IntroductionIn order to study social health inequalities, contextual (or ecologic) data may constitute an appropriate alternative to individual socioeconomic characteristics. Indices can be used to summarize the multiple dimensions of the neighborhood socioeconomic status. This work proposes a statistical procedure to create a neighborhood socioeconomic index.MethodsThe study setting is composed of three French urban areas. Socioeconomic data at the census block scale come from the 1999 census. Successive principal components analyses are used to select variables and create the index. Both metropolitan area-specific and global indices are tested and compared. Socioeconomic categories are drawn with hierarchical clustering as a reference to determine “optimal” thresholds able to create categories along a one-dimensional index.ResultsAmong the twenty variables finally selected in the index, 15 are common to the three metropolitan areas. The index explains at least 57% of the variance of these variables in each metropolitan area, with a contribution of more than 80% of the 15 common variables.ConclusionsThe proposed procedure is statistically justified and robust. It can be applied to multiple geographical areas or socioeconomic variables and provides meaningful information to public health bodies. We highlight the importance of the classification method. We propose an R package in order to use this procedure.

Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the k-means algorithm, a new class of recursive stochastic gradient algorithms designed for the k-medians loss criterion is proposed. By their recursive nature, these algorithms are very fast and are well adapted to deal with large samples of data that are allowed to arrive sequentially. It is proved that the stochastic gradient algorithm converges almost surely to the set of stationary points of the underlying loss criterion. A particular attention is paid to the averaged versions, which are known to have better performances, and a data-driven procedure that allows automatic selection of the value of the descent step is proposed. The performance of the averaged sequential estimator is compared on a simulation study, both in terms of computation speed and accuracy of the estimations, with more classical partitioning techniques such as k-means, trimmed k-means and PAM (partitioning around medoids). Finally, this new online clustering technique is illustrated on determining television audience profiles with a sample of more than 5000 individual television audiences measured every minute over a period of 24 hours.

The present study addresses the problem of sequential least square multidimensional linear regression, particularly in the case of a data stream, using a stochastic approximation process. To avoid the phenomenon of numerical explosion which can be encountered and to reduce the computing time in order to take into account a maximum of arriving data, we propose using a process with online standardized data instead of raw data and the use of several observations per step or all observations until the current step. Herein, we define and study the almost sure convergence of three processes with online standardized data: a classical process with a variable step-size and use of a varying number of observations per step, an averaged process with a constant step-size and use of a varying number of observations per step, and a process with a variable or constant step-size and use of all observations until the current step. Their convergence is obtained under more general assumptions than classical ones. These processes are compared to classical processes on 11 datasets for a fixed total number of observations used and thereafter for a fixed processing time. Analyses indicate that the third-defined process typically yields the best results.

Virtually all cancer biological attributes are heterogeneous. Because of this, it is currently difficult to reconcile results of cancer transcriptome and proteome experiments. It is also established that cancer somatic mutations arise at rates higher than suspected, but yet are insufficient to explain all cancer cell heterogeneity. We have analyzed sequence variations of 17 abundantly expressed genes in a large set of human ESTs originating from either normal or cancer samples. We show that cancer ESTs have greater variations than normal ESTs for >70% of the tested genes. These variations cannot be explained by known and putative SNPs.

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Online learning is a method for analyzing very large datasets ("big data") as well as data streams. In this article, we consider the case of constrained binary logistic regression and show the interest of using processes with an online standardization of the data, in particular to avoid numerical explosions or to allow the use of shrinkage methods. We prove the almost sure convergence of such a process and propose using a piecewise constant step-size such that the latter does not decrease too quickly and does not reduce the speed of convergence. We compare twenty-four stochastic approximation processes with raw or online standardized data on five real or simulated data sets. Results show that, unlike processes with raw data, processes with online standardized data can prevent numerical explosions and yield the best results.

We present a methodology for constructing a short-term event risk score from an ensemble predictor using bootstrap samples, two different classification rules, logistic regression and linear discriminant analysis for mixed data, continuous or categorical, and random selections of variables into the construction of predictors. We establish a property of linear discriminant analysis for mixed data and define an event risk measure by an odds-ratio. This methodology is applied to heart failure patients on whom biological, clinical and medical history variables were measured and the results obtained from our data are detailed.

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