NMR data of plant extracts and herbal medicines.     

Multivariate statistical analysis of organ weights in toxicity studies.

Toxicity studies with drugs in animals are performed to establish the toxicity profile including the no-toxic-effect-level in the animals. One of the responses used in the search for effects is organ weight. Since organ weight is related to body weight of the animal, the analysis of organ weight has to be adjusted. A traditional analysis of covariance with body weight as covariate is not always appropriate since the body weight itself can be affected by the test compound. Hence, a multivariate analysis of variance is suggested, where the correlation between organ weight and body weight is taken into account in testing an overall treatment effect. Two dimensional plots of the contour curves are used to visualize the treatment effect on organ weight and body weight simultaneously. The test procedure suggested for comparing differences between control and treated groups of animals is: start by testing hypotheses of equality of covariance matrices for the different treatment groups and then, depending on the results from the first test, test equality of the mean vectors.     

Multivariate symptom analysis related to response to lorazepam treatment.

In an attempt to explain the marked inter-trial differences in the percentage of patients reported to benefit from the anxiolytic agent lorazepam, a statistical analysis was carried out on the scores from a psychiatric symptom questionnaire, completed before and after treatment with lorazepam, by 69 psychiatric out-patients. Most of the patients presented with a mixture of different syndromes, with moderate to severe symptoms, and had already failed to respond to other treatment. Forty of the patients showed a favourable response to lorazepam. Multivariate analysis of the strength of 6 symptom clusters versus therapeutic response in this diagnostically heterogeneous patient sample revealed that, in addition to anxiety, there was a high relationship also between phobic and psychosomatic symptom scores and response to lorazepam. The relationship between depression scores and response was only of borderline significance, and that for hysteria and obsessionality was poor. It is suggested that one explanation of inter-trial differences in the percentages of patients improved by lorazepam may be that they are due to differences in the diagnostic composition of the patient populations studied.     

Multivariate analysis in the pharmacological evaluation of a saluretic compound.

The pharmacological evaluation of the diuretic activity of a compound -- performed measuring the urinary volume and determining its electrolyte content -- may be usefully integrated by a multivariate analysis, in order to: express a general evaluation for each animal in terms of positive or negative response; evaluate the false positive responses of the control group animals and the negative responses in the treated animals on the basis of the general response. An example of application relating to a well-known saluretic, 4-chloro-N-(2-furfuryl)-5-sulfamoyl-anthranilic acid (furosemide), is reported.     

Multivariate genome-wide analysis of stress-related quantitative phenotypes

Exposure to traumatic stress increases the odds of developing a broad range of psychiatric conditions. Genetic studies targeting multiple stress-related quantitative phenotypes may shed light on mechanisms underlying vulnerability to psychopathology in the aftermath of stressful events. We applied a multivariate genome-wide association study (GWAS) to a unique military cohort (N = 583) in which we measured biochemical and behavioral phenotypes. The availability of pre- and post-deployment measurements allowed to capture changes in these phenotypes in response to stress. For genome-wide significant loci, we performed functional annotation, phenome-wide analysis and quasi-replication in PTSD case-control GWASs. We discovered one genetic variant reaching genome-wide significant association, surviving permutation and sensitivity analyses (rs10100651, p = 9.9 × 10⁻⁹). Functional annotation prioritized the genes INTS8 and TP53INP1. A phenome-wide scan revealed a significant association of these same genes with sleeping problems, hypertension and subjective well-being. Finally, a targeted lookup revealed nominally significant association of rs10100651 in a PTSD case-control GWAS in the UK Biobank (p = 0.02). We provide comprehensive evidence from multiple resources hinting at a role of the highlighted genetic variant in the human stress response, marking the power of multivariate genome-wide analysis of quantitative measures in stress research. Future genetic and functional studies can target this locus to further assess its effects on stress mediation and its possible role in psychopathology or resilience.     

Semiparametric analysis of non-steady-state pharmacodynamic data.

We present an approach to the analysis of pharmacodynamic (PD) data arising from non-steady-state experiments, meant to be used when only PD data, not pharmacokinetic (PK) data, are available. The approach allows estimation of the steady-state relationship between drug input and effect. The analysis is based on a model describing the time dependence of drug effect (E) on (unobserved) drug concentration (Ce) in an hypothetical effect compartment. The model consists of (i) a known model for the input rate of drug I(t), (ii) a parametric model; L(t, alpha) (a function of time t, and vector of parameters alpha), relating I to an observed variable X, (iii) a nonparametric model relating X to E. Ce is proportional to X. X (t) is given by I(t) * L(t, alpha)/AL, where L(t, alpha) = e-alpha 1t * sigma k m = 1 alpha 2k e-alpha 2k + 1t, sigma k m = 1 alpha 2k = 1, AL = integral of 0 infinity L(t) dt, and * indicates convolution. The nonparametric model relating X to E is a cubic spline, a function of X and a vector of (linear) parameters beta. The values of alpha and beta are chosen to minimize the sum of squared residuals between predicted and observed E. We also describe a similar model, generalizing a previously described one, to analyze PK/PD data. Applications of the approach to different drug-effect relationships (verapamil-PR interval, hydroxazine-wheal and flare, flecainide and/or verapamil-PR, and left ventricular ejection fraction) are reported.     

