Goodness-of-fit tests in proportional hazards models with random effects.

This paper deals with testing the functional form of the covariate effects in a Cox proportional hazards model with random effects. We assume that the responses are clustered and incomplete due to right censoring. The estimation of the model under the null (parametric covariate effect) and the alternative (nonparametric effect) is performed using the full marginal likelihood. Under the alternative, the nonparametric covariate effects are estimated using orthogonal expansions. The test statistic is the likelihood ratio statistic, and its distribution is approximated using a bootstrap method. The performance of the proposed testing procedure is studied through simulations. The method is also applied on two real data sets one from biomedical research and one from veterinary medicine.

A generalized model to estimate the statistical power in mitochondrial disease studies involving 2×k tables.

BACKGROUND: Mitochondrial DNA (mtDNA) variation (i.e. haplogroups) has been analyzed in regards to a number of multifactorial diseases. The statistical power of a case-control study determines the a priori probability to reject the null hypothesis of homogeneity between cases and controls. METHODS/PRINCIPAL FINDINGS: We critically review previous approaches to the estimation of the statistical power based on the restricted scenario where the number of cases equals the number of controls, and propose a methodology that broadens procedures to more general situations. We developed statistical procedures that consider different disease scenarios, variable sample sizes in cases and controls, and variable number of haplogroups and effect sizes. The results indicate that the statistical power of a particular study can improve substantially by increasing the number of controls with respect to cases. In the opposite direction, the power decreases substantially when testing a growing number of haplogroups. We developed mitPower (http://bioinformatics.cesga.es/mitpower/), a web-based interface that implements the new statistical procedures and allows for the computation of the a priori statistical power in variable scenarios of case-control study designs, or e.g. the number of controls needed to reach fixed effect sizes. CONCLUSIONS/SIGNIFICANCE: The present study provides with statistical procedures for the computation of statistical power in common as well as complex case-control study designs involving 2×k tables, with special application (but not exclusive) to mtDNA studies. In order to reach a wide range of researchers, we also provide a friendly web-based tool--mitPower--that can be used in both retrospective and prospective case-control disease studies.

Extending induced ROC methodology to the functional context.

The receiver operating characteristic (ROC) curve is the most widely used measure for evaluating the discriminatory performance of a continuous marker. Often, covariate information is also available and several regression methods have been proposed to incorporate covariate information in the ROC framework. Until now, these methods are only developed for the case where the covariate is univariate or multivariate. We extend ROC regression methodology for the case where the covariate is functional rather than univariate or multivariate. To this end, semiparametric- and nonparametric-induced ROC regression estimators are proposed. A simulation study is performed to assess the performance of the proposed estimators. The methods are applied to and motivated by a metabolic syndrome study in Galicia (NW Spain).

Lasso logistic regression, GSoft and the cyclic coordinate descent algorithm: application to gene expression data.

Statistical methods generating sparse models are of great value in the gene expression field, where the number of covariates (genes) under study moves about the thousands while the sample sizes seldom reach a hundred of individuals. For phenotype classification, we propose different lasso logistic regression approaches with specific penalizations for each gene. These methods are based on a generalized soft-threshold (GSoft) estimator. We also show that a recent algorithm for convex optimization, namely, the cyclic coordinate descent (CCD) algorithm, provides with a way to solve the optimization problem significantly faster than with other competing methods. Viewing GSoft as an iterative thresholding procedure allows us to get the asymptotic properties of the resulting estimates in a straightforward manner. Results are obtained for simulated and real data. The leukemia and colon datasets are commonly used to evaluate new statistical approaches, so they come in useful to establish comparisons with similar methods. Furthermore, biological meaning is extracted from the leukemia results, and compared with previous studies. In summary, the approaches presented here give rise to sparse, interpretable models that are competitive with similar methods developed in the field.

Non-parametric estimation of the odds ratios for continuous exposures using generalized additive models with an unknown link function.

The generalized additive, model (GAM) is a powerful and widely used tool that allows researchers to fit, non-parametrically, the effect of continuous predictors on a transformation of the mean response variable. Such a transformation is given by a so-called link function, and in GAMs this link function is assumed to be known. Nevertheless, if an incorrect choice is made for the link, the resulting GAM is misspecified and the results obtained may be misleading. In this paper, we propose a modified version of the local scoring algorithm that allows for the non-parametric estimation of the link function, by using local linear kernel smoothers. To better understand the effect that each covariate produces on the outcome, results are expressed in terms of the non-parametric odds ratio (OR) curves. Bootstrap techniques were used to correct the bias in the OR estimation and to construct point-wise confidence intervals. A simulation study was carried out to assess the behaviour of the resulting estimates. The proposed methodology was illustrated using data from the AIDS Register of Galicia (NW Spain), with a view to assessing the effect of the CD4 lymphocyte count on the probability of being AIDS-diagnosed via Tuberculosis (TB). This application shows how the link's flexibility makes it possible to obtain OR curve estimates that are less sensitive to the presence of outliers and unusual values that are often present in the extremes of the covariate distributions.

Prediction of SO2 levels using neural networks.

In this paper, we present an adaptation of the air pollution control help system in the neighborhood of a power plant in As Pontes (A Coruña, Spain), property of Endesa Generación S.A., to the European Council Directive 1999/30/CE. This system contains a statistic prediction made half an hour before the measurement, and it helps the staff in the power plant prevent air quality level episodes. The prediction is made using neural network models. This prediction is compared with one made by a semiparametric model.