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PubMedDate not supplied

[Statistical parametric mapping (SPM) in nuclear medicine].

In the scope of medical research, functional neuroimaging analysis permits the study of pathological or cognitive cerebral processes by using statistical quantification techniques. A tool of increasing use is the SPM (Statistical Parametric Mapping) software due to its wide availability and the variety of statistical studies that can be made. Nevertheless, being unaware of the theoretical background on which it is based may easily lead to inaccurate results and even to the reaching of erroneous conclusions. The present article summarizes these theoretical principles and discusses the main key points of the method without requiring advanced mathematical knowledge.

Data Interpretation, Statistical↗

PubMed2002

A statistical approach to estimate O3 uptake of ponderosa pine in a mediterranean climate.

In highly polluted sites, stomatal behavior is sluggish with respect to light, vapor pressure deficit, and internal CO2 concentration (Ci) and poorly described by existing models. Statistical models were developed to estimate stomatal conductance (gs) of 40-year-old ponderosa pine at three sites differing in pollutant exposure for the purpose of calculating O3 uptake. Gs was estimated using julian day, hour of day, pre-dawn xylem potential and photosynthetic photon flux density (PPFD). The median difference between estimated and observed field gs did not exceed 10 mmol H2O m(-2) s(-1), and estimated gs within 95% confidence intervals. 03 uptake was calculated from hourly estimated gs, hourly O3 concentration, and a constant to correct for the difference in diffusivity between water vapor and 03. The simulation model TREGRO was also used to calculate the cumulative 03 uptake at all three sites. 03 uptake estimated by the statistical model was higher than that simulated by TREGRO because gas exchange rates were proportionally higher. O3 exposure and uptake were significantly correlated (r2>0.92), because O3 exposure and gs were highly correlated in both statistical and simulation models.

Air Pollutants↗

PubMed1997

Graphs in sequence spaces: a review of statistical geometry.

Statistical geometry is a method of comparative sequence analysis of genes. Based on the concept of the sequence space of nucleic acids it computes the geometries of sequence sets, mainly quartets, by combining both the vertical and horizontal information content of the sequences. The geometries can be used to deduce, for example, the degree of tree-likeness of the data set without any a priori assumption of an evolution model. Furthermore, statistical geometry allows to detect varying positional substitution rates in sequences. Applications of the method to tRNA sequences have provided an assessment for the age of the genetic code. Furthermore, applications of statistical geometry to homeoboxes as well as different virus families have helped to assign reliable kinship relationships. In addition, a lower bound for the age of the common ancestor of the human and simian immunodeficiency viruses has been established.

DNA, Viral↗

PubMed2003

Statistical modeling of atherosclerotic plaque in carotid B mode images--a feasibility study.

A feasibility study undertaken to model atherosclerotic plaque in carotid B-mode images is presented. The study is based on 33 regions-of-interest collected from arterial images obtained from four patients. A bimodal gamma distribution with five parameters is proposed to model the statistics of the pixels in the gray-level images. The parameters of the distribution are evaluated for regions containing plaque using curve-fitting techniques. This bimodal distribution appears to be a reasonable fit to the statistics of the pixels. This statistical model may aid in the objective classification of arterial plaque through the use of its parameters.

Algorithms↗

PubMed1985

[EEG mapping during a visuo-spatial task. Averaged maps and group statistics].

Twenty young volunteers (10 men, 10 women), righthanded, students, have been recorded in EEG cartography in different situations. We have compared the quantified EEGs when the subjects were resting, eyes closed and later, eyes opened, looking at a cartoon. The EEGs were quantified by spectral Fourier analysis and submitted to data reduction. Ten spectral parameters were computed, yielding 51 variables allowing computations and drawings of 90 EEG maps. Mean parameters, mean variables, averaged EEG maps have been computed for the entire group, between sub-groups, between hemispheres. Non-parametric permutation Fisher tests have been applied for statistical comparisons and statistical validations of the EEG maps computed between subjects. The activation of EEG tracings produced by the opening of the eyes were caracterized topographically by: mean alpha frequencies increased over temporal and rolandic areas; mean alpha amplitudes in microV divided by a factor 3 for occipital areas but unchanged in topography; mean relative amplitudes divided by a factor 2 but with a topography being more parietal than occipital for the alpha rhythm; a resonance coefficient greater over the left parietal than the right (alpha more regular), whereas it was greater over the right occipital than the left during the resting condition. Statistically for the whole group, the left hemisphere, recorded after the right, is more 'activated' in the eyes closed situation. During visual attention, the left hemisphere is less activated than the right.

