Structural components in functional data

Analyzing functional data often leads to finding common factors, for which functional principal component analysis proves to be a useful tool to summarize and characterize the random variation in a function space. The representation in terms of eigenfunctions is optimal in the sense of L-2 approximation. However, the eigenfunctions are not always directed towards an interesting and interpretable direction in the context of functional data and thus could obscure the underlying structure. To overcome such difficulty, an alternative to functional principal component analysis is proposed that produces directed components which may be more informative and easier to interpret. These structural components are similar to principal components, but are adapted to situations in which the domain of the function may be decomposed into disjoint intervals such that there is effectively independence between intervals and positive correlation within intervals. The approach is demonstrated with synthetic examples as well as real data. Properties for special cases are also studied.

Multilayer perceptron with local constraint as an emerging method in spatial data analysis

The use of Geographic Information Systems has revolutionalized the handling and the visualization of geo-referenced data and has underlined the critic role of spatial analysis. The usual tools for such a purpose are geostatistics which are widely used in Earth science. Geostatistics are based upon several hypothesis which are not always verified in practice. On the other hand, Artificial Neural Network (ANN) a priori can be used without special assumptions and are known to be flexible. This paper proposes to discuss the application of ANN in the case of the interpolation of a geo-referenced variable.

Subclinical hypothyroidism and the risk of coronary heart disease and mortality: an individual participant data analysis from nine prospective cohort studies

Texte intégral: http://www.springerlink.com/content/3q68180337551r47/fulltext.pdf

Subclinical thyroid dysfunction and the risk of heart failure events: an individual participant data analysis from 6 prospective cohorts.

BACKGROUND: American College of Cardiology/American Heart Association guidelines for the diagnosis and management of heart failure recommend investigating exacerbating conditions such as thyroid dysfunction, but without specifying the impact of different thyroid-stimulation hormone (TSH) levels. Limited prospective data exist on the association between subclinical thyroid dysfunction and heart failure events. METHODS AND RESULTS: We performed a pooled analysis of individual participant data using all available prospective cohorts with thyroid function tests and subsequent follow-up of heart failure events. Individual data on 25 390 participants with 216 248 person-years of follow-up were supplied from 6 prospective cohorts in the United States and Europe. Euthyroidism was defined as TSH of 0.45 to 4.49 mIU/L, subclinical hypothyroidism as TSH of 4.5 to 19.9 mIU/L, and subclinical hyperthyroidism as TSH <0.45 mIU/L, the last two with normal free thyroxine levels. Among 25 390 participants, 2068 (8.1%) had subclinical hypothyroidism and 648 (2.6%) had subclinical hyperthyroidism. In age- and sex-adjusted analyses, risks of heart failure events were increased with both higher and lower TSH levels (P for quadratic pattern <0.01); the hazard ratio was 1.01 (95% confidence interval, 0.81-1.26) for TSH of 4.5 to 6.9 mIU/L, 1.65 (95% confidence interval, 0.84-3.23) for TSH of 7.0 to 9.9 mIU/L, 1.86 (95% confidence interval, 1.27-2.72) for TSH of 10.0 to 19.9 mIU/L (P for trend <0.01) and 1.31 (95% confidence interval, 0.88-1.95) for TSH of 0.10 to 0.44 mIU/L and 1.94 (95% confidence interval, 1.01-3.72) for TSH <0.10 mIU/L (P for trend=0.047). Risks remained similar after adjustment for cardiovascular risk factors. CONCLUSION: Risks of heart failure events were increased with both higher and lower TSH levels, particularly for TSH ≥10 and <0.10 mIU/L.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Advanced geostatistical and machine-learning models for spatial data analysis of radioactively contaminated regions

Radioactive soil-contamination mapping and risk assessment is a vital issue for decision makers. Traditional approaches for mapping the spatial concentration of radionuclides employ various regression-based models, which usually provide a single-value prediction realization accompanied (in some cases) by estimation error. Such approaches do not provide the capability for rigorous uncertainty quantification or probabilistic mapping. Machine learning is a recent and fast-developing approach based on learning patterns and information from data. Artificial neural networks for prediction mapping have been especially powerful in combination with spatial statistics. A data-driven approach provides the opportunity to integrate additional relevant information about spatial phenomena into a prediction model for more accurate spatial estimates and associated uncertainty. Machine-learning algorithms can also be used for a wider spectrum of problems than before: classification, probability density estimation, and so forth. Stochastic simulations are used to model spatial variability and uncertainty. Unlike regression models, they provide multiple realizations of a particular spatial pattern that allow uncertainty and risk quantification. This paper reviews the most recent methods of spatial data analysis, prediction, and risk mapping, based on machine learning and stochastic simulations in comparison with more traditional regression models. The radioactive fallout from the Chernobyl Nuclear Power Plant accident is used to illustrate the application of the models for prediction and classification problems. This fallout is a unique case study that provides the challenging task of analyzing huge amounts of data ('hard' direct measurements, as well as supplementary information and expert estimates) and solving particular decision-oriented problems.

