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PubMed1999

Basic applications of the chi-square statistic using counting data.

The chi-square statistic has many scientific applications, including the evaluation of variance in counting data and the proper functioning of a radiation counting system. This paper provides a discussion of the fundamental aspects of the chi-square test using counting data. Practical applications of the chi-square statistic are discussed, including the estimation of extra-Poisson variance and dead time for a counting system. The consequences of passing or failing the chi-square test are discussed regarding the proper estimator for the population variance of the counting data. Example scenarios are used to provide insight into the applications of the chi-square statistic and the interpretation of values obtained in hypothesis testing.

Cesium Radioisotopes↗
PubMed1998

Contribution of initial median-nerve somatosensory evoked potentials and brainstem auditory evoked potentials to prediction of clinical outcome in cerebrovascular critical care patients: a statistical evaluation.

In a prospective study of 200 patients with cerebrovascular disease (48 intracerebral hemorrhages, [ICH]; 64 subarachnoid hemorrhages, [SAH]; 48 supratentorial and 40 infratentorial ischemic strokes), we assessed the individual and combined prognostic value of median-nerve somatosensory evoked potentials (SEP) and brainstem auditory evoked potentials (BAEP) within 72 hours of admission. Clinical outcome was graded in three ranked categories according to a modified Glasgow Outcome Scale. Likewise, the initial SEP and BAEP findings were graded in a three-class score. In all groups, the SEP were significantly correlated with outcome (P < 0.01). Likewise, after partialling out the prognostic effect of SEP, the contingency between BAEP and outcome was statistically significant, except in ICH (P = 0.07). The contingencies of SEP and outcome in ICH and supratentorial infarcts were higher than the corresponding partial contingencies for BAEP, while the latter were higher in infratentorial infarction and SAH. Therefore, in all disease groups except for SAH, the multiple contingency coefficients ranging from 0.67 to 0.75 were statistically significant and greater than either simple or partial contingencies alone. The results of the two evoked potential modalities combined permit statistically significant superior prognostication in most cerebrovascular diseases when compared to those of either of the modalities alone.

Cerebrovascular Disorders↗
PubMed1995

Uses and abuses of statistical models for evaluating trauma care.

OBJECTIVE: A statistical model is a powerful tool for evaluating trauma care. With accident and emergency clinicians becoming more aware of the importance of monitoring their department's performance, there is a danger that such models may be inappropriately applied to new sets of trauma cases, resulting in misleading evaluations. The primary objective is to present a method for assessing whether an existing survival probability model can be correctly applied to a different data set. METHODS: Correct and incorrect utilization of statistical models for evaluating the mortality of trauma patients are presented. Circumstances that may lead to the modification of an existing model, and the use of statistical models for evaluating different aspects of trauma care, are suggested.

England↗
PubMed1981

Statistical analysis of an attitude scale to measure patient satisfaction with medical care.

Patient satisfaction with medical care is concept that is viewed as important to consider but difficult to measure. The most widely reported and most standardized measure of patient attitudes toward medical care is the scale developed by Hulka et al. The purpose of this article is first to present the results of three separate administrations of this scale and, second, to detail the statistical analysis performed using these data sets. The results of these three administrations show remarkable similarity of results, thus leading to an inference of high reliability. Through the statistical analysis of the validity of the scale, however, it is demonstrated that further work is needed before the attitude scale can be generally used. The three phases of the statistical analysis include an item analysis, a Guttman scalogram analysis and a factor analysis. The results of these three validity analyses do not support the attitude scale in its current form. The result of this work leads us to conclude that this attitude scale is not ready to be used in a community setting for predictive purposes, as has been suggested. Our results indicate that further revision and analysis are necessary before we can approach a valid as well as reliable attitude scale to measure patient satisfaction with medical care. Although this suggests the need for extensive theoretical research, the effort is clearly worthwhile, as a valid and reliable measurement of patient satisfaction will provide us with invaluable insights into the process of health care delivery.

Consumer Behavior↗
PubMed1998

Instrumental measurement of skin colour and skin type as risk factors for melanoma: a statistical classification procedure.

A statistical procedure to evaluate melanoma risk in Caucasian subjects on the basis of colorimetric measurement of skin colour and Fitzpatrick phototype is described. One hundred and sixty melanoma patients and 546 randomized healthy subjects of similar age, sex and place of origin were examined in the same period for skin colour using a tristimulus colorimeter and for Fitzpatrick phototype. A clinical score for classification purposes was obtained by statistical discriminant analysis with multivariate data transformation and dimension reduction techniques. A Fisher linear classifier was chosen for its simplicity and robustness in correctly predicting melanoma risk in new subjects. The classification rule was designed to avoid classifying subjects at high risk for melanoma as low risk, i.e. to give a negligible number of false negatives at the expense of more false positives. The procedure is objective and readily adapted to different clinical requirements. This is only a preliminary study but it is hoped that by performing more complex statistical analyses, e.g. neural networks, and adding other parameters (proven risk factors such as number of naevi) the performance will be further improved.

