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PubMed1994

An exact statistical method for comparing topographic maps, with any number of subjects and electrodes.

Statistical methods for testing differences between neural images (e.g., PET, MRI or EEG maps) are problematic because they require (1) an untenable assumption of data sphericity and (2) a high subject to electrode ratio. We propose and demonstrate an exact and distribution-free method of significance testing which avoids the sphericity assumption and may be computed for any combination of electrode and subject numbers. While this procedure is rigorously rooted in permutation test theory, it is intuitively comprehensible. The sensitivity of the permutation test to graded changes in dipole location for systematically varying levels of signal/noise ratio, intersubject variability and number of subjects was demonstrated through a simulation of 70 different conditions, generating 5,000 different data sets for each condition. Data sets were simulated from a homogeneous single-shell dipole model. For noise levels commonly encountered in evoked potential studies and for situations where the number of subjects was less than the number of electrodes, the permutation test was very sensitive to a change in dipole location of less than 0.75 cm. This method is especially sensitive to localized changes that would be "washed-out" by more traditional methods of analysis. It is superior to all previous methods of statistical analysis for comparing topographical maps, because the test is exact, there is no assumption of a multivariate normal distribution or of the correlation structure of the data requiring correction, the test can be tailored to the specific experimental hypotheses rather than allowing the statistical tests to limit the experimental design, and there is no limitation on the number of electrodes that can be simultaneously analyzed.

Analysis of Variance↗
PubMed1991

A regularity statistic for medical data analysis.

A new statistic has been developed to quantify the amount of regularity in data. This statistic, ApEn (approximate entropy), appears to have potential application throughout medicine, notably in electrocardiogram and related heart rate data analyses and in the analysis of endocrine hormone release pulsatility. The focus of this article is ApEn. We commence with a simple example of what we are trying to discern. We then discuss exact regularity statistics and practical difficulties of using them in data analysis. The mathematic formula development for ApEn concludes the Solution section. We next discuss the two key input requirements, followed by an account of a pilot study successfully applying ApEn to neonatal heart rate analysis. We conclude with the important topic of ApEn as a relative (not absolute) measure, potential applications, and some caveats about appropriate usage of ApEn. Appendix A provides example ApEn and entropy computations to develop intuition about these measures. Appendix B contains a Fortran program for computing ApEn. This article can be read from at least three viewpoints. The practitioner who wishes to use a "black box" to measure regularity should concentrate on the exact formula, choices for the two input variables, potential applications, and caveats about appropriate usage. The physician who wishes to apply ApEn to heart rate analysis should particularly note the pilot study discussion. The more mathematically inclined reader will benefit from discussions of the relative (comparative) property of ApEn and from Appendix A.

Algorithms↗
PubMed1990

Compositional statistics: an improvement of evolutionary parsimony and its application to deep branches in the tree of life.

We present compositional statistics, a new method of phylogenetic inference, which is an extension of evolutionary parsimony. Compositional statistics takes account of the base composition of the compared sequences by using nucleotide positions that evolutionary parsimony ignores. It shares with evolutionary parsimony the features of rate invariance and the fundamental distinction between transitions and transversions. Of the presently available methods of phylogenetic inference, compositional statistics is based on the fewest and mildest assumptions about the mode of DNA sequence evolution. It is therefore applicable to phylogenetic studies of the most distantly related organisms or molecules. This was illustrated by analyzing conservative positions in the DNA sequences of the large subunit of RNA polymerase from three archaebacterial groups, a eubacterium, a chloroplast, and the three eukaryotic polymerases. Internally consistent results, which are in accord with our knowledge of organelle origin and archaebacterial physiology, were achieved.

Amino Acid Sequence↗
PubMed1992

Poisson, compound Poisson and process approximations for testing statistical significance in sequence comparisons.

DNA and protein sequence comparisons are performed by a number of computational algorithms. Most of these algorithms search for the alignment of two sequences that optimizes some alignment score. It is an important problem to assess the statistical significance of a given score. In this paper we use newly developed methods for Poisson approximation to derive estimates of the statistical significance of k-word matches on a diagonal of a sequence comparison. We require at least q of the k letters of the words to match where 0 less than q less than or equal to k. The distribution of the number of matches on a diagonal is approximated as well as the distribution of the order statistics of the sizes of clumps of matches on the diagonal. These methods provide an easily computed approximation of the distribution of the longest exact matching word between sequences. The methods are validated using comparisons of vertebrate and E. coli protein sequences. In addition, we compare two HLA class II transplantation antigens by this method and contrast the results with a dynamic programming approach. Several open problems are outlined in the last section.