Adult↗

PubMed1999

Interpreting data on thoracic aortic aneurysms. Statistical issues.

Reliable information on growth rates and risk factors for growth of thoracic aortic aneurysms (TAA) is important for managing patients with this potentially lethal condition. This article reviews existing procedures for ascertaining TAA growth rates and describes improved statistical methodologies. Using data from the Yale Center for Thoracic Aortic Disease, the article demonstrates that the statistical procedure of instrumental variables (IV) estimation leads to substantially more precise and robust estimates of TAA growth rates and associated risk factors. We recommend that IV estimation be routinely employed in estimating the progression of thoracic aortic aneurysms and in identifying risk factors for growth. The article also discusses the issue of sample selection effects that arise when patients receive graft surgery and therefore are removed from the data set, and describes statistical procedures fro addressing this issue.

Aortic Dissection↗

PubMedDate not supplied

Statistical efficiency of adaptive algorithms.

The statistical efficiency of a learning algorithm applied to the adaptation of a given set of variable weights is defined as the ratio of the quality of the converged solution to the amount of data used in training the weights. Statistical efficiency is computed by averaging over an ensemble of learning experiences. A high quality solution is very close to optimal, while a low quality solution corresponds to noisy weights and less than optimal performance. In this work, two gradient descent adaptive algorithms are compared, the LMS algorithm and the LMS/Newton algorithm. LMS is simple and practical, and is used in many applications worldwide. LMS/Newton is based on Newton's method and the LMS algorithm. LMS/Newton is optimal in the least squares sense. It maximizes the quality of its adaptive solution while minimizing the use of training data. Many least squares adaptive algorithms have been devised over the years, but no other least squares algorithm can give better performance, on average, than LMS/Newton. LMS is easily implemented, but LMS/Newton, although of great mathematical interest, cannot be implemented in most practical applications. Because of its optimality, LMS/Newton serves as a benchmark for all least squares adaptive algorithms. The performances of LMS and LMS/Newton are compared, and it is found that under many circumstances, both algorithms provide equal performance. For example, when both algorithms are tested with statistically nonstationary input signals, their average performances are equal. When adapting with stationary input signals and with random initial conditions, their respective learning times are on average equal. However, under worst-case initial conditions, the learning time of LMS can be much greater than that of LMS/Newton, and this is the principal disadvantage of the LMS algorithm. But the strong points of LMS are ease of implementation and optimal performance under important practical conditions. For these reasons, the LMS algorithm has enjoyed very widespread application. It is used in almost every modem for channel equalization and echo cancelling. Furthermore, it is related to the famous backpropagation algorithm used for training neural networks.

Algorithms↗

PubMed2002

Exploring regions of interest with cluster analysis (EROICA) using a spectral peak statistic for selecting and testing the significance of fMRI activation time-series.

Much relevant information about activations and artifacts in a functional magnetic resonance imaging (fMRI) dataset can be obtained from an exploratory cluster analysis. In contrast to testing the significance of the measured experimental effect for a given model, unsupervised pattern recognition techniques, such as fuzzy clustering, often find unexpected behavior in addition to expected activations, allowing the exploitation of this element of surprise. The many artifact clusters often discovered might aid the experimenter in deciding whether the dataset is usable, whether some additional preprocessing step is required, or whether the one used has introduced spurious effects. However, clustering alone does not complete the analysis because the membership values that are generated are not indicative of the level of statistical significance with respect to the cluster activation patterns (centroids). This is of particular importance for fMRI datasets for which most time-series are "noise", with no activation patterns. We propose that an initial partition step should precede the clustering step. Only time-series that meet a certain statistical criterion (using a scaled version of Fisher's g-order statistic) are selected for clustering; this typically represents <5% of the whole brain region. The purpose of clustering is to generate a set of cluster centers that are the possible activation patterns; these are used in forming a linear model of all the time-series. The model parameter is tested for significance in both the time and frequency domains. We present a novel method of conducting these tests, which limits the number of false positives. We call the three-step process of initial partition, clustering and the two-domain significance test as exploring regions of interest with cluster analysis (EROICA).