Colorimetry↗
PubMed2004

Statistical approaches to handling uncertainty in health economic evaluation.

Not so long ago, uncertainty in economic evaluation was handled almost exclusively using simple one-way sensitivity analysis methods whereby individual parameters of an analysis were varied one-by-one over a range of (often ad-hoc) values. With the increasing use of the clinical trial as a vehicle for economic evaluation, there has been increasing interest in the use of statistical methods for handling uncertainty in patient-level data on both costs and effects. However, even for studies based on secondary data, the use of statistical methods for specifying parameter distributions in so-called probabilistic analyses is becoming increasingly common and is now the method recommended by a number of good-practice guides and regulatory agencies. The aim of this paper is to review these statistical approaches to the handling of uncertainty, both for primary studies where patient level cost and effect information is available and in secondary studies that typically use decision analytical methods to synthesize summary information from the published literature. The approach throughout the paper will be to emphasize the intuition behind the methods rather than the technical details. Although the methodology is generally applicable, examples will be drawn from both primary and secondary economic evaluations in the area of gastroenterology. The first example relates to a primary care trial of dyspepsia management which sought to estimate the cost-effectiveness of managing patients through early endoscopy compared to usual care. The second example is a secondary study of the management of gastro-oesophageal reflux disease symptoms which considered six potential strategies simultaneously.

Confidence Intervals↗
PubMed2005

Evaluation of nucleic acid amplification tests in the absence of a perfect gold-standard test: a review of the statistical and epidemiologic issues.

During the past 10 years, medical diagnostic testing for sexually transmitted infections (STIs) has changed markedly as a result of the rapid expansion and marketing of nucleic acid amplification tests (NAATs). Among such new DNA/RNA-amplification techniques are the polymerase chain reaction (PCR), the ligase chain reaction (LCR), and the transcription-mediated amplification (TMA) tests. Regrettably, the test evaluation process undergone by these tests has not always been rigorous or scientifically sound. Here, we review the controversy surrounding the statistical evaluation of these NAATs. We also review some of the traditional and recent statistical methods developed to estimate test sensitivity and specificity parameters in the absence of reliable gold-standard tests. In particular, we review the traditional latent class modeling approach that requires the assumption of independence between diagnostic tests conditional on the true disease status, and the more recent procedures that relax the conditional independence assumption. Finally, we apply some of these statistical modeling techniques to real data to estimate the sensitivity and specificity of a NAAT for Chlamydia trachomatis. On the basis of the latent class modeling approach with a pessimistic prior for culture sensitivity, the NAAT specificity estimate was 97.6% and, on the basis of an optimistic prior, the specificity was 95.3%. Similarly, the sensitivity estimates ranged from 88.1% to 89.6%.

Biometry↗
PubMedDate not supplied

Assessment of shape variation of the levator ani with optimal scan planning and statistical shape modeling.

OBJECTIVE: To capture 3D shape variation of the levator ani during straining with open access MR imaging. METHODS: Optimal scan-planning based on statistical shape modeling is developed for recovering the entire 3D structure of the levator ani from a limited number of 2D imaging planes. Statistical shape modeling ensures optimum material correspondence, and Subspace Reprojection is used to identify the optimum orientation of the imaging plans. The accuracy of the method in using limited 2D imaging planes to instantiate the dynamic structure of the levator ani is assessed with data acquired from 10 asymptomatic subjects. RESULTS: Leave-one-out analysis was performed whereby a model based on a training set consisting of all but one surface was used to instantiate the dynamic surface structure from the corresponding optimal planes. The mean surface distance error for the proposed Subspace Reprojection method is 3.989 +/- 0.790 mm, which is significantly smaller than other approaches. CONCLUSIONS: Surfaces of the levator ani may be instantiated using a limited number of imaging planes as well as a statistical shape model based on a training set of subjects. The proposed technique offers a new way forward for studying dynamic shape changes of 3D structures where complete volumetric imaging is prohibited by the inherent temporal resolution of the scanning technique.

Adult↗
PubMed1995

A geographic gradient in small rodent density fluctuations: a statistical modelling approach.