Algorithms↗
PubMed2003

Biosurveillance applying scan statistics with multiple, disparate data sources.

Researchers working on the Department of Defense Global Emerging Infections System (DoD-GEIS) pilot system, the Electronic Surveillance System for the Early Notification of Community-Based Epidemics (ESSENCE), have applied scan statistics for early outbreak detection using both traditional and nontraditional data sources. These sources include medical data indexed by International Classification of Disease, 9th Revision (ICD-9) diagnosis codes, as well as less-specific, but potentially timelier, indicators such as records of over-the-counter remedy sales and of school absenteeism. Early efforts employed the Kulldorff scan statistic as implemented in the SaTScan software of the National Cancer Institute. A key obstacle to this application is that the input data streams are typically based on time-varying factors, such as consumer behavior, rather than simply on the populations of the component subregions. We have used both modeling and recent historical data distributions to obtain background spatial distributions. Data analyses have provided guidance on how to condition and model input data to avoid excessive clustering. We have used this methodology in combining data sources for both retrospective studies of known outbreaks and surveillance of high-profile events of concern to local public health authorities. We have integrated the scan statistic capability into a Microsoft Access-based system in which we may include or exclude data sources, vary time windows separately for different data sources, censor data from subsets of individual providers or subregions, adjust the background computation method, and run retrospective or simulated studies.

Bioterrorism↗
PubMed2001

Statistical models to predict the need for postoperative intensive care and hospitalization in pediatric surgical patients.

OBJECTIVE: To develop statistical models for predicting postoperative hospital and ICU stay in pediatric surgical patients based on preoperative clinical characteristics and operative factors related to the degree of surgical stress. We hypothesized that preoperative and operative factors will predict the need for ICU admission and may be used to forecast the length of ICU stay or postoperative hospital stay. DESIGN: Prospective data collection from 1,763 patients. SETTING: Tertiary care children's hospital. PATIENTS AND PARTICIPANTS: All pediatric surgical patients, including those undergoing day surgery. Patients undergoing dental or ophthalmologic surgical procedures were excluded. INTERVENTIONS: None. MEASUREMENTS AND RESULTS: A logistic regression model predicting ICU admission was developed from all patients. Poissonregression models were developed from 1,161 randomly selected patients and validated from the remaining 602 patients. The logistic regression model for ICU admission was highlypredictive (area under the receiver operating characteristics (ROC) curve = 0.981). In the data set used for development of Poisson regression models, significant correlations occurred between the observed and predicted ICU stay (Pearson r = 0.468, p < 0.0001, n = 131) and between the observed and predicted hospital stay for patients undergoing general (r = 0.695, p < 0.0001), orthopedic (r = 0.717, p < 0.0001), cardiothoracic (r = 0.746, p < 0.0001), urologic (r = 0.458, p < 0.0001), otorhinolaryngologic (r = 0.962, p < 0.0001), neurosurgical (r = 0.7084, p < 0.0001) and plastic surgical (r = 0.854, p < 0.0001) procedures. In the validation data set, correlations between predicted and observed hospital stay were significant for general (p < 0.0001), orthopedic (p < 0.0001), cardiothoracic (p = 0.0321) and urologic surgery (p = 0.0383). The Poisson models for length of ICU stay, otorhinolaryngology, neurosurgery or plastic surgery could not be validated because of small numbers of patients. CONCLUSIONS: Preoperative and operative factors may be used to develop statistical models predicting the need for ICU admission in pediatric surgical patients, and hospital stay following general surgical, orthopedic, cardiothoracic and urologic procedures. These statistical models need to be refined and validatedfurther, perhaps using data collection from multiple institutions.

Arkansas↗
PubMed2001

A statistical method to minimize magnification errors in serial vertebral radiographs.

Incident vertebral deformities are commonly defined by observed changes in height between measurements on two consecutive radiographs. However, conventional radiographs are subject to magnification, and this magnification may differ between films, leading to artifactual changes in height. In order to minimize this effect, it is common practice to record the spine-film and film-focus distances, and from this to calculate a magnification factor for each film. We present a simple statistical method for correcting for differences in magnification between two films if the spine-film and film-focus distances are unknown. This method is shown to reduce the variance of the magnification differences in vertebral heights by 14%, considerably more than is possible using the spine-film distance. Using the statistical method, the number of vertebrae that showed not only a reduction in one or more height of 15%, but were also judged clinically to be free from any incident deformity by an expert radiologist, was reduced from 100 to 46. The number showing a reduction of 20% that were judged fracture-free was reduced from 15 to 9. In the subset of subjects for whom the spine-film distance was known, the reduction in false positives was similar, whichever method was used to correct for magnification. There was no difference in the number of confirmed incident fractures detected when magnification correction by either method was employed. It is concluded that correcting for magnification differences using the statistical method outlined here reduces the number of false positive deformities very substantially and by a similar extent as correcting the magnification using reliable, measured spine-film and film-focus distances. A further advantage of this method is that it can be used retrospectively.