NMR spectroscopy in pharmaceutical analysis. VII. Determination of the component composition of gentamicin by13C NMR spectroscopy

The preceding communication described the identification and quantitative analysis of the relative contents of the Z- and E-isomers of derivatives of 2-(2-amino-1,3-thiazol-4-yl)-2-methoxyiminoacetic acid by¹H and¹³C NMR [A].     

Pharmacokinetic analysis of sparse in vivo NMR spectroscopy data using relative parameters and the population approach

NMR spectroscopy in vivo when applied to studying drugs and their metabolites usually measures relative concentration in a tissue over time. Only ratios of clearance and volume parameters can be estimated from these data. Low drug dosages (relative to the sensitivity of in vivo NMR) or rapid drug elimination create the additional problem of data sparsity where a pharmacokinetic model cannot be fitted individually. We have investigated whether relative and absolute pharmacokinetic parameters can be estimated from such data by applying a population model.The data analysed were relative concentractions of 5-fluorouracil (FU) and of the sum of its catabolits -fluoro--ureido-propanoic acid (FUPA) and -fluoro--alanine (FBAL) in te liver, as monitored in 16 cancer patients by [¹⁹F]-NMP spectroscopy during and after a 10-min intravenous infusion of 650 mg FU·m^–2. The structural part of the population model was a non-linear, two-compartment model featuring one FU compartment with volume V _FU , a saturable clearance of FU by conversion into the catabolites where CL=v _max /(k _M +C _FU ), a catabolite compartment with volume V _cat , and a concentration-independent clearance of the catabolites, CL _cat . The parameters actually fitted were: , v _max , k _M ·V _FU , V _cat /V _FU , and CL _cat /V _cat where is a proportionality factor relating the NMR signal intensity of FU to the amount of FU in the body and, therefore, has no purely pharmacokinetic interpretation. All parameters were checked for random interindividual variation; and v _max were also tested for inter-occasion variation. The program system NONMEM was used for model fitting.The estimated mean population parameters were: v _max =121 mol·min^–1, k _M ·V _FU =2590 mol, V _cat /V _FU =0.0648, CL _cat /V _cat =0.0555·min^–1. The proportionality factor was found to depend on body weight and, in addition, to have an inter-occasion random variation (within patients, between examinations). No other random variation of a kinetic parameter could be identified. The estimated v _max is similar to a reported estimate of 2.02 mol·min^–1·kg^–1 derived from FU plasma kinetics.This study shows that sparse relative concentration data can be analysed by using relative parameters in a population model. Only one parameter has no unequivocal pharmacokinetic meaning due to the lack of absolute concentration information. Any contribution of the measuring procedure to the inter-occasion variation of in vivo NMP spectroscopy measurements should be minimized in order to allow the detection of possible inter-individual variances of the pharmacokinetic parameters.Dedicated to Prof. Dr. Rudolf Preussmann on the occasion of his 65th birthday     

Multivariate analysis and quantitative structure-activity relationships. Inhibition of dihydrofolate reductase and thymidylate synthetase by quinazolines.

Quantitative structure-activity relationships (QSAR) have been established for the inhibition of dihydrofolate reductase and thymidylate synthetase by 2,4-diaminoquinazoline-glutamic acid analogues. For dihydrofolate reductase from both human acute lymphocytic leukemia cells and murine L1210R cells, QSAR's obtained with 50 quinazolines were similar. On the other hand, for the inhibition of thymidylate synthetase from murine L1210S cells and from Lactobacillus casei, QSAR's formulated on the basis of data measured with 33 compounds were different, indicating that the two enzymes are dissimilar. The use of multivariate statistics including cluster analysis, factor analysis, and discriminant analysis is shown to facilitate the formulation of a satisfactory correlation equation. The procedure is demonstrated by the development of QSAR for the inhibition of thymidylate synthetase.     

Multivariate analysis of drug-effects on electrophysiological signals in man

A multidimensional analysis method (Principal Component Analysis) is applied to the study of drug-effects upon electrophysiological signals (EEG, EKG…). It is shown how the developed method can provide a mapping of the data allowing formulation of hypotheses on their structure and elaboration of a statistical processing strategy. In particular, this method can permit detection and correction of parasite-effects which could distort or conceal the drug-effect itself.