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PubMed1987

Integrating uncertainty and interindividual variability in environmental risk assessment.

An integrated, quantitative approach to incorporating both uncertainty and interindividual variability into risk prediction models is described. Individual risk R is treated as a variable distributed in both an uncertainty dimension and a variability dimension, whereas population risk I (the number of additional cases caused by R) is purely uncertain. I is shown to follow a compound Poisson-binomial distribution, which in low-level risk contexts can often be approximated well by a corresponding compound Poisson distribution. The proposed analytic framework is illustrated with an application to cancer risk assessment for a California population exposed to 1,2-dibromo-3-chloropropane from ground water.

California↗
PubMed2000

Total deviation index for measuring individual agreement with applications in laboratory performance and bioequivalence.

In areas of inter-laboratory quality control, method comparisons, assay validation and individual bioequivalence, etc., the agreement between observations and target (reference) values is of interest. The mean of the squared difference between observations and target values (MSD) is a good measure of the total deviation. A new user-friendly statistic, the total deviation index (TDI(1-p)), is introduced that translates the MSD into an index that can be directly compared to a predetermined criterion. The TDI(1-p) describes a boundary such that a majority, 100(1-p) per cent, of the observations are within the boundary (measurement unit and/or per cent) from their target values. Statistical inference using the sample counter part (estimate) is presented. A Monte Carlo experiment with 5000 runs was performed to confirm the estimate's validity. Applications in laboratory performance and validation, as well as individual bioequivalence, are presented.

Analysis of Variance↗
PubMed2006

Further notes on the application of zero-inflated models in highway safety.

The intent of this note is to succinctly articulate additional points that were not provided in the original paper (Lord et al., 2005) and to help clarify a collective reluctance to adopt zero-inflated (ZI) models for modeling highway safety data. A dialogue on this important issue, just one of many important safety modeling issues, is healthy discourse on the path towards improved safety modeling. This note first provides a summary of prior findings and conclusions of the original paper. It then presents two critical and relevant issues: the maximizing statistical fit fallacy and logic problems with the ZI model in highway safety modeling. Finally, we provide brief conclusions.

Accidents, Traffic↗
PubMed1995

Basic models for disease occurrence in epidemiology.

BACKGROUND: One of the epidemiologist's most basic tasks is estimation of disease occurrence. To perform this task, the epidemiologist frequently models variability in disease occurrence using one of three distributions--the binomial, the Poisson or the exponential distribution. Although epidemiologists often use them and their properties appear in standard texts, we know of no text or review that compares and contrasts epidemiological application of these distributions. METHODS: In this commentary, we discuss these three basic distributions. We note key assumptions as well as limitations, and compare results from analyses based on each distribution. RESULTS AND CONCLUSIONS: We illustrate that the three distributions, although superficially different, often lead to similar results. We argue that epidemiologists should often obtain similar results regardless of which distribution they use. We also point out that application of all three distributions can be inappropriate if assumptions of independence or homogeneity of risks fail to hold. Finally, we briefly review how these basic distributions can be used to justify use of other distributions, such as the Gaussian distribution, for studying disease-exposure associations.

Binomial Distribution↗
PubMed2003

A proposed method to determine the decision level for radioactivity measurements.

When measuring radioactivity, the problem rises of deciding whether or not a sample contains radioactivity in excess of background and above which value the result is meaningful. This decision process is why the notion of decision level was introduced. Whereas there is unanimity about its definition, this is not the case for its calculation, and many expressions have been proposed. This article contains a comparison of several decision level models by means of the calculation of actual false positive probability. First, three models are compared for the case of a well-known background, then a proposed model is developed and the four models are compared for the case of a poorly-known background. It appears from this study that, in order to be valid, the formula of the decision level must verify three conditions. First, the counting times have to appear symmetrically in the formula of the decision level; second, for long background counting times, the expression has to be equivalent to the one obtained with the corrected normal distribution corresponding to the Poisson law for the case of a well-known background; and, third, for large background, the expression has to be equivalent to those given by the three former models. It will be demonstrated that only the proposed model fulfills these requirements.

Algorithms↗
PubMed2000

Factorial moments analyses show a characteristic length scale in DNA sequences.

A unique feature of most of the DNA sequences, found through the factorial moments analysis, is the existence of a characteristic length scale around which the density distribution is nearly Poissonian. Above this point, the DNA sequences, irrespective of their intron contents, show long range correlations with a significant deviation from the Gaussian statistics, while, below this point, the DNA statistics are essentially Gaussian. The famous DNA walk representation is also shown to be a special case of the present analysis.

