David Causeur

A Factor Model Approach to Multiple Testing Under Dependence

The impact of dependence between individual test statistics is currently among the most discussed topics in the multiple testing of high-dimensional data literature, especially since Benjamini and Hochberg (1995) introduced the false discovery rate (FDR). Many papers have first focused on the impact of dependence on the control of the FDR. Some more recent works have investigated approaches that account for common information shared by all the variables to stabilize the distribution of the error rates. Similarly, we propose to model this sharing of information by a factor analysis structure for the conditional variance of the test statistics. It is shown that the variance of the number of false discoveries increases along with the fraction of common variance. Test statistics for general linear contrasts are deduced, taking advantage of the common factor structure to reduce the variance of the error rates. A conditional FDR estimate is proposed and the overall performance of multiple testing procedure is shown to be markedly improved, regarding the nondiscovery rate, with respect to classical procedures. The present methodology is also assessed by comparison with leading multiple testing methods.

Hierarchy of factors affecting behavioural signs used for oestrus detection of Holstein and Normande dairy cows in a seasonal calving system

As oestrous expression of dairy cows has decreased over the last decades oestrus detection has become more difficult. The objective of this study is to identify the main factors that affect oestrus detection in seasonal calving dairy cows, and to establish their relative importance. In each of 5 years 36 Normande and 36 Holstein cows were assigned to a Low or High winter-feeding level group. Half of each group was then assigned to a Low or High pasture-feeding group. The Low-Low strategy resulted in the lowest milk yield and the greatest body condition (BC) loss from calving to nadir BC score (6302 kg; -0.98 unit). The High-High strategy had the converse effect (7549 kg; -0.75 units). Low-High and High-Low strategies had intermediate values. The Normande cows had lower milk yield and BC loss than Holstein cows (6153 kg versus 7620 kg; -0.82 unit versus -1.20 unit). A database of 415 observed spontaneous oestruses was created. Oestruses were classified according to detection signs: (1) standing to be mounted, (2) mounting without standing, (3) other signs without standing or mounting (slight signs). Presence of another cow in oestrus, access to pasture, Normande breed and Low-Low strategy increased standing detection. In the Normande breed, 97% of oestruses were detected by standing while combining the presence of a herdmate in oestrus and access to pasture with a milk production of less than 6550 kg. Holstein cows had a higher frequency of slight signs oestruses than Normande ones, which was associated with a decreased subsequent calving rate (P<0.05). In multiparous Holstein cows, the odds of slight signs detection was multiplied by 7.8 for the High-High group in comparison with the Low-Low group (P<0.05). In our study milk yield had an effect on oestrus detection which was not explained by BC loss. As High-High cows produced more milk than others, we logically found that an increase in milk yield increased slight signs detection. Conversely, as they lost less BC than others, BC loss improved the chance of standing or mounting detection. These two results show that an increase in milk yield may reduce oestrous behaviour even if BC loss is moderate. Oestrus detection is crucial in seasonal compact calving systems. High phenotypic milk yields appear unsuitable with such systems in regard to depressed oestrous behaviour.

A factor model to analyze heterogeneity in gene expression.

BackgroundMicroarray technology allows the simultaneous analysis of thousands of genes within a single experiment. Significance analyses of transcriptomic data ignore the gene dependence structure. This leads to correlation among test statistics which affects a strong control of the false discovery proportion. A recent method called FAMT allows capturing the gene dependence into factors in order to improve high-dimensional multiple testing procedures. In the subsequent analyses aiming at a functional characterization of the differentially expressed genes, our study shows how these factors can be used both to identify the components of expression heterogeneity and to give more insight into the underlying biological processes.ResultsThe use of factors to characterize simple patterns of heterogeneity is first demonstrated on illustrative gene expression data sets. An expression data set primarily generated to map QTL for fatness in chickens is then analyzed. Contrarily to the analysis based on the raw data, a relevant functional information about a QTL region is revealed by factor-adjustment of the gene expressions. Additionally, the interpretation of the independent factors regarding known information about both experimental design and genes shows that some factors may have different and complex origins.ConclusionsAs biological information and technological biases are identified in what was before simply considered as statistical noise, analyzing heterogeneity in gene expression yields a new point of view on transcriptomic data.

