Mariano J. Valderrama

Robust principal component analysis for functional data

A method for exploring the structure of populations of complex objects, such as images, is considered. The objects are summarized by feature vectors. The statistical backbone is Principal Component Analysis in the space of feature vectors. Visual insights come from representing the results in the original data space. In an ophthalmological example, endemic outliers motivate the development of a bounded influence approach to PCA.

Using principal components for estimating logistic regression with high-dimensional multicollinear data

The logistic regression model is used to predict a binary response variable in terms of a set of explicative ones. The estimation of the model parameters is not too accurate and their interpretation in terms of odds ratios may be erroneous, when there is multicollinearity (high dependence) among the predictors. Other important problem is the great number of explicative variables usually needed to explain the response. In order to improve the estimation of the logistic model parameters under multicollinearity and to reduce the dimension of the problem with continuous covariates, it is proposed to use as covariates of the logistic model a reduced set of optimum principal components of the original predictors. Finally, the performance of the proposed principal component logistic regression model is analyzed by developing a simulation study where different methods for selecting the optimum principal components are compared.

Principal component estimation of functional logistic regression: discussion of two different approaches

Over the last few years many methods have been developed for analyzing functional data with different objectives. The purpose of this paper is to predict a binary response variable in terms of a functional variable whose sample information is given by a set of curves measured without error. In order to solve this problem we formulate a functional logistic regression model and propose its estimation by approximating the sample paths in a finite dimensional space generated by a basis. Then, the problem is reduced to a multiple logistic regression model with highly correlated covariates. In order to reduce dimension and to avoid multicollinearity, two different approaches of functional principal component analysis of the sample paths are proposed. Finally, a simulation study for evaluating the estimating performance of the proposed principal component approaches is developed.

Eradication of Enterococcus faecalis biofilms by cetrimide and chlorhexidine.

INTRODUCTION Enterococcus faecalis is the most commonly isolated bacteria from root canals of teeth with persistent periapical periodontitis. Its ability to grow as a biofilm impedes the elimination of E. faecalis by using irrigating solutions. The purpose of this study was to assess the efficacy of cetrimide and chlorhexidine (CHX), alone and in association, in combined and alternating form, in eradicating biofilms of E. faecalis. METHODS Biofilms grown in the MBEC-high-throughput device for 24 hours were exposed to irrigating solutions for 30 seconds and 1 and 2 minutes. Eradication was defined as 100% kill of biofilm bacteria. The Student t test was used to compare the efficacy of the associations of the 2 irrigants. RESULTS Cetrimide eradicated E. faecalis biofilms at concentrations of 0.5%, 0.0312%, and 0.0078% at 30 seconds and 1 and 2 minutes of contact time, respectively. CHX did not eradicate the biofilms at any of the concentrations (4% initial concentration) or times assayed. The association of 0.1% and 0.05% cetrimide with any concentration of CHX, whether in combined or alternating application, effectively eradicated E. faecalis biofilms at all the contact times tested. Eradication was also achieved with 0.02% and 0.01% cetrimide at 2 minutes. Statistical analysis revealed significantly better results with alternating rather than combined use of cetrimide and CHX (P < .05). CONCLUSIONS The associated use of cetrimide and CHX provided better results than their applications as single agents against E. faecalis biofilms, and the alternating application was significantly more effective than the combined mode of application.

Functional PLS logit regression model

Functional logistic regression has been developed to forecast a binary response variable from a functional predictor. In order to fit this model, it is usual to assume that the functional observations and the parameter function of the model belong to a same finite space generated by a basis of functions. This consideration turns the functional model into a multiple logit model whose design matrix is the product of the matrix of sample paths basic coefficients and the matrix of the inner products between basic functions. The likelihood estimation of the parameter function of this model is very inaccurate due to the high dependence structure of the so obtained design matrix (multicollinearity). In order to solve this drawback several approaches have been proposed. These employ standard multivariate data analysis methods on the design matrix. This is the case of the functional principal component logistic regression model. As an alternative a functional partial least squares logit regression model is proposed, that has as covariates a set of partial least squares components of the design matrix of the multiple logit model associated to the functional one.

Approximation of estimators in the PCA of a stochastic process using B-splines

The objective of this paper is to estimate the principal factors of a continuous time real valued process when we have a collection of independent sample functions which are observed only at discrete time points. We propose to approximate the Principal Component Analysis (PCA) of the process, when the sample functions are regular, by means of the PCA of the natural cubic spline interpolation of the sample curves between the sampling time points. A physical application testing the accuracy of this approach by simulating sample functions of the harmonic oscillator stochastic process is also included. The approximated PCA of this well known process is compared with the exact one and with the classical PCA of the discrete time simulated data.

Effect of chlorhexidine-thymol varnish on root caries in a geriatric population: A randomized double-blind clinical trial

OBJECTIVES Little is known about the effect of Cervitec, a chlorhexidine-thymol varnish, on root caries. Our objective was to determine whether a 3-monthly application of Cervitec over 1 year would limit the progress of existing root caries lesions and reduce the incidence of dental root caries in a group of dentate institutionalized elderly, as a complement to their usual oral hygiene practices. METHODS A double-blind randomized clinical trial was conducted in 68 subjects (34 per group) in two residences in Almería (Spain). Twenty-one subjects with 60 root caries lesions and 25 with 65 lesions, in the Cervitec and placebo groups, respectively, completed the study. Varnishes were applied twice in the first week, 1 month later, and every 3 months until the end of the study. Clinical parameters associated with established lesions were determined at baseline and after 6 and 12 months, as was the incidence of root caries lesions. RESULTS The clinical evolution of lesions was significantly better in the Cervitec group as opposed to the placebo group in terms of width, height, color, and texture. The increase in root caries was significantly lower (p=0.039) in the Cervitec group. CONCLUSION According to these results, Cervitec may help to control established root lesions and reduce the incidence of root caries lesion among institutionalized elderly.

AN APPROXIMATED PRINCIPAL COMPONENT PREDICTION MODEL FOR CONTINUOUS-TIME STOCHASTIC PROCESSES

SUMMARY In this paper, a linear model for forecasting a continuous-time stochastic process in a future interval in terms of its evolution in a past interval is developed. This model is based on linear regression of the principal components in the future against the principal components in the past. In order to approximate the principal factors from discrete observations of a set of regular sample paths, cubic spline interpolation is used. An application for forecasting tourism evolution in Granada is also included. ( 1997 by John Wiley & Sons, Ltd.

Forecasting with unequally spaced data by a functional principal component approach

The Principal Component Regression model of multiple responses is extended to forccast a continuous-time stochastic process. Orthogonal projection on a subspace of trigonometric functions is applied in order to estimate the principal components using discrete-time observations from a sample of regular curves. The forecasts provided by this approach are compared with classical principal component regression on simulated data.

Modelling the mean of a doubly stochastic Poisson process by functional data analysis

A new procedure for estimating the mean process of a doubly stochastic Poisson process is introduced. The proposed estimation is based on monotone piecewise cubic interpolation of the sample paths of the mean. In order to estimate the continuous time structure of the mean process functional principal component analysis is applied to its trajectories previously adapted to their functional form. A validation of the estimation method is presented by means of some simulations.