Analysis of Variance↗
PubMed2003

Signal detectability in digital radiography: spatial domain figures of merit.

The usefulness of Fourier-based measures of imaging performance has come into question for the evaluation of digital imaging systems. Figures of merit such as detective quantum efficiency (DQE) based on Fourier domain parameters are relevant for linear, shift-invariant systems with stationary noise. However, no digital imaging system is shift invariant, and realistic images do not satisfy the stationarity condition. Our methods for the task-based evaluation of imaging systems, based on signal detectability in the spatial domain, do not require such assumptions. We have computed the performance of ideal and quasi-ideal observers for the task of signal detection in digital radiography. Signal detectability in terms of an observer signal-to-noise-ratio (SNR) has been compared to results obtained from a Monte Carlo simulation of the digital image-acquisition process. The simulation incorporates the effects of random amplification and secondary quantum blur, integration over pixel area, and electronic noise. The observer figures of merit that have been previously shown to bracket human performance directly specify the usefulness of the images for the stated diagnostic task. In addition, the observer figures of merit give a task-dependent measure of imaging system efficiency in terms of the ratio of an output SNR2 to an input SNR2. Thus, the concept of "detective quantum efficiency" reappears in a natural way but based in the spatial domain and not dependent on shift invariance and stationarity assumptions. With respect to the optimum amount of system blur, our simulations indicate that under certain task-dependent conditions, large signals are fairly insensitive to blur in the x-ray transducer, while an optimum blur is found for small signals.

Humans↗
PubMedDate not supplied

An introduction to multilevel regression models.

Data in health research are frequently structured hierarchically. For example, data may consist of patients nested within physicians, who in turn may be nested in hospitals or geographic regions. Fitting regression models that ignore the hierarchical structure of the data can lead to false inferences being drawn from the data. Implementing a statistical analysis that takes into account the hierarchical structure of the data requires special methodologies. In this paper, we introduce the concept of hierarchically structured data, and present an introduction to hierarchical regression models. We then compare the performance of a traditional regression model with that of a hierarchical regression model on a dataset relating test utilization at the annual health exam with patient and physician characteristics. In comparing the resultant models, we see that false inferences can be drawn by ignoring the structure of the data.

Bias↗
PubMed2000

Impact of correlated inputs on the output of the integrate- and-fire model.

For the integrate-and-fire model with or without reversal potentials, we consider how correlated inputs affect the variability of cellular output. For both models, the variability of efferent spike trains measured by coefficient of variation (CV) of the interspike interval is a nondecreasing function of input correlation. When the correlation coefficient is greater than 0.09, the CV of the integrate-and-fire model without reversal potentials is always above 0.5, no matter how strong the inhibitory inputs. When the correlation coefficient is greater than 0.05, CV for the integrate-and-fire model with reversal potentials is always above 0. 5, independent of the strength of the inhibitory inputs. Under a given condition on correlation coefficients, we find that correlated Poisson processes can be decomposed into independent Poisson processes. We also develop a novel method to estimate the distribution density of the first passage time of the integrate-and-fire model.

Action Potentials↗
PubMed2000

Efficacy estimates from parasite count data that include zero counts.

Because of the positive skewness of parasite distributions and the greater constancy of percentage of response of therapy in animal populations, parasite count data are conventionally transformed logarithmically before combining results from different animals, either all controls or all treated. Observations of zero counts raise difficulties, since the logarithm of zero is not useful. In this study, several types of zero count adjustments are compared. Two systems for assigning values to zero counts were considered: a fixed system, which assigns the same value to all zero counts regardless of the proportion of such counts in a treatment group, and a variable system, which replaces zero counts with a value based on the proportion of zero counts in the group. The values assigned by either system are then adjusted to reflect aliquot size. An evaluation was performed by using 32 compound Poisson lognormal distributions, three sample sizes, and three representatives of each zero count adjustment system. The Poisson lognormal distribution provides a convenient method with which to provide variability greater than Poisson. Expected values of the sample estimate of the (known) population mean were calculated for each of the 576 combinations of these factors, and the bias associated with each combination was derived. The bias associated with the three representatives of the variable adjustment system was similar. The variable adjustment system had a lower overall bias than any representatives of the fixed adjustment system.

