Monica Chiogna

Some results on the scalar Skew-normal distribution

Miscellaneous results about basic properties of the scalar Skew-normal distribution are presented. In particular, some recurrence relations on incomplete moments are derived and some results on moments of order statistics are illustrated. Moreover, some results on probability transformations are introduced.

A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution

Abstract.We consider likelihood based inference for the parameter of a skew-normal distribution. One of the problems shown by this model is the singularity of the Fisher information matrix when skewness is absent. We derive the rate of convergence to the asymptotic distribution of the maximum likelihood estimator and study an alternative parameterization which overcomes problems related to the singularity of the information matrix.

Gene set analysis exploiting the topology of a pathway

BackgroundRecently, a great effort in microarray data analysis is directed towards the study of the so-called gene sets. A gene set is defined by genes that are, somehow, functionally related. For example, genes appearing in a known biological pathway naturally define a gene set. The gene sets are usually identified from a priori biological knowledge. Nowadays, many bioinformatics resources store such kind of knowledge (see, for example, the Kyoto Encyclopedia of Genes and Genomes, among others). Although pathways maps carry important information about the structure of correlation among genes that should not be neglected, the currently available multivariate methods for gene set analysis do not fully exploit it.ResultsWe propose a novel gene set analysis specifically designed for gene sets defined by pathways. Such analysis, based on graphical models, explicitly incorporates the dependence structure among genes highlighted by the topology of pathways. The analysis is designed to be used for overall surveillance of changes in a pathway in different experimental conditions. In fact, under different circumstances, not only the expression of the genes in a pathway, but also the strength of their relations may change. The methods resulting from the proposal allow both to test for variations in the strength of the links, and to properly account for heteroschedasticity in the usual tests for differential expression.ConclusionsThe use of graphical models allows a deeper look at the components of the pathway that can be tested separately and compared marginally. In this way it is possible to test single components of the pathway and highlight only those involved in its deregulation.

A modified LOESS normalization applied to microRNA arrays

MOTIVATION Microarray normalization is a fundamental step in removing systematic bias and noise variability caused by technical and experimental artefacts. Several approaches, suitable for large-scale genome arrays, have been proposed and shown to be effective in the reduction of systematic errors. Most of these methodologies are based on specific assumptions that are reasonable for whole-genome arrays, but possibly unsuitable for small microRNA (miRNA) platforms. In this work, we propose a novel normalization (loessM), and we investigate, through simulated and real datasets, the influence that normalizations for two-colour miRNA arrays have on the identification of differentially expressed genes. RESULTS We show that normalizations usually applied to large-scale arrays, in several cases, modify the actual structure of miRNA data, leading to large portions of false positives and false negatives. Nevertheless, loessM is able to outperform other techniques in most experimental scenarios. Moreover, when usual assumptions on differential expression distribution are missed, channel effect has a strikingly negative influence on small arrays, bias that cannot be removed by normalizations but rather by an appropriate experimental design. We find that the combination of loessM with eCADS, an experimental design based on biological replicates dye-swap recently proposed for channel-effect reduction, gives better results in most of the experimental conditions in terms of specificity/sensitivity both on simulated and real data. AVAILABILITY LoessM R function is freely available at http://gefu.cribi.unipd.it/papers/miRNA-simulation/

Power spectral analysis of heart rate and diastolic blood pressure variability in migraine with and without aura

Autonomic function in migraineurs during headache-free periods was studied by means of cardiovascular reflexes and power spectral analysis of heart rate and diastolic blood pressure variability. We examined 56 patients: 37 suffering from migraine without aura and 19 from migraine with aura. Cardiovascular responses to the tilt test and Valsalva manoeuvre showed a normal function of the overall baroreceptor reflex arc. Normal heart rate responses to valsalva manoeuvre and deep breathing suggested an intact parasympathetic function. Power spectral analysis of both heart rate and diastolic blood pressure variability in basal conditions and during orthostatic test showed similar sympathovagal interactions modulating cardiovascular control in migraine patients and in controls.

Dynamic generalized linear models with application to environmental epidemiology

We propose modelling short-term pollutant exposure effects on health by using dynamic generalized linear models. The time series of count data are modelled by a Poisson distribution having mean driven by a latent Markov process; estimation is performed by the extended Kalman filter and smoother. This modelling strategy allows us to take into account possible overdispersion and time-varying effects of the covariates. These ideas are illustrated by reanalysing data on the relationship between daily non-accidental deaths and air pollution in the city of Birmingham, Alabama. Copyright 2002 Royal Statistical Society.

A comparison on effects of normalisations in the detection of differentially expressed genes

BackgroundVarious normalisation techniques have been developed in the context of microarray analysis to try to correct expression measurements for experimental bias and random fluctuations. Major techniques include: total intensity normalisation; intensity dependent normalisation; and variance stabilising normalisation. The aim of this paper is to discuss the impact of normalisation techniques for two-channel array technology on the process of identification of differentially expressed genes.ResultsThrough three precise simulation plans, we quantify the impact of normalisations: (a) on the sensitivity and specificity of a specified test statistic for the identification of deregulated genes, (b) on the gene ranking induced by the statistic.ConclusionAlthough we found a limited difference of sensitivities and specificities for the test after each normalisation, the study highlights a strong impact in terms of gene ranking agreement, resulting in different levels of agreement between competing normalisations. However, we show that the combination of two normalisations, such as glog and lowess, that handle different aspects of microarray data, is able to outperform other individual techniques.

Automatic identification of seasonal transfer function models by means of iterative stepwise and genetic algorithms

In this article, we introduce an automatic identification procedure for transfer function models. These models are commonplace in time-series analysis, but their identification can be complex. To tackle this problem, we propose to couple a nonlinear conditional least-squares algorithm with a genetic search over the model space. We illustrate the performances of our proposal by examples on simulated and real data. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

Partially parametric interval estimation of Pr{Y>X}

Let X and Y be two independent continuous random variables. Three techniques to obtain confidence intervals for @r=Pr{Y>X} are discussed in a partially parametric framework. One method relies on the asymptotic normality of an estimator for @r; the remaining methods involve empirical likelihood and combine it with maximum likelihood estimation and with full parametric likelihood, respectively. Finite-sample accuracy of the confidence intervals is assessed through a simulation study. An illustration is given using a data set on the detection of carriers of Duchenne Muscular Dystrophy.

An empirical comparison of expert-derived and data-derived classification trees

Classification trees provide an attractively transparent discrimination technique, and may be derived from both expert opinion and from data analysis. We consider a real and complex problem concerning the diagnosis of babies with suspected critical congenital heart disease into one of 27 classes. A full loss matrix for all possible misclassifications was obtained from clinical assessments. A tree derived from expert opinion was compared with those derived from analysis of 571 past cases, both for the full problem and for a subset of 6 diseases. Automatic methods for tree creation and pruning were found to have problems for rare diseases, and hand-pruning was carried out. Inclusion of costs led to much improved clinical performance, even for trees that had originally been constructed to minimize classification errors. The expert tree showed a specific building strategy that could not be reproduced automatically. The expert tree generally outperformed those derived from data, particularly in the ability to identify important composite features.