How to interprete subclinical thyroid dysfunction in the prevention and management of heart failure events? Individual participant data analysis from six prospective cohorts

Background: Guidelines of the Diagnosis and Management of Heart Failure (HF) recommend investigating exacerbating conditions, such as thyroid dysfunction, but without specifying impact of different TSH levels. Limited prospective data exist regarding the association between subclinical thyroid dysfunction and HF events. Methods: We performed a pooled analysis of individual participant data using all available prospective cohorts with thyroid function tests and subsequent follow-up of HF events. Individual data on 25,390 participants with 216,247 person-years of follow-up were supplied from 6 prospective cohorts in the United States and Europe. Euthyroidism was defined as TSH 0.45-4.49 mIU/L, subclinical hypothyroidism as TSH 4.5-19.9 mIU/L and subclinical hyperthyroidism as TSH <0.45 mIU/L, both with normal free thyroxine levels. HF events were defined as acute HF events, hospitalization or death related to HF events. Results: Among 25,390 participants, 2068 had subclinical hypothyroidism (8.1%) and 648 subclinical hyperthyroidism (2.6%). In age- and gender-adjusted analyses, risks of HF events were increased with both higher and lower TSH levels (P for quadratic pattern<0.01): hazard ratio (HR) was 1.01 (95% confidence interval [CI] 0.81-1.26) for TSH 4.5-6.9 mIU/L, 1.65 (CI 0.84-3.23) for TSH 7.0-9.9 mIU/L, 1.86 (CI 1.27-2.72) for TSH 10.0-19.9 mIUL/L (P for trend <0.01), and was 1.31 (CI 0.88-1.95) for TSH 0.10-0.44 mIU/L and 1.94 (CI 1.01-3.72) for TSH <0.10 mIU/L (P for trend=0.047). Risks remained similar after adjustment for cardiovascular risk factors. Conclusion: Risks of HF events were increased with both higher and lower TSH levels, particularly for TSH ≥10 mIU/L and for TSH <0.10 mIU/L. Our findings might help to interpret TSH levels in the prevention and investigation of HF.

Thyroid antibody status, subclinical hypothyroidism, and the risk of coronary heart disease: an individual participant data analysis.

CONTEXT: Subclinical hypothyroidism has been associated with increased risk of coronary heart disease (CHD), particularly with thyrotropin levels of 10.0 mIU/L or greater. The measurement of thyroid antibodies helps predict the progression to overt hypothyroidism, but it is unclear whether thyroid autoimmunity independently affects CHD risk. OBJECTIVE: The objective of the study was to compare the CHD risk of subclinical hypothyroidism with and without thyroid peroxidase antibodies (TPOAbs). DATA SOURCES AND STUDY SELECTION: A MEDLINE and EMBASE search from 1950 to 2011 was conducted for prospective cohorts, reporting baseline thyroid function, antibodies, and CHD outcomes. DATA EXTRACTION: Individual data of 38 274 participants from six cohorts for CHD mortality followed up for 460 333 person-years and 33 394 participants from four cohorts for CHD events. DATA SYNTHESIS: Among 38 274 adults (median age 55 y, 63% women), 1691 (4.4%) had subclinical hypothyroidism, of whom 775 (45.8%) had positive TPOAbs. During follow-up, 1436 participants died of CHD and 3285 had CHD events. Compared with euthyroid individuals, age- and gender-adjusted risks of CHD mortality in subclinical hypothyroidism were similar among individuals with and without TPOAbs [hazard ratio (HR) 1.15, 95% confidence interval (CI) 0.87-1.53 vs HR 1.26, CI 1.01-1.58, P for interaction = .62], as were risks of CHD events (HR 1.16, CI 0.87-1.56 vs HR 1.26, CI 1.02-1.56, P for interaction = .65). Risks of CHD mortality and events increased with higher thyrotropin, but within each stratum, risks did not differ by TPOAb status. CONCLUSIONS: CHD risk associated with subclinical hypothyroidism did not differ by TPOAb status, suggesting that biomarkers of thyroid autoimmunity do not add independent prognostic information for CHD outcomes.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

Subclinical Hypothyroidism and the Risk of Stroke Events and Fatal Stroke: An Individual Participant Data Analysis.