Animals↗
PubMed1998

The mirror effect and attention-likelihood theory: a reflective analysis.

The mirror effect refers to findings from studies of recognition memory consistent with the idea that the underlying "strength" distributions are symmetric around their midpoint separating studied and nonstudied items. Attention-likelihood theory assumes underlying binomial distributions of marked features and claims that old-item differences result from differential attention across conditions during study. The symmetry arises because subjects use the likelihood ratio as the basis for decision. The author analyzes the model and argues that one of the main criticisms (the complexity of the likelihood-ratio decision rule) is unwarranted. A further analysis shows that other distributions (the Poisson and the hypergeometric) can also produce a mirror effect. Even with the binomial distribution, a variety of parameter values can produce a mirror effect, and with the right combination of parameter values, differential attention across conditions is not necessary for a mirror effect to occur.

Attention↗
PubMed2002

Exact and approximate Bayesian estimation of net counting rates.

The stochastic fluctuations in the number of disintegrations, which had already been studied experimentally by Rutherford and other investigators at the beginning of the twentieth century, make estimation of net counting rates in the presence of background counts a challenging statistical problem. Exact and approximate Bayesian estimates of net count rates using Poisson and normal distributions for the number of counts detected during varying counting intervals are derived. The posterior densities for the net count rate are derived and plotted for uniform priors. The graphs for the exact, Poisson based, and for the approximate posterior densities of the background and net count rates, resulting from the normal approximation to the Poisson distribution, were compared. No practical differences were found when the number of observed gross counts is large. Small numerical differences in the posterior expectations and standard deviations of the counting rates appeared when the number of observed counts was small. A table showing some of these numerical differences for different background and gross counts is included. A normal approximation to the Poisson is satisfactory for the analysis of counting data when the number of observed counts is large. Some caution has to be exercised when the number of observed counts is small.

Artifacts↗
PubMed1996

Distribution of genome shared IBD by half-sibs: approximation by the Poisson clumping heuristic.

The distribution of the proportion of genome shared identical by descent (IBD) by c half-sibs is calculated for a general c. With data availability the consideration of the chromosome as a whole rather than discrete loci becomes of increasing practical importance. Assuming the genomic continuum model, which allows for recombination, the crossover process in a chromosome pedigree is viewed as a continuous-time Markov random walk on the vertices of a hypercube with time parameter map distance along the chromosome. The desired distribution corresponds to the distribution of sojourn times of the process in a small set of vertices. The sojourn times are well approximated via the Poisson clumping heuristic. It is shown explicitly that there is no "equivalent" number of independently segregating loci that will yield the same results as with the genomic continuum model. Results are given for the human genome.

Crossing Over, Genetic↗
PubMed2006

Anomalous small angle x-ray scattering determination of ion distribution around a polyelectrolyte biopolymer in salt solution.

The distribution of counterions in solutions of high molecular mass hyaluronic acid, in near-physiological conditions where mono- and divalent ions are simultaneously present, is studied by small angle neutron scattering and anomalous small angle x-ray scattering. The solutions contain either sodium or rubidium chloride together with varying concentrations of calcium or strontium chloride. The effects of monovalent-divalent ion exchange dominate the amplitude and the form of the counterion cloud. In the absence of divalent ions, the shape of the anomalous scattering signal from the monovalent ions is consistent with the distribution calculated from the Poisson-Boltzmann equation, as found by other workers. In mixtures of monovalent and divalent ions, however, as the divalent ion concentration increases, both the diameter and the amplitude of the monovalent ion cloud decrease. The divalent counterions always occupy the immediate neighborhood of the charged polyanion. Above a given concentration their anomalous scattering signal saturates. Even in a large excess of divalent ions, ion exchange is incomplete.

Chemistry, Physical↗
PubMed1995

[Starvation-induced mutagenesis in Salmonella typhimurium].

