Use of Bayesian Methods for Multivariate Bioequivalence Measures

In this paper, we introduce a Bayesian analysis for bioequivalence data assuming multivariate pharmacokinetic measures. With the introduction of correlation parameters between the pharmacokinetic measures or between the random effects in the bioequivalence models, we observe a good improvement in the bioequivalence results. These results are of great practical interest since they can yield higher accuracy and reliability for the bioequivalence tests, usually assumed by regulatory offices. An example is introduced to illustrate the proposed methodology by comparing the usual univariate bioequivalence methods with multivariate bioequivalence. We also consider some usual existing discrimination Bayesian methods to choose the best model to be used in bioequivalence studies.

Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

Determinantes da evolução do peso e altura em crianças de 3 meses a 6 anos assistidas em creche: Análise por modelo linear não hierarquizado em ensaio quase-experimental

Objective. To assess factors determining growth in a group of children between 3 months and 6 years old enrolled in a public municipal (i.e., government-supported, not private) day-care center, in comparison to a group of children with similar characteristics but who were not enrolled in the center. Methods. A quasi-experimental study was designed to observe 444 children aged 3 to 72 months from a low-income neighborhood in the city of Sorocaba, in the state of São Paulo, Brazil. Two groups were studied: 164 children enrolled in a local municipal day-care center (intervention group) and 280 not receiving care at the center (nonintervention, comparison group) but instead being cared for at home. Both groups were seen four times over a period of 16 months. At each observation session, the children's weight and height were measured. Information was also collected on the mother's sociodemographic characteristics and the illnesses she had suffered as well as the child's weight and other health characteristics at birth, the child's illnesses in the 15 days before each observation, and any hospitalizations. Results. The children in both groups were from low-income families, with 65% of the families having an average monthly income below US$ 100; 80% of the mothers had received 8 years of schooling or less. Multivariate linear regression analysis showed that at the first observation (just before enrollment in the day-care center), birth weight was the only factor that explained the nutritional differences between the two groups. Subsequent analyses showed that being in day care was the factor that best explained the differences between the groups, especially in terms of the adequacy of weight for age, after controlling for birthweight, sex, age at the beginning of the study, and illnesses in the 15 days before an observation session. The nutritional impact of the intervention was significant as early as 3 months after being enrolled in day care. Conclusions. The nutritional benefits of the care provided at the center outweighed the negative effects sometimes seen in such centers, such as the greater morbidity that children in day-care centers often experience in comparison to children receiving care at home.

Multivariate analyses of UV-Vis absorption spectral data from cachaca wood extracts: a model to classify aged Brazilian cachacas according to the wood species used

Multivariate analyses of UV-Vis spectral data from cachaca wood extracts provide a simple and robust model to classify aged Brazilian cachacas according to the wood species used in the maturation barrels. The model is based on inspection of 93 extracts of oak and different Brazilian wood species by a non-aged cachaca used as an extraction solvent. Application of PCA (Principal Components Analysis) and HCA (Hierarchical Cluster Analysis) leads to identification of 6 clusters of cachaca wood extracts (amburana, amendoim, balsamo, castanheira, jatoba, and oak). LDA (Linear Discriminant Analysis) affords classification of 10 different wood species used in the cachaca extracts (amburana, amendoim, balsamo, cabreuva-parda, canela-sassafras, castanheira, jatoba, jequitiba-rosa, louro-canela, and oak) with an accuracy ranging from 80% (amendoim and castanheira) to 100% (balsamo and jequitiba-rosa). The methodology provides a low-cost alternative to methods based on liquid chromatography and mass spectrometry to classify cachacas aged in barrels that are composed of different wood species.