OBJECTIVE: The objective was to determine the risk of stroke associated with subclinical hypothyroidism. DATA SOURCES AND STUDY SELECTION: Published prospective cohort studies were identified through a systematic search through November 2013 without restrictions in several databases. Unpublished studies were identified through the Thyroid Studies Collaboration. We collected individual participant data on thyroid function and stroke outcome. Euthyroidism was defined as TSH levels of 0.45-4.49 mIU/L, and subclinical hypothyroidism was defined as TSH levels of 4.5-19.9 mIU/L with normal T4 levels. DATA EXTRACTION AND SYNTHESIS: We collected individual participant data on 47 573 adults (3451 subclinical hypothyroidism) from 17 cohorts and followed up from 1972-2014 (489 192 person-years). Age- and sex-adjusted pooled hazard ratios (HRs) for participants with subclinical hypothyroidism compared to euthyroidism were 1.05 (95% confidence interval [CI], 0.91-1.21) for stroke events (combined fatal and nonfatal stroke) and 1.07 (95% CI, 0.80-1.42) for fatal stroke. Stratified by age, the HR for stroke events was 3.32 (95% CI, 1.25-8.80) for individuals aged 18-49 years. There was an increased risk of fatal stroke in the age groups 18-49 and 50-64 years, with a HR of 4.22 (95% CI, 1.08-16.55) and 2.86 (95% CI, 1.31-6.26), respectively (p trend 0.04). We found no increased risk for those 65-79 years old (HR, 1.00; 95% CI, 0.86-1.18) or ≥ 80 years old (HR, 1.31; 95% CI, 0.79-2.18). There was a pattern of increased risk of fatal stroke with higher TSH concentrations. CONCLUSIONS: Although no overall effect of subclinical hypothyroidism on stroke could be demonstrated, an increased risk in subjects younger than 65 years and those with higher TSH concentrations was observed.

Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project.

We report the generation and analysis of functional data from multiple, diverse experiments performed on a targeted 1% of the human genome as part of the pilot phase of the ENCODE Project. These data have been further integrated and augmented by a number of evolutionary and computational analyses. Together, our results advance the collective knowledge about human genome function in several major areas. First, our studies provide convincing evidence that the genome is pervasively transcribed, such that the majority of its bases can be found in primary transcripts, including non-protein-coding transcripts, and those that extensively overlap one another. Second, systematic examination of transcriptional regulation has yielded new understanding about transcription start sites, including their relationship to specific regulatory sequences and features of chromatin accessibility and histone modification. Third, a more sophisticated view of chromatin structure has emerged, including its inter-relationship with DNA replication and transcriptional regulation. Finally, integration of these new sources of information, in particular with respect to mammalian evolution based on inter- and intra-species sequence comparisons, has yielded new mechanistic and evolutionary insights concerning the functional landscape of the human genome. Together, these studies are defining a path for pursuit of a more comprehensive characterization of human genome function.

Structural and Resting State Functional Connectivity of the Subthalamic Nucleus: Identification of Motor STN Parts and the Hyperdirect Pathway.

Deep brain stimulation (DBS) for Parkinson's disease often alleviates the motor symptoms, but causes cognitive and emotional side effects in a substantial number of cases. Identification of the motor part of the subthalamic nucleus (STN) as part of the presurgical workup could minimize these adverse effects. In this study, we assessed the STN's connectivity to motor, associative, and limbic brain areas, based on structural and functional connectivity analysis of volunteer data. For the structural connectivity, we used streamline counts derived from HARDI fiber tracking. The resulting tracks supported the existence of the so-called "hyperdirect" pathway in humans. Furthermore, we determined the connectivity of each STN voxel with the motor cortical areas. Functional connectivity was calculated based on functional MRI, as the correlation of the signal within a given brain voxel with the signal in the STN. Also, the signal per STN voxel was explained in terms of the correlation with motor or limbic brain seed ROI areas. Both right and left STN ROIs appeared to be structurally and functionally connected to brain areas that are part of the motor, associative, and limbic circuit. Furthermore, this study enabled us to assess the level of segregation of the STN motor part, which is relevant for the planning of STN DBS procedures.