Pleiotropic effects of polymorphism of the gene diacylglycerol-O-transferase 1 (DGAT1) in the mammary gland tissue of dairy cows

Microarray analysis was used to identify genes whose expression in the mammary gland of Holstein-Friesian dairy cows was affected by the nonconservative Ala to Lys amino acid substitution at position 232 in exon VIII of the diacylglycerol-O-transferase 1 (DGAT1) gene. Mammary gland biopsies of 9 homozygous Ala cows, 13 heterozygous cows (Ala/Lys), and 4 homozygous Lys cows in midlactation were taken. Microarray ANOVA and factor analysis for multiple testing methods were used as statistical methods to associate the expression level of the genes present on Affymetrix bovine genome arrays (Affymetrix Inc., Santa Clara, CA) with the DGAT1 gene polymorphism. The data was also analyzed at the level of functional modules by gene set enrichment analysis. In this small-scale experimental setting, DGAT1 gene polymorphism did not modify milk yield and composition significantly, although expected changes occurred in the yields of C14:0, cis-9 C16:1, and long-chain fatty acids. Diacylglycerol-O-transferase 1 gene polymorphism affected the expression of 30 annotated genes related to cell growth, proliferation, and development, remodeling of the tissue, cell signaling and immune system response. Furthermore, the main affected functional modules were related to energy metabolism (lipid biosynthesis, oxidative phosphorylation, electron transport chain, citrate cycle, and propanoate metabolism), protein degradation (proteosome-ubiquitin pathways), and the immune system. We hypothesize that the observed differences in transcriptional activity reflect counter mechanisms of mammary gland tissue to respond to changes in milk fatty acid concentration or composition, or both.

Finite Sample Properties of a Multivariate Extension of Double Regression

This paper provides a study of a multivariate generalization of a method known as double regression, using information from concomitant variables in a double-sampling scheme in order to increase efficiency relative to the ordinary least squares estimator of the linear regression coefficients. Attention is given to the small-sample properties of the estimators in a biometrical context, and some improvements are made on former results concerning, among others, estimation of the residual variance. Emphasis is also made on the interest of the method on experimental costs reduction through an example in the context of carcass dissection studies.

HMI aspects of the usability of Internet services with an in-car terminal on a driving simulator

An experiment on the usability assessment of various control interfaces of an in-vehicle Internet browser, was carried out on the Renault driving simulator with a fictional web site that offers services such as: district map, route planning, electronic messaging, leisure programs, and phone directory. Twenty seven subjects aged from 26 to 69 years carried out this experiment; while performing a car-following task they manipulated an in-car web site by using three control devices: a keyboard, a touchpad, and a voice command. In the quantitative part of the experiment, subjects performed tasks such as writing names, selecting items and moving a cursor on a map, using the keyboard or the touchpad. In the qualitative part, subjects used the in-vehicle web service in a realistic scenario and were allowed to choose the control devices they wanted (voice, touchpad or keyboard). Assessment criteria were speed, distance to the target vehicle, lane position, visual activity, action on the system, operating time, error rate and post trial questionnaire. Based on these criteria, the results showed that browsing while driving seems to remain both complicated and dangerous even when using a simplified browser. However, the results also indicated that, depending on the type of tasks, the different control modes did not have the same efficiency.

