Correlation Approach (correlation + approach)

Distribution by Scientific Domains

Selected Abstracts

Validation of Surrogate Markers in Multiple Randomized Clinical Trials with Repeated Measurements: Canonical Correlation Approach

BIOMETRICS, Issue 4 2004
Ariel Alonso
Summary Part of the recent literature on the evaluation of biomarkers as surrogate endpoints starts from a multitrial context, which leads to a definition of validity in terms of the quality of both trial-level and individual-level association between the surrogate and true endpoints (Buyse et al., 2000, Biostatistics1, 49,67). These authors concentrated on cross-sectional continuous responses. However, in many randomized clinical studies, repeated measurements are encountered on either or both endpoints. A challenge in this setting is the formulation of a simple and meaningful concept of "surrogacy."Alonso et al. (2003, Biometrical Journal45, 931,945) proposed the variance reduction factor (VRF) to evaluate surrogacy at the individual level. They also showed how and when this concept should be extended to study surrogacy at the trial level. Here, we approach the problem from the natural canonical correlation perspective. We define a class of canonical correlation functions that can be used to study surrogacy at the trial and individual level. We show that the VRF and the R2 measure defined by Buyse et al. (2000) follow as special cases. Simulations are conducted to evaluate the performance of different members of this family. The methodology is illustrated on data from a meta-analysis of five clinical trials comparing antipsychotic agents for the treatment of chronic schizophrenia. [source]

The relationship between baseline value and its change: problems in categorization and the proposal of a new method

Yu-Kang Tu
Oral health researchers have shown great interest in the relationship between the initial status of diseases and subsequent changes following treatment. Two main approaches have been adopted to provide evidence of a positive association between baseline values and their changes following treatment. One approach is to use correlation or regression to test the relationship between baseline measurements and subsequent change (correlation/regression approach). The second approach is to categorize the lesions into subgroups, according to threshold values, and subsequently compare the treatment effects across the two (or more) subgroups (categorization approach). However, the correlation/regression approach suffers a methodological weakness known as mathematical coupling. Consequently, the statistical procedure of testing the null hypothesis becomes inappropriate. Categorization seems to avoid the problem of mathematical coupling, although it still suffers regression to the mean. We show, first, how the appropriate null hypothesis may be established to analyze the relationship between baseline values and change in the correlation approach and, second, we use computer simulations to investigate the impact of regression to the mean on the significance testing of the differences in the average treatment effects (or average baseline values) in the categorization approach. Data available from previous literature are reanalyzed by testing the appropriate null hypotheses and the results are compared to those from testing the usual (incorrect) null hypothesis. The results indicate that both the correlation and categorization approaches can give rise to misleading conclusions and that more appropriate methods, such as Oldham's method and our new approach of deriving the correct null hypothesis, should be adopted. [source]

Functional connectivity of default mode network components: Correlation, anticorrelation, and causality

Lucina Q. Uddin
Abstract The default mode network (DMN), based in ventromedial prefrontal cortex (vmPFC) and posterior cingulate cortex (PCC), exhibits higher metabolic activity at rest than during performance of externally oriented cognitive tasks. Recent studies have suggested that competitive relationships between the DMN and various task-positive networks involved in task performance are intrinsically represented in the brain in the form of strong negative correlations (anticorrelations) between spontaneous fluctuations in these networks. Most neuroimaging studies characterize the DMN as a homogenous network, thus few have examined the differential contributions of DMN components to such competitive relationships. Here, we examined functional differentiation within the DMN, with an emphasis on understanding competitive relationships between this and other networks. We used a seed correlation approach on resting-state data to assess differences in functional connectivity between these two regions and their anticorrelated networks. While the positively correlated networks for the vmPFC and PCC seeds largely overlapped, the anticorrelated networks for each showed striking differences. Activity in vmPFC negatively predicted activity in parietal visual spatial and temporal attention networks, whereas activity in PCC negatively predicted activity in prefrontal-based motor control circuits. Granger causality analyses suggest that vmPFC and PCC exert greater influence on their anticorrelated networks than the other way around, suggesting that these two default mode nodes may directly modulate activity in task-positive networks. Thus, the two major nodes comprising the DMN are differentiated with respect to the specific brain systems with which they interact, suggesting greater heterogeneity within this network than is commonly appreciated. Hum Brain Mapp, 2009. © 2008 Wiley-Liss, Inc. [source]

Iterative correlation-based controller tuning

A. Karimi
Abstract This paper gives an overview on the theoretical results of recently developed algorithms for iterative controller tuning based on the correlation approach. The basic idea is to decorrelate the output error between the achieved and designed closed-loop systems by iteratively tuning the controller parameters. Two different approaches are investigated. In the first one, a correlation equation involving a vector of instrumental variables is solved using the stochastic approximation method. It is shown that, with an appropriate choice of instrumental variables and a finite number of data at each iteration, the algorithm converges to the solution of the correlation equation. The convergence conditions are derived and the accuracy of the estimates are studied. The second approach is based on the minimization of a correlation criterion. The frequency analysis of the criterion shows that the two norm of the error between the desired and achieved closed-loop transfer functions is minimized independent of the noise characteristics. This analysis leads to the definition of a generalized correlation criterion which allows the mixed sensitivity problem to be handled in two norm. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Zonal circulations over the Indian and Pacific Oceans and the level of lakes Victoria and Tanganyika