Brain↗

PubMed2000

Summary measures and statistics in the analysis of quality of life data: an example from an EORTC-NCIC-SAKK locally advanced breast cancer study.

Quality of Life (QL) is now included as an endpoint in many phase III cancer clinical trials. Numerous statistical techniques have been presented in the literature to analyse QL data but there is still no agreement as to what is the optimal approach of analysis. In this paper we, therefore, present and compare various techniques which have all appeared in the literature and which may be globally described as summary measures and summary statistics. These techniques are illustrated using data from an EORTC clinical trial in locally advanced breast cancer (EORTC trial 10921). It is also explained in this paper how and when these techniques may be used in other cancer settings. For EORTC trial 10921, it is shown that by choosing different techniques different conclusions may be drawn concerning the QL outcome. This highlights the importance of choosing an appropriate primary statistical method and for describing it a priori in the protocol and analysis plan. In this paper, we show the importance of performing sensitivity or supportive analysis to support conclusions drawn from the primary analysis.

Antineoplastic Combined Chemotherapy Protocols↗

PubMed1999

Bootstrap prediction and confidence bands: a superior statistical method for analysis of gait data.

Gait analysis studies typically utilize continuous curves of data measured over the gait cycle, or a portion of the gait cycle. Statistical methods which are appropriate for use in studies involving a single point of data are not adequate for analysis of continuous curves of data. This paper determines the operating characteristics for two methods of constructing statistical prediction and confidence bands. The methods are compared, and their performance is evaluated using cross-validation methodology with a data set of the sort commonly evaluated in gait analysis. The methods evaluated are the often-used point-by-point Gaussian theory intervals, and the simultaneous bootstrap intervals of Sutherland et al. The Development of Mature Walking, MacKeith Press, London, 1988 and Olshen et al. Ann. Statist. 17 (1989) 1419-40. The bootstrap bands are shown to provide appropriate coverage for continuous curve gait data (86% coverage for a targeted coverage of 90%). The Gaussian bands are shown to provide inadequate coverage (54% for a targeted coverage of 90%). The deficiency in the Gaussian method can lead to inaccurate conclusions in gait studies. Bootstrap prediction and confidence bands are advocated for use as a standard method for evaluating gait data curves because the method is non-parametric and maintains nominal coverage levels for entire curves of gait data.

Gait↗

PubMed1999

The Emerging Importance of Genetics in Epidemiologic Research III. Bioinformatics and statistical genetic methods.

PURPOSE: To outline potential benefits of integrating recent developments in bioinformatics and statistical genetics with traditional epidemiologic studies to localize genes influencing complex phenotypes and examine genetic effects on disease susceptibility. METHODS: An overview of bioinformatic and statistical approaches for localizing disease-susceptibility genes as well as challenges associated with identifying functional DNA variants and context-dependent genetic effects concludes this three-part series on the importance of genetics in epidemiologic research. RESULTS: Rapidly evolving bioinformatic and statistical methods are providing invaluable information on newly-discovered genes and molecular variation influencing human diseases that is readily available to epidemiologic researchers. CONCLUSIONS: Integrating bioinformatics and molecular biotechnology with epidemiologic methods of assessing disease risk is rapidly expanding our ability to identify genetic influences on complex human diseases. These technological advances are likely to have a profound impact on current knowledge of complex disease etiology, and may reveal novel approaches to disease treatment and prevention.

Data Interpretation, Statistical↗

PubMed2003

Detection of cortical transition regions utilizing statistical analyses of excess masses.

