Jean-Jacques Daudin

A mixture model for random graphs

AbstractnThe Erdös–Rényi model of a network is simple and possesses many explicit expressions for average and asymptotic properties, but it does not fit well to real-world networks. The vertices of those networks are often structured in unknown classes (functionally related proteins or social communities) with different connectivity properties. The stochastic block structures model was proposed for this purpose in the context of social sciences, using a Bayesian approach. We consider the same model in a frequentest statistical framework. We give the degree distribution and the clustering coefficient associated with this model, a variational method to estimate its parameters and a model selection criterion to select the number of classes. This estimation procedure allows us to deal with large networks containing thousands of vertices. The method is used to uncover the modular structure of a network of enzymatic reactions.n

Meta-analyses of experimental data in animal nutrition ⋆

Research in animal sciences, especially nutrition, increasingly requires processing and modeling of databases. In certain areas of research, the number of publications and results per publications is increasing, thus periodically requiring quantitative summarizations of literature data. In such instances, statistical methods dealing with the analysis of summary (literature) data, known as meta-analyses, must be used. The implementation of a meta-analysis is done in several phases. The first phase concerns the definition of the study objectives and the identification of the criteria to be used in the selection of prior publications to be used in the construction of the database. Publications must be scrupulously evaluated before being entered into the database. During this phase, it is important to carefully encode each record with pertinent descriptive attributes (experiments, treatments, etc.) to serve as important reference points for the rest of the analysis. Databases from literature data are inherently unbalanced statistically, leading to considerable analytical and interpretation difficulties; missing data are frequent, and data structures are not the outcomes of a classical experimental system. An initial graphical examination of the data is recommended to enhance a global view as well as to identify specific relationships to be investigated. This phase is followed by a study of the meta-system made up of the database to be interpreted. These steps condition the definition of the applied statistical model. Variance decomposition must account for inter- and intrastudy sources; dependent and independent variables must be identified either as discrete (qualitative) or continuous (quantitative). Effects must be defined as either fixed or random. Often, observations must be weighed to account for differences in the precision of the reported means. Once model parameters are estimated, extensive analyses of residual variations must be performed. The roles of the different treatments and studies in the results obtained must be identified. Often, this requires returning to an earlier step in the process. Thus, meta-analyses have inherent heuristic qualities.

Consistency of maximum-likelihood and variational estimators in the Stochastic Block Model

The stochastic block model (SBM) is a probabilistic model de- signed to describe heterogeneous directed and undirected graphs. In this paper, we address the asymptotic inference on SBM by use of maximum- likelihood and variational approaches. The identi ability of SBM is proved, while asymptotic properties of maximum-likelihood and variational esti- mators are provided. In particular, the consistency of these estimators is settled, which is, to the best of our knowledge, the rst result of this type for variational estimators with random graphs.

Assessing the exceptionality of network motifs

Getting and analyzing biological interaction networks is at the core of systems biology. To help understanding these complex networks, many recent works have suggested to focus on motifs which occur more frequently than expected in random. To identify such exceptional motifs in a given network, we propose a statistical and analytical method which does not require any simulation. For this, we first provide an analytical expression of the mean and variance of the count under any exchangeable random graph model. Then we approximate the motif count distribution by a compound Poisson distribution whose parameters are derived from the mean and variance of the count. Thanks to simulations, we show that the compound Poisson approximation outperforms the Gaussian approximation. The compound Poisson distribution can then be used to get an approximate p-value and to decide if an observed count is significantly high or not. Our methodology is applied on protein-protein interaction (PPI) networks, and statistical issues related to exceptional motif detection are discussed.

Multi-residue analysis of pharmaceuticals in aqueous environmental samples by online solid-phase extraction-ultra-high-performance liquid chromatography-tandem mass spectrometry: Optimisation and matrix effects reduction by quick, easy, cheap, effective, rugged and safe extraction

The aim of this study was to develop and optimise an analytical method for the quantification of a bactericide and 13 pharmaceutical products, including 8 antibiotics (fluoroquinolones, tetracyclines, sulfonamides, macrolide), in various aqueous environmental samples: soil water and aqueous fractions of pig slurry, digested pig slurry and sewage sludge. The analysis was performed by online solid-phase extraction coupled to ultra-high performance liquid chromatography with tandem mass spectrometry (online SPE-UHPLC-MS-MS). The main challenge was to minimize the matrix effects observed in mass spectrometry, mostly due to ion suppression. They depended on the dissolved organic carbon (DOC) content and its origin, and ranged between -22% and +20% and between -38% and -93% of the signal obtained without matrix, in soil water and slurry supernatant, respectively. The very variable levels of these matrix effects suggested DOC content cut-offs above which sample purification was required. These cut-offs depended on compounds, with concentrations ranging from 30 to 290mgC/L for antibiotics (except tylosine) up to 600-6400mgC/L for the most apolar compounds. A modified Quick, Easy, Cheap, Effective, Rugged and Safe (QuEChERS) extraction procedure was therefore optimised using an experimental design methodology, in order to purify samples with high DOC contents. Its performance led to a compromise, allowing fluoroquinolone and tetracycline analysis. The QuEChERS extraction salts consisted therefore of sodium acetate, sodium sulfate instead of magnesium sulfate, and sodium ethylenediaminetetraacetate (EDTA) as a ligand of divalent cations. The modified QuEChERS procedure employed for the extraction of pharmaceuticals in slurry and digested slurry liquid phases reduced the matrix effects for almost all the compounds, with extraction recoveries generally above 75%. The performance characteristics of the method were evaluated in terms of linearity, intra-day and inter-day precision, accuracy and limits of quantification, which reached concentration ranges of 5-270ng/L in soil water and sludge supernatant, and 31-2400ng/L in slurry and digested slurry supernatants, depending on the compounds. The new method was then successfully applied for the determination of the target compounds in environmental samples.