Diagnostic Errors↗
PubMed1996

Inhalation experiments with mixtures of hydrocarbons. Experimental design, statistics and interpretation of kinetics and possible interactions.

The paper describes experimental and statistical methods for toxicokinetic evaluation of mixtures in inhalation experiments. Synthetic mixtures of three C9 n-paraffinic, naphthenic and aromatic hydrocarbons (n-nonane, trimethylcyclohexane and trimethylbenzene, respectively) were studied in the rat after inhalation for 12h. The hydrocarbons were mixed according to principles for statistical experimental design using mixture design at four vapour levels (75, 150, 300 and 450 ppm) to support an empirical model with linear, interaction and quadratic terms (Taylor polynome). Immediately after exposure, concentrations of hydrocarbons were measured by head space gas chromatography in blood, brain, liver, kidneys and perirenal fat. Multivariate data analysis and modelling were performed with PLS (projections to latent structures). The best models were obtained after removing all interaction terms, suggesting that there were no interactions between the hydrocarbons with respect to absorption and distribution. Uptake of paraffins and particularly aromatics is best described by quadratic models, whereas the uptake of the naphthenic hydrocarbons is nearly linear. All models are good, with high correlation (r2) and prediction properties (Q2), the latter after cross validation. The concentrations of aromates in blood were high compared to the other hydrocarbons. At concentrations below 250 ppm, the naphthene reached higher concentrations in the brain compared to the paraffin and the aromate. Statistical experimental design, multivariate data analysis and modelling have proved useful for the evaluation of synthetic mixtures. The principles may also be used in the design of liquid mixtures, which may be evaporated partially or completely.

Adipose Tissue↗
PubMed2006

Testing introgressive hybridization hypotheses using statistical network analysis of nuclear and cytoplasmic haplotypes in the leaf beetle Timarcha goettingensis species complex.

Previous studies of leaf beetles (Chrysomelidae) in the Timarcha goettingensis species complex using mitochondrial (cox2) and nuclear (ITS-2 rRNA) markers revealed two main clades confined to the Iberian Peninsula and the rest of Europe but showing incongruent distributions indicative of gene exchange between both groups. Because of the anastomosing nature of hybridization, which disrupts the cladistic structure of character variation, phylogenetic trees might be inappropriate to represent and study this process. Here we test for evidence of hybridization in the T. goettingensis complex by analyzing the extra homoplasy arising in hybrid genomes from the simultaneous analysis of genetically independent markers. Haplotype networks obtained by Templeton's statistical parsimony analysis were generated for combined (concatenated) cox2 and ITS-2 sequences from 167 individuals of the T. goettingensis complex. Networks were used to detect runs of homoplasious characters physically clustered along a nucleotide sequence, as evidence for recombination between both gene partitions. A hypergeometric tail probability for the chance occurrence of physically clustered character changes on the connections linking networks of genotypes was applied. The test recognized two instances of statistically significant clustering, indicating the presence of cox2-ITS-2 mosaic genotypes and reticulation of both main T. goettingensis clades, supporting the reticulate origin of samples of T. maritima in southwestern France and T. sinuatocollis/T. monserratensis in the eastern Pyrenees. Although the assessment of reticulation in DNA sequences does not provide direct proof for hybridization, the geographical distribution of mosaic genotypes in the vicinity of "pure" genotypes supports the effect of gene flow between the two divergent lineages. The study demonstrates the utility of statistical parsimony networks for the detection of hybrids in the growing number of phylogeographic studies based on multiple gene markers.

Adaptor Proteins, Vesicular Transport↗
PubMed2005

Statistical model of pesticide penetration through woven work clothing fabrics.

Statistical models estimating the level of protection and thermal comfort performance of woven fabrics were developed using simple fabric and liquid parameters. Eighteen woven fabrics were evaluated against three pesticide mixtures of atrazine and pendimethalin at different concentrations. Using three mixtures that represent a range of both surface tension and viscosity, percentages of pesticide penetration are measured, along with fabric thickness, fabric cover factor, yarn twist factor, yarn packing factor, solid volume fraction, wicking height, and air permeability. Statistical analyses are performed to examine the relationship between liquid/fabric parameters and pesticide penetration. Statistical analyses show that fabric cover factor, yarn twist factor, viscosity of pesticide mixture, critical surface tension of solid, and wicking height are significant parameters affecting pesticide penetration. For this purpose, cover factor and twist factor are better parameters in describing the geometry of woven fabrics than solid volume fraction. Modeling of comfort performance of woven fabric based on simple textile parameters shows that the combination of fabric thickness, cover factor, yarn twist factor and yarn packing factor can be used to estimate air permeability of woven fabric. These findings could be used for developing selection charts or tools as guidelines for the selection of personal protective equipment for use in hot, humid environments.

