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Statistical modeling and reconstruction of randoms precorrected PET data.

Randoms precorrected positron emission tomography (PET) data is formed as the difference of two Poisson random variables. Its exact probability mass function (PMF) is inconvenient for use in likelihood-based iterative image reconstruction as it contains an infinite summation. The shifted Poisson model is a tractable approximation to this PMF but requires that negative values are truncated, resulting in positively biased reconstructions in low count studies. Here we analyze the properties of the exact PMF and propose a simple but accurate approximation that allows negative valued data. We investigate the properties of this approximation and demonstrate its application to penalized maximum likelihood image reconstruction.

Algorithms↗

A statistical model and computer program to estimate association constants for the binding of fluorescent-labelled monoclonal antibodies to cell surface antigens and to interpret shifts in flow cytometry data resulting from alterations in gene expression.

Flow cytometry is used to obtain estimates for the distribution of fluorescent ligands bound to cell surface receptors throughout a cell sample. The equipment used provides light scattering parameters and also cell staining data in the form of dot plots and histograms of fluorescence intensities and the frequency of occurrence of particular fluorescence intensities. It is then assumed that fluorescence intensity is proportional to the number of labelled ligands bound to surface receptors. In this paper we present an outline of a statistical theory to account for the stretching and translation of such flow cytometry profiles which occur either as a result of alterations in gene expression, or from changing the sub-saturating concentration of fluorescent-labelled monoclonal antibodies or lectins used to stain the cells. We describe how the theory has been incorporated into two programs CSAFIT (cell surface antigen fit) and MAKCSA (make data to test CSAFIT). The program CSAFIT can be used to estimate two parameters, alpha and beta, by constrained non-linear regression analysis of the flow cytometry profiles. If the shift results from changes in the concentration of a staining agent then the estimates alpha and beta calculated by CSAFIT are functions of the ligand concentration, the ligand type and the cell line characteristics. They quantify the stretch and translation events that are encountered in flow cytometry. So when the parameter estimates alpha and beta are then further analysed as functions of ligand concentration, estimates for the average association constant K for the binding-site/ligand interaction can be obtained. This paper describes details of the development of programs CSAFIT and MAKCSA. We also discuss the distribution of parameter estimates calculated by CSAFIT and the overall performance of CSAFIT as assessed by simulation studies using data generated by MAKCSA.

Antibodies, Monoclonal↗

Efficacy of extracorporeal shock wave lithotripsy for solitary lower calyceal stone: a statistical model.

OBJECTIVE: To evaluate the effect of inferior calyceal radiographic anatomy, number of extracorporeal shock wave lithotripsy (ESWL) sessions and stone size on the successful clearance of solitary inferior calyceal calculi after ESWL. PATIENTS AND METHODS: In a prospective study between January 2001 and November 2002, 66 renal units with a solitary inferior calyceal calculus of < or = 2 cm were treated with electrohydraulic ESWL. The infundibulopelvic angle (two definitions), infundibulovertebral angle, inferior calyceal infundibular diameter, infundibular length, cortical thickness over the lower pole, number of minor calyces and stone size were determined from intravenous urography before treatment. The number of ESWL sessions was also included in the analysis. Treatments which produced residual fragments not clearing within 3 months of satisfactory fragmentation were considered as failures. All patients in whom the treatment failed were treated successfully by percutaneous nephrolithotomy. The data were then analysed using two different statistical methods; first by intravariable differences using the test of proportion (Fisher's test) and then all the variables together using logistic regression. RESULTS: At 3 months 78.8% of the renal units were clear of stone. All intravariable differences were statistically significant except stone size (<1 cm, 1-2 cm). In a multivariate analysis of all variables, only stone size was the most important predictor for successful stone clearance (P = 0.03). CONCLUSIONS: ESWL is the initial treatment of choice in selected patients with inferior calyceal stones. The stone size appears to be the most important predictor for stone clearance.

Adolescent↗

Statistical modeling of the effects of drug combinations.