Spontaneous reversion to prototrophy of two his alleles of Salmonella typhimurium--hisG428 (ochre) and hisC527 (amber)--was studied. Strains containing hisG428 allele in the chromosome and within the multicopy plasmid pAQ1 were used. When the hisG428 allele was chromosomally located, no sharp fluctuations in the number of His+ revertant were observed in fluctuation experiments and the distribution of revertants obeyed the Poisson law. The pattern of revertants distribution in strains carrying plasmid pAQ1 was intermediate between the Poisson distribution and jackpot distribution described by Luria and Delbruck. Conversely, sharp fluctuations were observed in the distribution of His+ revertants of the hisC527 allele obtained from independent cultures. The data presented here suggest that His+ revertants, including ochre suppressors, appear under the influence of histidine starvation, when the hisG428 allele is chromosomally located. At the same time, reversion to prototrophy at the hisC527 allele does not strictly depend on the presence or absence of this amino acid in the medium. Plasmid location and novobiocin-resistance mutation promoted the identifying of preexisting mutants among His+ revertants of the hisG428 allele. The data obtained also demonstrate that the presence of the mutator plasmid pKM101 preferentially increases the frequency of adaptive His+ reversions.

Alleles↗
PubMedDate not supplied

[Statistical (Poisson) motor unit number estimation. Methodological aspects and normal results in the extensor digitorum brevis muscle of healthy subjects].

INTRODUCTION: Among the differents techniques for motor unit number estimation (MUNE) there is the statistical one (Poisson), in which the activation of motor units is carried out by electrical stimulation and the estimation performed by means of a statistical analysis based on the Poisson s distribution. OBJECTIVES: The study was undertaken in order to realize an approximation to the MUNE Poisson technique showing a coprehensible view of its methodology and also to obtain normal results in the extensor digitorum brevis muscle (EDB) from a healthy population. SUBJECTS AND METHODS: One hundred fourteen normal volunteers with age ranging from 10 to 88 years were studied using the MUNE software contained in a Viking IV system. RESULTS: The normal subjects were divided into two age groups (10 59 and 60 88 years). The EDB MUNE from all them was 184 49. Both, the MUNE and the amplitude of the compound muscle action potential (CMAP) were significantly lower in the older age group (p< 0.0001), showing the MUNE a better correlation with age than CMAP amplitude ( 0.5002 and 0.4142, respectively p< 0.0001). CONCLUSION: Statistical MUNE method is an important way for the assessment to the phisiology of the motor unit. The value of MUNE correlates better with the neuromuscular aging process than CMAP amplitude does.

Action Potentials↗
PubMedDate not supplied

Analyzing counts, durations, and recurrences in clinical trials.

In 1985 the (Byar and Blackard, Urology, Vol. X, 556-561, 1978) data set on bladder cancer became available to researchers. Since then, a number of studies have made use of it. However, none of these has fully utilized all of the data nor have they developed a methodology in which it is possible to estimate models of the number of recurrences and durations that are consistent with each other. The purpose of this research is to determine which, if any, of the two drugs used in the trial, pyridoxine and theotepa, were effective and, by example, illustrate procedures that could be useful in the analysis of other clinical trial data sets. First, the number of recurrences is modeled as a count using the Poisson and negative binomial distributions with covariates. Then Poisson models are tested on the durations. Finally, durations and tumor counts per recurrence are fitted to more general autoregressive Wiebull and negative binomial distributions, respectively. Poisson models for durations are rejected in favor of the more general autoregressive models. The data on durations and tumor counts are shown to be more reliable from an inference point of view than the data on the number of recurrences. The data on durations and tumor counts show quite conclusively that both drugs are effective in treating bladder cancer, a result that differs from what others have found.

Antineoplastic Agents, Alkylating↗
PubMed1990

[Revision of th distribution of chromosome aberrations induced by chemical mutagens using the BUDR label].

Cell distribution was analysed with the help of the BrDU label for the number of chromosome aberrations and breaks induced by one-center (thiophosphamide and phosphamide) and two-center (dipine and fotrine) mutagens at the stage G0 in the Ist mitosis of human lymphocytes harvested at different times of culturing (from 56 to 96 h). The comparison was made between the type of aberration distribution in cells and the dependence of their frequency on the harvesting point for various mutagens. Poisson aberration distribution in cells for two-center mutagens was found to correspond to their constant frequency observed at different times of harvesting. On the other hand, for one-center mutagens, a geometrical distribution of chromosome breaks corresponded to an exponential decrease in their frequency in time. It is suggested that two-center chemical mutagens and ionizing radiation cause largely short-live damages which are realized into chromosome aberrations rather quickly (during one cell cycle). One-center mutagens, however, cause such damages that the probability of their transformation into chromosome aberrations is decreasing rather slowly in time, under the exponential law, and their realization into chromosome aberrations can occur in subsequent cell cycle.

Bromodeoxyuridine↗