Materials Testing↗
PubMed2005

Reliability of statistical associations between genes and disease.

Many statistical associations between a disease and alleles of specific genes have proven to be irreproducible. In part, this irreproducibility can be attributed to a lack of replication before publication and the fact that, until recently, the relationship between statistical significance and various measures of reproducibility was not widely understood. This review proposes a classification system, the Better Associations for Disease and GEnes (BADGE) system, for describing genetic associations. The BADGE classes, first class through fifth class, are based on the P value of the association. A first-class association, with P < 2 x 10(-7), is expected to be reproducible even in the absence of other evidence supporting the association. A fifth-class association corresponds to conventional statistical significance (P < 5 x 10(-2)), which provides almost no assurance of reproducibility. Three intervening classes, described as second-, third-, and fourth-class associations, are defined by P values separated by factors of 20 or 25 from these extremes.

Animals↗
PubMed2003

Application of statistical parametric mapping to SPET in the assessment of intractable childhood epilepsy.

Statistical parametric mapping (SPM) quantification and analysis has been successfully applied to functional imaging studies of partial epilepsy syndromes in adults. The present study evaluated whether localisation of the epileptogenic zone (determined by SPM) improves upon visually examined single-photon emission tomography (SPET) imaging in presurgical assessment of children with temporal lobe epilepsy (TLE) and frontal lobe epilepsy (FLE). The patient sample consisted of 24 children (15 males) aged 2.1-17.8 years (9.8+/-4.3 years; mean+/-SD) with intractable TLE or FLE. SPET imaging was acquired routinely in presurgical evaluation. All patient images were transformed into the standard stereotactic space of the adult SPM SPET template prior to SPM statistical analysis. Individual patient images were contrasted with an adult control group of 22 healthy adult females. Resultant statistical parametric maps were rendered over the SPM canonical magnetic resonance imaging (MRI). Two corresponding sets of ictal and interictal SPM and SPET images were then generated for each patient. Experienced clinicians independently reviewed the image sets, blinded to clinical details. Concordance of the reports between SPM and SPET images, syndrome classification and MRI abnormality was studied. A fair level of inter-rater reliability (kappa=0.73) was evident for SPM localisation. SPM was concordant with SPET in 71% of all patients, the majority of the discordance being from the FLE group. SPM and SPET localisation were concordant with epilepsy syndrome in 80% of the TLE cases. Concordant localisation to syndrome was worse for both SPM (33%) and SPET (44%) in the FLE group. Data from a small sample of patients with varied focal structural pathologies suggested that SPM performed poorly relative to SPET in these cases. Concordance of SPM and SPET with syndrome was lower in patients younger than 6 years than in those aged 6 years and above. SPM is effective in localising the potential epileptogenic zone but does not provide additional benefit beyond SPET in presurgical assessment of children with intractable epilepsy. The impact of different pathologies on the efficacy of SPM warrants further study.

Algorithms↗
PubMed1997

Exposure levels for persons involved in recovery operations after the Chernobyl accident. Statistical analysis based on the data of the Russian National Medical and Dosimetric Registry (RNMDR).

We present a detailed description of dosimetric data entered in the Russian National Medical and Dosimetric Registry (RNMDR) for emergency workers (liquidators) involved in recovery operations (RO) after the Chernobyl accident. The data on the absorbed doses from external exposure are based on the documents given to liquidators by organizations that performed dosimetric monitoring in the zones of operation. Using the data on external doses currently available in the RNMDR for 119,416 liquidators (78.4% of the total number of 152,325 persons), different statistical characteristics were derived to assess the reliability of the information. The paper also discusses dose distributions according to the date of beginning work in the RO zone [up to 250 km from the Chernobyl nuclear power plant (NPP)], on the distance of the settlement where the liquidators were accommodated or worked from the NPP, and on the duration of their stay in the RO zone. To analyse the reliability of the dosimetric data, the notion of an effective exposure dose rate (EEDR), i.e. the ratio of the dose registered in RNMDR and the duration of stay in the RO zone, was introduced for each liquidator, and corresponding statistical characteristics for the distribution of EEDR depending on the date of entry into the RO zone and distance from the place of residence or work to the NPP were obtained. The analysis for different groups of liquidators shows that the dosimetric information of the RNMDR is, as a statistical aggregate, generally consistent with the data on the radiation situation in the RO zones.