The patterns of density dependence in Fennoscandian rodents are investigated statistically using a linear autoregressive scheme. Nineteen time series of microtine abundances along a latitudinal gradient in Fennoscandia from 60 degrees N to 69 degrees N are analysed. We provide statistical evidence that there exists a latitudinal gradient in density dependence in Fennoscandian microtines. Southern populations experience significantly stronger direct density dependence than northern populations. Delayed density dependence was significantly negative throughout the region and appeared constant across the latitudinal gradient. The populations consistently exhibit dynamics of second order throughout the region. Together, the clinal direct density dependence and constant delayed density dependence give rise to a cline in cycle period from 3 to 4.5 years. The statistical results are compared to assumptions and predictions made in previous studies on the geographic gradient in the population dynamics of these rodents. The results are in agreement with the predictions of the 'generalist predator hypothesis'.

Animals↗
PubMed1995

Systematic analysis of coding and noncoding DNA sequences using methods of statistical linguistics.

We compare the statistical properties of coding and noncoding regions in eukaryotic and viral DNA sequences by adapting two tests developed for the analysis of natural languages and symbolic sequences. The data set comprises all 30 sequences of length above 50 000 base pairs in GenBank Release No. 81.0, as well as the recently published sequences of C. elegans chromosome III (2.2 Mbp) and yeast chromosome XI (661 Kbp). We find that for the three chromosomes we studied the statistical properties of noncoding regions appear to be closer to those observed in natural languages than those of coding regions. In particular, (i) a n-tuple Zipf analysis of noncoding regions reveals a regime close to power-law behavior while the coding regions show logarithmic behavior over a wide interval, while (ii) an n-gram entropy measurement shows that the noncoding regions have a lower n-gram entropy (and hence a larger "n-gram redundancy") than the coding regions. In contrast to the three chromosomes, we find that for vertebrates such as primates and rodents and for viral DNA, the difference between the statistical properties of coding and noncoding regions is not pronounced and therefore the results of the analyses of the investigated sequences are less conclusive. After noting the intrinsic limitations of the n-gram redundancy analysis, we also briefly discuss the failure of the zeroth- and first-order Markovian models or simple nucleotide repeats to account fully for these "linguistic" features of DNA. Finally, we emphasize that our results by no means prove the existence of a "language" in noncoding DNA.

Animals↗
PubMed2004

Effect of chain connectivity on the structure of Lennard-Jones liquid and its implicationon statistical potentials for protein folding.

Statistical contact potentials and bead-spring models have been widely used for computational studies of protein folding. However, there has been speculation that systematic error may arise in the contact energy calculations when the statistical potentials are deduced under the assumption that the chain connectivity in proteins can be ignored. To address this issue, we have performed molecular-dynamics simulations to study the structure and dynamics of a simple liquid system in which the beads are either connected or unconnected with springs. Results from the present study provide useful information for assessing the accuracy of the statistical potentials for protein structure simulations.

Base Sequence↗
PubMed2003

Statistical aging and nonergodicity in the fluorescence of single nanocrystals.

The relation between single particle and ensemble measurements is addressed for semiconductor CdSe nanocrystals. We record their fluorescence at the single molecule level and analyze their emission intermittency, which is governed by unusual random processes known as Lévy statistics. We report the observation of statistical aging and ergodicity breaking, both related to the occurrence of Lévy statistics. Our results show that the behavior of ensemble quantities, such as the total fluorescence of an ensemble of nanocrystals, can differ from the time-averaged individual quantities, and must be interpreted with care.

Cadmium Compounds↗
PubMed1997

Counting nurses: interpreting nursing workforce statistics.

Discusses the interpretation of nursing statistics, the problem of counting how many nurses there are in the workforce, and the need to be aware of how statistics are compiled when presenting numerical data to support arguments relating to nursing and the nursing workforce. Argues that NHS workforce statistics provide considerable evidence for claiming that there is a significant decline in the number of nursing staff doing the work of nursing in the NHS. Explains that although there was an increase in the number of qualified nurses working in the NHS throughout the 1980s (over a ten-year period the number of qualified nurses increased by 22 per cent), the increase in qualified nursing staff has not compensated for the loss of student learners in the workforce. Emphasizes that during the last three years for which figures are available, however, these gains have been wiped out, and the number of qualified nurses has declined to pre-Project 2000 levels.

Data Collection↗
PubMed1997

Statistical approach to segmentation of single-channel cerebral MR images.

A statistical model is presented that represents the distributions of major tissue classes in single-channel magnetic resonance (MR) cerebral images. Using the model, cerebral images are segmented into gray matter, white matter, and cerebrospinal fluid (CSF). The model accounts for random noise, magnetic field inhomogeneities, and biological variations of the tissues. Intensity measurements are modeled by a finite Gaussian mixture. Smoothness and piecewise contiguous nature of the tissue regions are modeled by a three-dimensional (3-D) Markov random field (MRF). A segmentation algorithm, based on the statistical model, approximately finds the maximum a posteriori (MAP) estimation of the segmentation and estimates the model parameters from the image data. The proposed scheme for segmentation is based on the iterative conditional modes (ICM) algorithm in which measurement model parameters are estimated using local information at each site, and the prior model parameters are estimated using the segmentation after each cycle of iterations. Application of the algorithm to a sample of clinical MR brain scans, comparisons of the algorithm with other statistical methods, and a validation study with a phantom are presented. The algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of MR images in the presence of the random noise and intensity inhomogeneities.