Occurrence Probability of Structured Motifs in Random Sequences

The problem of extracting from a set of nucleic acid sequences motifs which may have biological function is more and more important. In this paper, we are interested in particular motifs that may be implicated in the transcription process. These motifs, called structured motifs, are composed of two ordered parts separated by a variable distance and allowing for substitutions. In order to assess their statistical significance, we propose approximations of the probability of occurrences of such a structured motif in a given sequence. An application of our method to evaluate candidate promoters in E. coli and B. subtilis is presented. Simulations show the goodness of the approximations.

A semi-parametric approach for mixture models: Application to local false discovery rate estimation

A procedure to estimate a two-component mixture model where one component is known is proposed. The unknown part is estimated with a weighted kernel function. The weights are defined in an adaptive way. The convergence to a unique solution of our estimation procedure is proven. The procedure is compared with two classical approaches using simulation. In addition, the results obtained are applied to multiple testing procedure in order to estimate the posterior population probabilities and the local false discovery rate.

Deciphering the connectivity structure of biological networks using MixNet

BackgroundAs biological networks often show complex topological features, mathematical methods are required to extract meaningful information. Clustering methods are useful in this setting, as they allow the summary of the networks topology into a small number of relevant classes. Different strategies are possible for clustering, and in this article we focus on a model-based strategy that aims at clustering nodes based on their connectivity profiles.ResultsWe present MixNet, the first publicly available computer software that analyzes biological networks using mixture models. We apply this method to various networks such as the E. coli transcriptional regulatory network, the macaque cortex network, a foodweb network and the Buchnera aphidicola metabolic network. This method is also compared with other approaches such as module identification or hierarchical clustering.ConclusionWe show how MixNet can be used to extract meaningful biological information, and to give a summary of the networks topology that highlights important biological features. This approach is powerful as MixNet is adaptive to the network under study, and finds structural information without any a priori on the structure that is investigated. This makes MixNet a very powerful tool to summarize and decipher the connectivity structure of biological networks.

Biases induced by pooling samples in microarray experiments

MOTIVATIONnIf there is insufficient RNA from the tissues under investigation from one organism, then it is common practice to pool RNA. An important question is to determine whether pooling introduces biases, which can lead to inaccurate results. In this article, we describe two biases related to pooling, from a theoretical as well as a practical point of view.nnnRESULTSnWe model and quantify the respective parts of the pooling bias due to the log transform as well as the bias due to biological averaging of the samples. We also evaluate the impact of the bias on the statistical differential analysis of Affymetrix data.

Characterization of the Three-Factor Eating Questionnaire scores of a young French cohort.

The aims of our study were to characterize the psychological dimensions of eating behaviour of young French adults as measured by the Three Factor Eating Questionnaire (TFEQ) and to analyze the association between the 3 TFEQ mean scores (main scales and subscales) and gender, Body Mass Index (BMI) and socio-demographic data in this population. An online TFEQ questionnaire was used with a nationally representative sample of 1000 young French people (aged 20-39yrs). The average scores were 6.3±0.1 (sem) for dietary restraint, 6.0±0.1 for disinhibition and 5.0±0.1 for hunger. Compared to the limit commonly used in human food studies, young French adults were characterized by low restraint and low disinhibition levels. There was a significant gender effect on both restraint and disinhibition scores, with women showing significantly higher scores than men. Concerning the link between TFEQ scores and BMI, there was a significant effect of the BMI category on cognitive restraint, disinhibition and hunger. Disinhibition was the factor most strongly associated to BMI, independently of gender. Our results highlight both the importance of taking into account not only disinhibition but also cognitive restraint and the usefulness of subscales when studying eating behaviour and its link to body weight. We characterize the eating behaviour of a French cohort with criteria often chosen for healthy volunteers in human food studies. Consequently, we suggest new TFEQ limits (6 for cognitive restraint and disinhibition, 5 for hunger) lower than those traditionally used for this category of the population in clinical food studies.