A method is described for identifying and quantitating departures from additivity (i.e., synergism and antagonism) when drugs having like effects are given in combination. It is applicable for both graded and quantal (e.g., after probit or logit transformation) responses. Log(dose)-response curves of both drugs should be linear but need not be parallel. The following model is fitted to dose-response data for both the individual drugs and combinations of drugs: Y = beta 0 + beta 1 log(A + P.B + beta 4(A.P.B)1/2) where Y is the response, A is the amount of drug A, B is the amount of drug B, and P is a relative potency of the drugs given by log(P) = beta 2 + beta 3 log(B'), in which B' is the solution to B' - B - A/P = 0. If log(dose)-response curves of the two drugs are parallel, beta 3 = 0, and P becomes a constant parameter to be estimated. A positive value of beta 4 corresponds to synergism and a negative value to antagonism. Hypothesis tests may be carried out to determine whether beta 4 is significantly different from zero.

Dose-Response Relationship, Drug↗

A note on the use of statistical models in epidemiologic research on illicit drug use.

This essay aims to stimulate thinking or to remind readers about the shortcomings of standardized regression coefficients and related statistical measures in epidemiologic research on illicit drug use. This is accomplished primarily with a set of examples based on simulated epidemiologic data in which the standardized regression coefficient is shown to co-vary dramatically with frequency of the outcome variable. The basic thrust of this critique of commonly used regression models is not new; it has appeared elsewhere several times. Nevertheless, in epidemiologic research on illicit drug use, there is a continuing use of standardized regression coefficients and other margin-sensitive statistical measures without comment on their shortcomings. Thus, a specific critique with illustrations might have value.

Adolescent↗

A statistical model for interpreting computerized dynamic posturography data.

Computerized dynamic posturography (CDP) is widely used for assessment of altered balance control. CDP trials are quantified using the equilibrium score (ES), which ranges from zero to 100, as a decreasing function of peak sway angle. The problem of how best to model and analyze ESs from a controlled study is considered. The ES often exhibits a skewed distribution in repeated trials, which can lead to incorrect inference when applying standard regression or analysis of variance models. Furthermore, CDP trials are terminated when a patient loses balance. In these situations, the ES is not observable, but is assigned the lowest possible score--zero. As a result, the response variable has a mixed discrete-continuous distribution, further compromising inference obtained by standard statistical methods. Here, we develop alternative methodology for analyzing ESs under a stochastic model extending the ES to a continuous latent random variable that always exists, but is unobserved in the event of a fall. Loss of balance occurs conditionally, with probability depending on the realized latent ES. After fitting the model by a form of quasi-maximum-likelihood, one may perform statistical inference to assess the effects of explanatory variables. An example is provided, using data from the NIH/NIA Baltimore Longitudinal Study on Aging.

Adult↗

Simple statistical models predict C-to-U edited sites in plant mitochondrial RNA.

BACKGROUND: RNA editing is the process whereby an RNA sequence is modified from the sequence of the corresponding DNA template. In the mitochondria of land plants, some cytidines are converted to uridines before translation. Despite substantial study, the molecular biological mechanism by which C-to-U RNA editing proceeds remains relatively obscure, although several experimental studies have implicated a role for cis-recognition. A highly non-random distribution of nucleotides is observed in the immediate vicinity of edited sites (within 20 nucleotides 5' and 3'), but no precise consensus motif has been identified. RESULTS: Data for analysis were derived from the the complete mitochondrial genomes of Arabidopsis thaliana, Brassica napus, and Oryza sativa; additionally, a combined data set of observations across all three genomes was generated. We selected datasets based on the 20 nucleotides 5' and the 20 nucleotides 3' of edited sites and an equivalently sized and appropriately constructed null-set of non-edited sites. We used tree-based statistical methods and random forests to generate models of C-to-U RNA editing based on the nucleotides surrounding the edited/non-edited sites and on the estimated folding energies of those regions. Tree-based statistical methods based on primary sequence data surrounding edited/non-edited sites and estimates of free energy of folding yield models with optimistic re-substitution-based estimates of approximately 0.71 accuracy, approximately 0.64 sensitivity, and approximately 0.88 specificity. Random forest analysis yielded better models and more exact performance estimates with approximately 0.74 accuracy, approximately 0.72 sensitivity, and approximately 0.81 specificity for the combined observations. CONCLUSIONS: Simple models do moderately well in predicting which cytidines will be edited to uridines, and provide the first quantitative predictive models for RNA edited sites in plant mitochondria. Our analysis shows that the identity of the nucleotide -1 to the edited C and the estimated free energy of folding for a 41 nt region surrounding the edited C are the most important variables that distinguish most edited from non-edited sites. However, the results suggest that primary sequence data and simple free energy of folding calculations alone are insufficient to make highly accurate predictions.

