MOTIVATION: In the field of oncology, statistical models are used for the discovery of candidate factors that influence the development of the pathology or its outcome. These statistical models can be designed in a multiblock framework to study the relationship between different multiomic data, and variable selection is often achieved by imposing constraints on the model parameters. A priori graph constraints have been used in the literature as a way to improve feature selection in the model, yielding more interpretability. However, it is still unclear how these graphs interact with the models and how they impact the feature selection. Additionally, with the availability of different graphs encoding different information, one can wonder how the choice of the graph meaningfully impacts the results obtained. RESULTS: We proposed to study the graph penalty impact on a multiblock model. Specifically, we used the SGCCA as the multiblock framework. We studied the effect of the penalty on the model using the TCGA-LGG dataset. Our findings are 3-fold. We showed that the graph penalty increases the number of selected genes from this dataset, while selecting genes already identified in other works as pertinent biomarkers in the pathology. We demonstrated that using different graphs leads to different though consistent results, but that graph density is the main factor influencing the obtained results. Finally, we showed that the graph penalty increases the performance of the survival prediction from the model-derived components and the interpretability of the results. AVAILABILITY AND IMPLEMENTATION: Source code is freely available at https://github.com/neurospin/netSGCCA.

The growing number of modalities (e.g. multi-omics, imaging and clinical data) characterizing a given disease provides physicians and statisticians with complementary facets reflecting the disease process but emphasizes the need for novel statistical methods of data analysis able to unify these views. Such data sets are indeed intrinsically structured in blocks, where each block represents a set of variables observed on a group of individuals. Therefore, classical statistical tools cannot be applied without altering their organization, with the risk of information loss. Regularized generalized canonical correlation analysis (RGCCA) and its sparse generalized canonical correlation analysis (SGCCA) counterpart are component-based methods for exploratory analyses of data sets structured in blocks of variables. Rather than operating sequentially on parts of the measurements, the RGCCA/SGCCA-based integrative analysis method aims at summarizing the relevant information between and within the blocks. It processes a priori information defining which blocks are supposed to be linked to one another, thus reflecting hypotheses about the biology underlying the data blocks. It also requires the setting of extra parameters that need to be carefully adjusted.Here, we provide practical guidelines for the use of RGCCA/SGCCA. We also illustrate the flexibility and usefulness of RGCCA/SGCCA on a unique cohort of patients with four genetic subtypes of spinocerebellar ataxia, in which we obtained multiple data sets from brain volumetry and magnetic resonance spectroscopy, and metabolomic and lipidomic analyses. As a first step toward the extraction of multimodal biomarkers, and through the reduction to a few meaningful components and the visualization of relevant variables, we identified possible markers of disease progression.

Predictive models can be used on high-dimensional brain images to decode cognitive states or diagnosis/prognosis of a clinical condition/evolution. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to adhere to domain-specific constraints. Total variation (TV) is a promising candidate for structured penalization: it enforces spatial smoothness of the solution while segmenting predictive regions from the background. We consider the problem of minimizing the sum of a smooth convex loss, a non-smooth convex penalty (whose proximal operator is known) and a wide range of possible complex, non-smooth convex structured penalties such as TV or overlapping group Lasso. Existing solvers are either limited in the functions they can minimize or in their practical capacity to scale to high-dimensional imaging data. Nesterov's smoothing technique can be used to minimize a large number of non-smooth convex structured penalties. However, reasonable precision requires a small smoothing parameter, which slows down the convergence speed to unacceptable levels. To benefit from the versatility of Nesterov's smoothing technique, we propose a first order continuation algorithm, CONESTA, which automatically generates a sequence of decreasing smoothing parameters. The generated sequence maintains the optimal convergence speed toward any globally desired precision. Our main contributions are: gap to probe the current distance to the global optimum in order to adapt the smoothing parameter and the To propose an expression of the duality convergence speed. This expression is applicable to many penalties and can be used with other solvers than CONESTA. We also propose an expression for the particular smoothing parameter that minimizes the number of iterations required to reach a given precision. Furthermore, we provide a convergence proof and its rate, which is an improvement over classical proximal gradient smoothing methods. We demonstrate on both simulated and high-dimensional structural neuroimaging data that CONESTA significantly outperforms many state-of-the-art solvers in regard to convergence speed and precision.

MOTIVATION: In statistical bioinformatics research, different optimization mechanisms potentially lead to 'over-optimism' in published papers. So far, however, a systematic critical study concerning the various sources underlying this over-optimism is lacking. RESULTS: We present an empirical study on over-optimism using high-dimensional classification as example. Specifically, we consider a 'promising' new classification algorithm, namely linear discriminant analysis incorporating prior knowledge on gene functional groups through an appropriate shrinkage of the within-group covariance matrix. While this approach yields poor results in terms of error rate, we quantitatively demonstrate that it can artificially seem superior to existing approaches if we 'fish for significance'. The investigated sources of over-optimism include the optimization of datasets, of settings, of competing methods and, most importantly, of the method's characteristics. We conclude that, if the improvement of a quantitative criterion such as the error rate is the main contribution of a paper, the superiority of new algorithms should always be demonstrated on independent validation data. AVAILABILITY: The R codes and relevant data can be downloaded from http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/overoptimism/, such that the study is completely reproducible.

Reconstruction of gene-gene interactions from large-scale data such as microarrays is a first step toward better understanding the mechanisms at work in the cell. Two main issues have to be managed in such a context: 1) choosing which measures have to be used to distinguish between direct and indirect interactions from high-dimensional microarray data and 2) constructing networks with a low proportion of false-positive edges. We present an efficient methodology for the reconstruction of gene interaction networks in a small-sample-size setting. The strength of independence of any two genes is measured, in such "high-dimensional network," by a regularized estimation of partial correlation based on Partial Least Squares Regression. We finally emphasize specific properties of the proposed method. To assess the sensitivity and specificity of the method, we carried out the reconstruction of networks from simulated data. We also tested PLS-based partial correlation network on static and dynamic real microarray data. An R implementation of the proposed algorithm is available from http://biodev.extra.cea.fr/plspcnetwork/.