A new statistical approach for observer-assisted detection of transition regions of adjacent cytoarchitectonic areas within the human cerebral cortex was developed. This method analyzes the structural information of cytoarchitectural profiles (e.g., the modality of a gray level intensity distribution) based on observed excess mass differences verified by a suitable statistical test. Profiles were generated by scanning the cerebral cortex over respective regions of interest that were oriented to trajectories running parallel to the orientation of cell columns. For each single profile, determination of excess masses provided evidence for a certain number of peaks in the cell density, thereby avoiding fluctuation due solely to sampling anomalies. Comparing such excess mass measurements by means of multiple local rank tests over a wide range of profiles allowed for the detection of cytoarchitectural inhomogeneities at respective given confidence levels. Special parameters (e.g., level of significance, width of targeted region, number of peaks) then could be adapted to specific pattern recognition problems in lamination analyses. Such analyses of excess masses provided a general tool for observer-assisted evaluation of profile arrays. This observer-assisted statistical method was applied to five different cortical examples. It detected the same transition regions that had been determined earlier through direct examination of samples, despite cortical convexities, concavities, and some minor staining inhomogeneities.

Cerebral Cortex↗

PubMed2003

Influence of the normalization template on the outcome of statistical parametric mapping of PET scans.

Spatial normalization is an essential preprocessing step in statistical parametric mapping (SPM)-based analysis of PET scans. The standard template provided with the SPM99 software package was originally constructed using (15)O-H(2)O PET scans and is commonly applied regardless of the tracer actually used in the scans being analyzed. This work studies the effect of using three different normalization templates in the outcome of the statistical analysis of PET scans: (1) the standard SPM99 PET template; (2) an (18)F-FDG PET template, constructed by averaging PET scans previously normalized to the standard template; and (3) an MRI-aided (18)F-FDG PET template, constructed by averaging PET scans normalized according to the deformation parameters obtained from MRI scans. A strictly anatomical MRI normalization of each PET was used as a reference, under the rationale that a normalization based only upon MRI should provide higher spatial accuracy. The potential bias involved in the normalization process was estimated in a clinical SPM study comparing schizophrenic patients with control subjects. For each between-group comparison, three SPM maps were obtained, one for each template. To evaluate the influence of the template, these SPM maps were compared to the reference SPM map achieved using the anatomical normalization. SPMs obtained by MRI-aided normalization showed the highest spatial specificity, and also higher sensitivity when compared to the standard normalization using the SPM99 (15)O-H(2)O template. These results show that the use of the standard template under inappropriate conditions (different tracer or mental state) may lead to inconsistent interpretations of the statistical analysis.

Acute Disease↗

PubMed2002

Statistical power in observer-performance studies: comparison of the receiver operating characteristic and free-response methods in tasks involving localization.

RATIONALE AND OBJECTIVES: Statistical power, defined as the probability of detecting real differences between imaging modalities, determines the cost in terms of readers and cases of conducting receiver operating characteristic (ROC) studies. Neglect of location information in lesion-detection studies analyzed with the ROC method can compromise power. Use of the alternative free-response ROC (AFROC) method, which considers location information, has been discouraged, because it neglects intraimage correlations. The relative statistical powers of the two methods, however, have not been tested. The purpose of this study was to compare the statistical power of ROC and AFROC methods using simulations. MATERIALS AND METHODS: A new model including intraimage correlations was developed to describe the decision variable sampling and to simulate data for ROC and AFROC analyses. Five readers and 200 cases (half of which contained one signal) were simulated for each trial. Two hundred trials, equally split between the null hypothesis and alternative hypothesis, were run. Ratings were analyzed with the Dorfman-Berbaum-Metz method, and separation of the null hypothesis and alternative hypothesis distributions was calculated. RESULTS: The AFROC method yielded higher power than the ROC method. Separation of the null hypothesis and alternative hypothesis distributions was larger by a factor of 1.6 regardless of the presence or absence of intraimage correlations. The effect of the incorrect localizations during ROC analysis of localization data is believed to be the major reason for the enhanced power of the AFROC method. CONCLUSION: The AFROC method can yield higher power than the ROC method for studies involving lesion localization. Greater consideration of this methodology is warranted.

Computer Simulation↗

PubMed2001

Statistical test to assess rank-order imaging studies.