Multivariate spectroscopic methods for the analysis of solutions

In this thesis some multivariate spectroscopic methods for the analysis of solutions are proposed. Spectroscopy and multivariate data analysis form a powerful combination for obtaining both quantitative and qualitative information and it is shown how spectroscopic techniques in combination with chemometric data evaluation can be used to obtain rapid, simple and efficient analytical methods. These spectroscopic methods consisting of spectroscopic analysis, a high level of automation and chemometric data evaluation can lead to analytical methods with a high analytical capacity, and for these methods, the term high-capacity analysis (HCA) is suggested. It is further shown how chemometric evaluation of the multivariate data in chromatographic analyses decreases the need for baseline separation. The thesis is based on six papers and the chemometric tools used are experimental design, principal component analysis (PCA), soft independent modelling of class analogy (SIMCA), partial least squares regression (PLS) and parallel factor analysis (PARAFAC). The analytical techniques utilised are scanning ultraviolet-visible (UV-Vis) spectroscopy, diode array detection (DAD) used in non-column chromatographic diode array UV spectroscopy, high-performance liquid chromatography with diode array detection (HPLC-DAD) and fluorescence spectroscopy. The methods proposed are exemplified in the analysis of pharmaceutical solutions and serum proteins. In Paper I a method is proposed for the determination of the content and identity of the active compound in pharmaceutical solutions by means of UV-Vis spectroscopy, orthogonal signal correction and multivariate calibration with PLS and SIMCA classification. Paper II proposes a new method for the rapid determination of pharmaceutical solutions by the use of non-column chromatographic diode array UV spectroscopy, i.e. a conventional HPLC-DAD system without any chromatographic column connected. In Paper III an investigation is made of the ability of a control sample, of known content and identity to diagnose and correct errors in multivariate predictions something that together with use of multivariate residuals can make it possible to use the same calibration model over time. In Paper IV a method is proposed for simultaneous determination of serum proteins with fluorescence spectroscopy and multivariate calibration. Paper V proposes a method for the determination of chromatographic peak purity by means of PCA of HPLC-DAD data. In Paper VI PARAFAC is applied for the decomposition of DAD data of some partially separated peaks into the pure chromatographic, spectral and concentration profiles.

Valutazione della qualità ed autenticità di prodotti oleari e lattiero caseari mediante metodi fisici di analisi accoppiati a tecniche statistiche multivariate

Questa tesi descrive alcuni studi di messa a punto di metodi di analisi fisici accoppiati con tecniche statistiche multivariate per valutare la qualità e l’autenticità di oli vegetali e prodotti caseari. L’applicazione di strumenti fisici permette di abbattere i costi ed i tempi necessari per le analisi classiche ed allo stesso tempo può fornire un insieme diverso di informazioni che possono riguardare tanto la qualità come l’autenticità di prodotti. Per il buon funzionamento di tali metodi è necessaria la costruzione di modelli statistici robusti che utilizzino set di dati correttamente raccolti e rappresentativi del campo di applicazione. In questo lavoro di tesi sono stati analizzati oli vegetali e alcune tipologie di formaggi (in particolare pecorini per due lavori di ricerca e Parmigiano-Reggiano per un altro). Sono stati utilizzati diversi strumenti di analisi (metodi fisici), in particolare la spettroscopia, l’analisi termica differenziale, il naso elettronico, oltre a metodiche separative tradizionali. I dati ottenuti dalle analisi sono stati trattati mediante diverse tecniche statistiche, soprattutto: minimi quadrati parziali; regressione lineare multipla ed analisi discriminante lineare.

Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

An insulin infusion advisory system for type 1 diabetes patients based on non-linear model predictive control methods

In this paper, an Insulin Infusion Advisory System (IIAS) for Type 1 diabetes patients, which use insulin pumps for the Continuous Subcutaneous Insulin Infusion (CSII) is presented. The purpose of the system is to estimate the appropriate insulin infusion rates. The system is based on a Non-Linear Model Predictive Controller (NMPC) which uses a hybrid model. The model comprises a Compartmental Model (CM), which simulates the absorption of the glucose to the blood due to meal intakes, and a Neural Network (NN), which simulates the glucose-insulin kinetics. The NN is a Recurrent NN (RNN) trained with the Real Time Recurrent Learning (RTRL) algorithm. The output of the model consists of short term glucose predictions and provides input to the NMPC, in order for the latter to estimate the optimum insulin infusion rates. For the development and the evaluation of the IIAS, data generated from a Mathematical Model (MM) of a Type 1 diabetes patient have been used. The proposed control strategy is evaluated at multiple meal disturbances, various noise levels and additional time delays. The results indicate that the implemented IIAS is capable of handling multiple meals, which correspond to realistic meal profiles, large noise levels and time delays.