Combining location-and-scale batch effect adjustment with data cleaning by latent factor adjustment

BackgroundIn the context of high-throughput molecular data analysis it is common that the observations included in a dataset form distinct groups; for example, measured at different times, under different conditions or even in different labs. These groups are generally denoted as batches. Systematic differences between these batches not attributable to the biological signal of interest are denoted as batch effects. If ignored when conducting analyses on the combined data, batch effects can lead to distortions in the results. In this paper we present FAbatch, a general, model-based method for correcting for such batch effects in the case of an analysis involving a binary target variable. It is a combination of two commonly used approaches: location-and-scale adjustment and data cleaning by adjustment for distortions due to latent factors. We compare FAbatch extensively to the most commonly applied competitors on the basis of several performance metrics. FAbatch can also be used in the context of prediction modelling to eliminate batch effects from new test data. This important application is illustrated using real and simulated data. We implemented FAbatch and various other functionalities in the R package bapred available online from CRAN.ResultsFAbatch is seen to be competitive in many cases and above average in others. In our analyses, the only cases where it failed to adequately preserve the biological signal were when there were extremely outlying batches and when the batch effects were very weak compared to the biological signal.ConclusionsAs seen in this paper batch effect structures found in real datasets are diverse. Current batch effect adjustment methods are often either too simplistic or make restrictive assumptions, which can be violated in real datasets. Due to the generality of its underlying model and its ability to perform well FAbatch represents a reliable tool for batch effect adjustment for most situations found in practice.

A factor-adjusted multiple testing procedure for ERP data analysis

Event-related potentials (ERPs) are now widely collected in psychological research to determine the time courses of mental events. When event-related potentials from treatment conditions are compared, often there is no a priori information on when or how long the differences should occur. Testing simultaneously for differences over the entire set of time points creates a serious multiple comparison problem in which the probability of false positive errors must be controlled, while maintaining reasonable power for correct detection. In this work, we extend the factor-adjusted multiple testing procedure developed by Friguet, Kloareg, and Causeur (Journal of the American Statistical Association, 104, 1406–1415, 2009) to manage the multiplicity problem in ERP data analysis and compare its performance with that of the Benjamini and Hochberg (Journal of the Royal Statistical Society B, 57, 289–300, 1995) false discovery rate procedure, using simulations. The proposed procedure outperformed the latter in detecting more truly significant time points, in addition to reducing the variability of the false discovery rate, suggesting that corrections for mass multiple testings of ERPs can be much improved by modeling the strong local temporal dependencies.

Stability of feature selection in classification issues for high-dimensional correlated data

Handling dependence or not in feature selection is still an open question in supervised classification issues where the number of covariates exceeds the number of observations. Some recent papers surprisingly show the superiority of naive Bayes approaches based on an obviously erroneous assumption of independence, whereas others recommend to infer on the dependence structure in order to decorrelate the selection statistics. In the classical linear discriminant analysis (LDA) framework, the present paper first highlights the impact of dependence in terms of instability of feature selection. A second objective is to revisit the above issue using a flexible factor modeling for the covariance. This framework introduces latent components of dependence, conditionally on which a new Bayes consistency is defined. A procedure is then proposed for the joint estimation of the expectation and variance parameters of the model. The present method is compared to recent regularized diagonal discriminant analysis approaches, assuming independence among features, and regularized LDA procedures, both in terms of classification performance and stability of feature selection. The proposed method is implemented in the R package FADA, freely available from the R repository CRAN.

Exact Distribution of the Regression Esti Mator in Double Sampling

Asymptotic results about the distribution of the regression estimator in a double sampling scheme when using an auxiliary covariate have been established by Engel and Walstra (1991). Conniffe (1985) studied in the finite sample case the closely related model of simultaneous regression equations in econometrics with unequal numbers of observations. The aim of this paper is to provide a normal approximation of the distribution of the regression estimator. First, the exact distribution is derived in the Gaussian framework and the exact moments of the regression estimator are deduced. An Edgeworth expansion of the exact distribution is then calculated in order to propose a normal approximation. The exact distribution, the Edgeworth expansion and the normal approximation are compared throughout an example.