Data Interpretation, Statistical↗
PubMed2001

Statistical analysis of endocrine granule size in gastrointestinal carcinoids.

Regarding the size of endocrine granules in endocrine neoplasms including carcinoids, most authors have reported only the range of granule diameters, and few studies on detailed morphometry of granule sizes have been documented. The statistically comparative study of endocrine granule sizes among such neoplasms, therefore, presented many difficulties. In the present study, we investigated more detailed findings on the endocrine granule sizes by using statistical analyses of diameters of numerous (n > 200 from each tumor) endocrine granules measured randomly throughout the cytoplasm in 18 gastrointestinal carcinoids. The measured data were analyzed statistically to obtain the histogram, distribution curve, mean value, and standard deviation of granule diameters in each carcinoid. It was disclosed by the analyses that all rectal carcinoids possessed uniformly small endocrine granules in contrast to gastric and duodenal carcinoids, which showed wide distribution of granule sizes, having significantly greater diameters than those in the rectal carcinoid series. The correlation between endocrine granule sizes and producing hormone(s) was, however, not confirmed.

Adult↗
PubMed2005

Answering cluster investigation requests: the value of simple simulations and statistical tools.

Cluster investigations remain an important public health issue as the number of reported clusters and public concern increase. This study shows how statistical considerations and a simulation tool may be helpful in providing communities with proper answers to the questions usually raised in such situations: How surprising is an observed childhood cancer excess? What could be learned from a statistical test? What could be learned from a case-control study? Using real demographic and incidence-rate data together with simulations based on the hypothesis that incidence rates are homogeneous, the probabilities of observing given situations were estimated. A number of real situations have been used as examples. The results of the simulation study showed, in detail, that no reliable information on the reality of an observed excess could be obtained a posteriori from a statistical test. A cluster of the same size may or may not be surprising, depending on the spatial area and time window to which the cases are related (i.e., the expected number of cases), and depending on the size of the referential territory to which this area is associated. The lack of power of a case-control study if no particular unusual exposure is present is also addressed. The approach described in this paper can easily be reproduced and adapted to many situations. It may be of assistance to health departments conducting cluster investigations and communicating with the public.

Adolescent↗
PubMed1976

A method for the statistical evaluation of results in external quality control surveys.

A method for the evaluation of results in external quality control surveys is developed on purely statistical grounds. This system allows to establish accuracy and precision of assay methods by comparing statistical data from subsequent surveys. However, for a particular survey the overall accuracy, precision and quality of each laboratory are defined in statistical terms and visually displayed. Results for each laboratory are summarized on a two-page computer printout. Per component assayed and combining all components determined in the particular survey, the laboratory is assigned one of the four possible qualifications i.e. "very good", "moderate" or "bad". A few general conclusions drawn from experimental data of previous surveys are reported.

Blood Glucose↗
PubMed1988

Study and performance evaluation of statistical methods in image processing.

Two statistical image processing formalisms involving the entropy concept and Bayesian analysis are studied. Iterative imaging algorithms of the formalisms are formulated by employing, for the purpose of performance evaluation and easy implementation, the steepest descent method for the solution of entropy concept and the expectation maximization technique for the solution of Bayesian analysis. Quantitative evaluation and comparison of the convergence performance of the iterative algorithms on computer generated ideal and experimental radioisotope phantom imaging noisy data are given. The study concludes that the entropy algorithm can converge relatively fast, but it is very sensitive to noise in measured data due to the ill-posed nature of inverse problems and its lack of ability to consider the statistics of data fluctuation; while the Bayesian algorithm converges monotonically even with noisy data and has the advantage of considering both the a priori source distribution information and the statistical fluctuation of measured data.

Algorithms↗
PubMed1990

The evaluation of radioactive microsphere data: remarks on the use of the BMDP and SAS statistical software packages.

We investigated the suitability of BMDP and SAS as an integrated tool for the evaluation of regional blood flow data obtained from the radioactive microsphere technique. Both packages were applied to a recent study on muscle blood flow with a 3-factorial design. The organization of data and files, the strategy of data reduction, and the evaluation by means of statistical and graphical techniques are shown. The method may be applied to any microsphere study design. A considerable amount of time can be saved and data integrity may be improved. The statistical quality of the results may benefit from the broad spectrum of statistical tests available.

Algorithms↗