Arabidopsis↗

A statistical model for investigating binding probabilities of DNA nucleotide sequences using microarrays.

There is considerable scientific interest in knowing the probability that a site-specific transcription factor will bind to a given DNA sequence. Microarray methods provide an effective means for assessing the binding affinities of a large number of DNA sequences as demonstrated by Bulyk et al. (2001, Proceedings of the National Academy of Sciences, USA 98, 7158-7163) in their study of the DNA-binding specificities of Zif268 zinc fingers using microarray technology. In a follow-up investigation, Bulyk, Johnson, and Church (2002, Nucleic Acid Research 30, 1255-1261) studied the interdependence of nucleotides on the binding affinities of transcription proteins. Our article is motivated by this pair of studies. We present a general statistical methodology for analyzing microarray intensity measurements reflecting DNA-protein interactions. The log probability of a protein binding to a DNA sequence on an array is modeled using a linear ANOVA model. This model is convenient because it employs familiar statistical concepts and procedures and also because it is effective for investigating the probability structure of the binding mechanism.

Analysis of Variance↗

Statistical models for estimating prevalence and incidence of parasitic diseases.

The estimation of prevalence and incidence of parasitic infections is considered. As the detectability of such infections is not 100% and may furthermore depend on their intensity, statistical methods are often required to arrive at meaningful results. It appears to be essential to distinguish between parasites that multiply within the (human) host and those that do not. An overview of some models discussed in the literature is presented. These models can indeed be used in assessing detectability of infection, and they indicate that observations may lead to considerable misinterpretation of 'true' prevalences and incidences.

Animals↗

Assessment of metal pollution based on multivariate statistical modeling of 'hot spot' sediments from the Black Sea.

The paper deals with application of different statistical methods like cluster and principal components analysis (PCA), partial least squares (PLSs) modeling. These approaches are an efficient tool in achieving better understanding about the contamination of two gulf regions in Black Sea. As objects of the study, a collection of marine sediment samples from Varna and Bourgas "hot spots" gulf areas are used. In the present case the use of cluster and PCA make it possible to separate three zones of the marine environment with different levels of pollution by interpretation of the sediment analysis (Bourgas gulf, Varna gulf and lake buffer zone). Further, the extraction of four latent factors offers a specific interpretation of the possible pollution sources and separates natural from anthropogenic factors, the latter originating from contamination by chemical, oil refinery and steel-work enterprises. Finally, the PLSs modeling gives a better opportunity in predicting contaminant concentration on tracer (or tracers) element as compared to the one-dimensional approach of the baseline models. The results of the study are important not only in local aspect as they allow quick response in finding solutions and decision making but also in broader sense as a useful environmetrical methodology.

Geologic Sediments↗

A Statistical Model of the Fluctuations in the Geomagnetic Field from Paleosecular Variation to Reversal

The statistical characteristics of the local magnetic field of Earth during paleosecular variation, excursions, and reversals are described on the basis of a database that gathers the cleaned mean direction and average remanent intensity of 2741 lava flows that have erupted over the last 20 million years. A model consisting of a normally distributed axial dipole component plus an independent isotropic set of vectors with a Maxwellian distribution that simulates secular variation fits the range of geomagnetic fluctuations, in terms of both direction and intensity. This result suggests that the magnitude of secular variation vectors is independent of the magnitude of Earth's axial dipole moment and that the amplitude of secular variation is unchanged during reversals.

Journal Article↗

[Statistic modeling of geographic and epidemiologic variations].

In epidemiology, studies of the geographical variations of mortality or incidence rates for some chronic diseases have often given rise to etiological clues concerning those diseases. In this framework the variables concerned have a spatially autocorrelated structure which has to be taken into account in the statistical analysis. The statistical techniques used to study in the first place the spatial variations of mortality rates and then the joint geographical variations of mortality and exposure indices are reviewed. Emphasis is placed on the importance played by the geographical scale of the analysed data in the modelling process as well as on the interpretation problems of geographical correlation studies.

Bias↗