RATIONALE AND OBJECTIVES: Rank-order experiments often provide a reasonable method of determining whether a large-scale receiver operating characteristic study can be justified. The authors' purpose was to formalize a proposed method for analyzing rank-order imaging experiments and provide methods that can be used in determining sample sizes for both cases and raters. MATERIALS AND METHODS: Simulations were conducted to determine the adequacy of the normal approximation of a statistic used to test the null hypothesis of random ordering. For a multireader experiment, formulas are presented and guidelines are provided to enable investigators to determine the number of required readers (raters) and cases for a specific study. RESULTS: When there are at least five ordered images per case, 10 cases are sufficient to test a random rank order. When there are only three or four images for a case, 20 cases are required. The authors constructed tables of statistical power for selected numbers of ordered images, numbers of cases, and degrees of trend, and they also provide an approximation for use in situations that are not tabled. CONCLUSION: The statistical methods for analyzing rank-order experiments and estimating sample sizes for study planning are relatively simple to implement. The derived formulas for sample size estimation, when applied to typical imaging experiments, indicate that modest numbers of cases and readers are required for rank-order studies.

Humans↗

PubMed2003

Parametric and non-parametric statistical analysis of DT-MRI data.

In this work parametric and non-parametric statistical methods are proposed to analyze Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data. A Multivariate Normal Distribution is proposed as a parametric statistical model of diffusion tensor data when magnitude MR images contain no artifacts other than Johnson noise. We test this model using Monte Carlo (MC) simulations of DT-MRI experiments. The non-parametric approach proposed here is an implementation of bootstrap methodology that we call the DT-MRI bootstrap. It is used to estimate an empirical probability distribution of experimental DT-MRI data, and to perform hypothesis tests on them. The DT-MRI bootstrap is also used to obtain various statistics of DT-MRI parameters within a single voxel, and within a region of interest (ROI); we also use the bootstrap to study the intrinsic variability of these parameters in the ROI, independent of background noise. We evaluate the DT-MRI bootstrap using MC simulations and apply it to DT-MRI data acquired on human brain in vivo, and on a phantom with uniform diffusion properties.

Artifacts↗

PubMed2003

A statistical analysis of NMR spectrometer noise.

Estimation of NMR spectral parameters, using e.g. maximum likelihood methods, is commonly based on the assumption of white complex Gaussian noise in the signal obtained by quadrature detection. Here we present a statistical analysis with the purpose of discussing and testing the validity of this fundamental assumption. Theoretical expressions are derived for the correlation structure of the noise under various conditions, showing that in general the noise in the sampled signal is not strictly white, even if the thermal noise in the receiver steps prior to digitisation can be characterised as white Gaussian noise. It is shown that the noise correlation properties depend on the ratio between the sampling frequency and the filter cut-off frequency, as well as the filter characteristics. The theoretical analysis identifies conditions that are expected to yield non-white noise in the sampled signal. Extensive statistical characterisation of experimental noise confirms the theoretical predictions. The statistical methods outlined here are also useful for residual analysis in connection with validation of the model and the parameter estimates.

Magnetic Resonance Spectroscopy↗

PubMed1999

Incorporating a statistically based shape model into a system for computer-assisted anterior cruciate ligament surgery.

This paper addresses the problem of extrapolating very sparse three-dimensional (3-D) data to obtain a complete surface representation. A new method that uses statistical shape models is proposed and its application to computer-assisted anterior cruciate ligament (ACL) reconstruction is detailed. The rupture of the ACL has become one of the most common knee injuries. One problem during reconstruction is to find the optimal attachment points for the graft. Therefore a system for computer-assisted reconstruction of the ACL has been proposed by TIMC laboratory. During surgery the surgeon collects several data points on the tibial and femoral joint surface with a 3-D localizer system. These 3-D data are used to find those attachment points resulting in a low anisometry of the graft, while preventing impingement between the graft and the femoral notch. As the collected data points only cover a small surface patch of the femur, it is desirable to extrapolate these data to also have a visualization in those areas where no data points are available. A sufficiently good approximation of the actual femur by the model would further allow us to better deal with the notch impingement problem of the graft. The chosen approach is to fit a deformable model to the data points, it can be subdivided into two steps, constructing the model and fitting this model to the data. To incorporate a priori knowledge into the model, the allowed deformations are determined by the statistics of the shape variation of a set of training objects. Matching the training objects together is obtained by elastic registration of surface points using octree splines. The fitting process of the sparse intra-operative data with the statistical model results in a non-linear multi-dimensional function minimization. A hybrid search strategy combining local and global methods is used to avoid local minima. First experimental results with a model generated from 10 femurs are presented, including fitting of the model with both simulated and real intra-operative data.

Anisotropy↗