Laurent Bergonzini
Abstract Level records of two East African Great Lakes, Lake Victoria and Lake Tanganyika, which are considered as hydro-climatic proxies, are analysed. Comparisons between the two lake signals show synchronisms, which can only be accounted for by large-scale mechanisms. Lake-level variations associated with the short rains season (October,January) appear to have a prominent effect on the annual lake levels. The relations between lake-level variations and atmospheric circulation indexes are then investigated. Over the period 1946,2000, four indexes are selected to characterize the October,December zonal circulation over the Pacific and Indian Oceans. Over the Indian Ocean two surface zonal wind indexes (ZWIs) are used. For the Pacific, the southern oscillation index (SOI) and the Niño3 index are held to account for the El Niño,southern oscillation (ENSO). It is shown that significant overall negative correlations of level fluctuations are preferentially obtained with Indian Ocean circulation indexes. Although ZWI is highly correlated with the ENSO indexes, the latter display weaker relations with East African lake levels. It is shown that, for the 1946,2000 period, the October,December zonal circulation cell over the Indian Ocean plays a key role in the equatorial lake-level anomalies, thus demonstrating their influence on the hydro-climatic interannual variability of a large region. However, lake-level variation is a function not only of regional hydro-climatic conditions, but also of the initial (October) absolute lake level. Higher correlations are evident in a multiple correlation approach taking into account the initial lake level status in addition to the ZWI and ENSO indexes. Copyright © 2004 Royal Meteorological Society [source]

Determination of lattice-transform density profiles for multilayered three-dimensional microcrystals in electron crystallography

Eva Dimmeler
Electron crystallography on multilayered three-dimensional microcrystals has been limited in application by the need to define precisely the three-dimensional shape of the diffraction density profiles. A new method is presented here to obtain this profile from experimental spot positions which are shifted in a characteristic way from the expected Bragg positions. While the Bragg positions are defined by the diffraction geometry, the characteristic shift additionally depends on the density profile in Fourier space. In general, these two effects are intermingled. A new correlation approach is presented which uses characteristic shift patterns to separate these effects. This technique also allows the determination of all three crystallographic unit-cell dimensions from a single tilted electron diffraction pattern. It was tested on simulated diffraction patterns and applied to experimental data of frozen hydrated crystals of the protein catalase. Since multilayered catalase crystals with different numbers of crystallographic layers were studied, an inhomogeneous data set had to be evaluated. Processing of such data is now possible using the new correlation approach. [source]


ABSTRACT Modeling of the heat transfer process in thermal processing is important for the process design and control. Artificial neural networks (ANNs) have been used in recent years in heat transfer modeling as a potential alternative to conventional dimensionless correlation approach and shown to be even better performers. In this study, ANN models were developed for apparent heat transfer coefficients associated with canned particulates in high viscous Newtonian and non-Newtonian fluids during end-over-end thermal processing in a pilot-scale rotary retort. A portion of experimental data obtained for the associated heat transfer coefficients were used for training while the rest were used for testing. The principal configuration parameters were the combination of learning rules and transfer functions, number of hidden layers, number of neurons in each hidden layer and number of learning runs. For the Newtonian fluids, the optimal conditions were two hidden layers, five neurons in each hidden layer, the delta learning rule, a sine transfer function and 40,000 learning runs, while for the non-Newtonian fluids, the optimal conditions were one hidden layer, six neurons in each hidden layer, the delta learning rule, a hyperbolic tangent transfer function and 50,000 learning runs. The prediction accuracies for the ANN models were much better compared with those from the dimensionless correlations. The trained network was found to predict responses with a mean relative error of 2.9,3.9% for the Newtonian fluids and 4.7,5.9% for the non-Newtonian fluids, which were 27,62% lower than those associated with the dimensionless correlations. Algebraic solutions were included, which could be used to predict the heat transfer coefficients without requiring an ANN. PRACTICAL APPLICATIONS The artificial neural network (ANN) model is a network of computational elements that was originally developed to mimic the function of the human brain. ANN models do not require the prior knowledge of the relationship between the input and output variables because they can discover the relationship through successive training. Moreover, ANN models can predict several output variables at the same time, which is difficult in general regression methods. ANN concepts have been successfully used in food processing for prediction, quality control and pattern recognition. ANN models have been used in recent years for heat transfer modeling as a potential alternative to conventional dimensionless correlation approach and shown to be even better performers. In this study, ANN models were successfully developed for the heat transfer parameters associated with canned particulate high viscous Newtonian and non-Newtonian fluids during an end-over-end rotation thermal processing. Optimized configuration parameters were obtained by choosing appropriate combinations of learning rule, transfer function, learning runs, hidden layers and number of neurons. The trained network was found to predict parameter responses with mean relative errors considerably lower than from dimensionless correlations. [source]