Adolescent↗
PubMed2003

Formula-based approach of statistical tests for peri-stimulus time histograms.

We introduce formula-based approaches for statistical tests regarding peri-stimulus time histograms (PSTHs) in cases when a conditioning stimulus was triggered by a motor-unit discharge with a constant delay time. The individual bin test and the cumulative sum test have recently been reported as methods for the quantitative analysis of PSTHs in the evaluation of human neural projections. These tests calculate confidence intervals using simulated point processes on the discharge of a motor unit, but require a significant amount of calculation time for the point process simulation. In order to overcome such a disadvantage in practical use, we provide a statistical formulization of the two above-mentioned tests using a combination theory. In general, the time required for calculating confidence intervals using these formula-based approaches was 2-13 times faster than when using the previous approaches. Unlike the previous ones, these formula-based approaches do not need to judge that a simulation process converges to the substationary state, and calculate an ideal distribution of statistical noise on the histogram, thereby providing high accuracy. We conclude that the formula-based approaches increase reliability and are sufficiently sophisticated for practical use.

Action Potentials↗
PubMed2005

Statistical encoding model for a primary motor cortical brain-machine interface.

A number of studies of the motor system suggest that the majority of primary motor cortical neurons represent simple movement-related kinematic and dynamic quantities in their time-varying activity patterns. An example of such an encoding relationship is the cosine tuning of firing rate with respect to the direction of hand motion. We present a systematic development of statistical encoding models for movement-related motor neurons using multielectrode array recordings during a two-dimensional (2-D) continuous pursuit-tracking task. Our approach avoids massive averaging of responses by utilizing 2-D normalized occupancy plots, cascaded linear-nonlinear (LN) system models and a method for describing variability in discrete random systems. We found that the expected firing rate of most movement-related motor neurons is related to the kinematic values by a linear transformation, with a significant nonlinear distortion in about 1/3 of the neurons. The measured variability of the neural responses is markedly non-Poisson in many neurons and is well captured by a "normalized-Gaussian" statistical model that is defined and introduced here. The statistical model is seamlessly integrated into a nearly-optimal recursive method for decoding movement from neural responses based on a Sequential Monte Carlo filter.

Algorithms↗
PubMed2005

The Rician inverse Gaussian distribution: a new model for non-Rayleigh signal amplitude statistics.

In this paper, we introduce a new statistical distribution for modeling non-Rayleigh amplitude statistics, which we have called the Rician inverse Gaussian (RiIG) distribution. It is a mixture of the Rice distribution and the inverse Gaussian distribution. The probability density function (pdf) is given in closed form as a function of three parameters. This makes the pdf very flexible in the sense that it may be fitted to a variety of shapes, ranging from the Rayleigh-shaped pdf to a noncentral chi2-shaped pdf. The theoretical basis of the new model is quite thoroughly discussed, and we also give two iterative algorithms for estimating its parameters from data. Finally, we include some modeling examples, where we have tested the ability of the distribution to represent locale amplitude histograms of linear medical ultrasound data and single-look synthetic aperture radar data. We compare the goodness of fit of the RiIG model with that of the K model, and, in most cases, the new model turns out as a better statistical model for the data. We also include a series of log-likelihood tests to evaluate the predictive performance of the proposed model.

Algorithms↗
PubMed2006

Shape statistics variational approach for the outer contour segmentation of left ventricle MR images.

Segmentation of left ventricles is one of the important research topics in cardiac magnetic resonance (MR) imaging. The segmentation precision influences the authenticity of ventricular motion reconstruction. In left ventricle MR images, the weak and broken boundary increases the difficulty of segmenting the outer contour precisely. In this paper, we present an improved shape statistics variational approach for the outer contour segmentation of left ventricle MR images. We use the Mumford-Shah model in an object feature space and incorporate the shape statistics and an edge image to the variational framework. The introduction of shape statistics can improve the segmentation with broken boundaries. The edge image can enhance the weak boundary and thus improve the segmentation precision. The generation of the object feature image, which has homogenous "intensities" in the left ventricle, facilitates the application of the Mumford-Shah model. A comparison of mean absolute distance analysis between different contours generated with our algorithm and that generated by hand demonstrated that our method can achieve a higher segmentation precision and a better stability than various approaches. It is a semiautomatic way for the segmentation of the outer contour of the left ventricle in clinical applications.

Algorithms↗

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