The combination of probabilities arising from data in discrete distributions.
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Biometry↗
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The moments of the z and F distributions.
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Biometry↗
[Cartography of epidemiologic data. The principal methods of making continuous data discrete and their importance in cartographic representation].
The cartographic representation of continuous quantitative data is often required in studies of the spatial distribution of health indicators. It imposes a succession of choices which directly affect the result obtained. The conversion of continuous data to discrete data is one of the most important steps in the development of epidemiological maps. This article presents the methods currently used to make data discrete, discusses the advantages and disadvantages of each method and assesses their appropriateness for various situations. As an example, and for comparison purposes, we mapped the same series of statistics (relative rates of avoidable male deaths, "associated with the health care system", for "employment zones" in France from 1988 to 1992), using each of the methods discussed.
Algorithms↗
Mann-Whitney/Wilcoxon's nonparametric cumulative probability distribution.
It is demonstrated how complete nonparametric, cumulative probability distributions for Mann-Whitney/Wilcoxon's nonparametric, two-sample test can be constructed based on algorithms published earlier in this journal. These procedures provide cumulative probabilities for all possible rank sums in the nonparametric two-sample test. Separate programs for MS(PC)-DOS and Macintosh computers are offered.
Algorithms↗
Normal ranges for bone loss rates.
We reported previously that the variability in bone loss rates among postmenopausal women decreases dramatically during the first few years of followup. In this paper, we have examined the distributions of bone loss rates measured at the calcaneus, distal radius and proximal radius. The incidence of physical impairment was five times greater among women with bone loss rates faster than 2 S.D. below the mean. Because the rate of change in bone density was skewed at the lower end of the distribution (representing rapid bone loss), the influence of values at the extreme ends of the distribution were statistically removed in order to estimate the normal distribution of bone loss rates. For the convenience of clinicians, the upper and lower limits of the 90 and 70% normal ranges are presented. Because average bone loss rates vary with age, normal ranges are provided separately by age group. The width of each normal range decreased by at least half after 3 or 4 years of followup, compared to less than 1 year. Consequently, measured loss rates which were well within the normal range at 1 year were sometimes far outside the normal range for longer followup times. We conclude that followup duration has a profound effect on estimates of the normal range, and must be considered when interpreting the clinical significance of measured loss rates.
Adult↗
Multipoint correlation functions for continuous-time random walk models of anomalous diffusion.
Recursive relations are developed for computing the multipoint correlation functions of a particle undergoing a biased continuous-time random walk (CTRW) in an external potential. Two- and three-point correlation functions are calculated for waiting-time distributions with an anomalous power-law profile t(-alpha-1), 0 < alpha < 1, on intermediate time scales with a crossover to an exponential long time decay. Comparison of the CTRW with the Brownian harmonic oscillator model (Gaussian process) illustrates how higher-order correlation functions may be used to distinguish between dynamical models that have the same two-point correlation function.
Colloids↗
Are our data symmetric?
Skewness indicates a lack of symmetry in a distribution. Knowing the symmetry of the underlying data is essential for parametric analysis, fitting distributions or doing transformations to the data. The coefficient of skewness is the commonly used measure to identify a lack of symmetry in the underlying data, although graphical procedures can also be effective. We discuss three different methods to assess skewness: traditional coefficient of skewness index, skewness index based on the L-moments discussed by Hosking and the asymptotic test of symmetry developed by Randles et al. With this work, we provide easy-to-implement S-PLUS functions as well as discuss the advantages and shortcomings of each technique.
Biometry↗
Statistical modelling of the spatial distribution of prevalence of Calicophoron daubneyi infection in sheep from central Italy.
Statistical modelling for Disease Mapping and Ecological Analysis is of particular importance in veterinary parasitology because environmental characteristics can affect parasite distribution. However, the main difficulties relate to the concentration of animal populations within farms, which contrasts to the study of wild animal populations. In the present paper we report the results of a cross-sectional coprological survey designed to study the presence and distribution of the rumen fluke Calicophoron daubneyi--which causes paramphistomosis, a snail borne disease--in pastured sheep living in the Latina province of central Italy. We show how techniques derived from human epidemiology can be used to study the spatial distribution of parasite infection in animals. We proposed a hierarchical Bayesian model with random terms for unstructured variability (heterogeneity) to account for local farm characteristics and spatially structure terms (clustering) to cope with medium-large scale environmental characteristics.
Animal Husbandry↗
Empirical power for distribution-free tests of incomplete longitudinal data with applications to AIDS clinical trials.
The design of AIDS clinical trials is of growing importance. These studies tend to be longitudinal and typically involve missing data. HIV-1 RNA is a common endpoint for these studies and is inherently non-normal, although viral load can be measured only within certain bounds, resulting in censored data. We compared several analysis methods, both univariate and multivariate, on the basis of empirical power and provide an illustrative example of data from a controlled clinical trial. Simulated viral load data demonstrate that methods adjusting for baseline data have power increasing with increasing positive intrasubject correlation expected with this type of data. Several summary measures considered have power compatible with multivariate tests.
Acquired Immunodeficiency Syndrome↗
Application of high-performance anion-exchange chromatography with pulsed amperometric detection and statistical analysis to study oligosaccharide distributions--a complementary method to investigate the structure and some properties of alginates.
Alginates comprised of essentially alternating units of mannuronic (M) acid-guluronic (G) acid (MG-alginate), and G-blocks isolated from a seaweed where subjected to partial acid hydrolysis at pH 3.5 The chain-length distribution of oligosaccharides in the hydrolysate were investigated by statistical analysis after their separation with high-performance anion-exchange chromatography and pulsed amperometric detection (HPAEC-PAD). Simulated depolymerisation of the MG-alginate provided an estimate of the ratio between two acid hydrolysis rate constants (p=8.3+/-1) and the average distribution of the MM linkages in the original sample of polysaccharide chains. In conclusion, we found HPAEC-PAD together with statistical analysis was a useful method to investigate the fine structure and some properties of binary polysaccharides.
Alginates↗
Correlation spectroscopy of minor fluorescent species: signal purification and distribution analysis.
We are performing experiments that use fluorescence resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) to monitor the movement of an individual donor-labeled sliding clamp protein molecule along acceptor-labeled DNA. In addition to the FRET signal sought from the sliding clamp-DNA complexes, the detection channel for FRET contains undesirable signal from free sliding clamp and free DNA. When multiple fluorescent species contribute to a correlation signal, it is difficult or impossible to distinguish between contributions from individual species. As a remedy, we introduce "purified FCS", which uses single molecule burst analysis to select a species of interest and extract the correlation signal for further analysis. We show that by expanding the correlation region around a burst, the correlated signal is retained and the functional forms of FCS fitting equations remain valid. We demonstrate the use of purified FCS in experiments with DNA sliding clamps. We also introduce "single-molecule FCS", which obtains diffusion time estimates for each burst using expanded correlation regions. By monitoring the detachment of weakly-bound 30-mer DNA oligomers from a single-stranded DNA plasmid, we show that single-molecule FCS can distinguish between bursts from species that differ by a factor of 5 in diffusion constant.
Computer Simulation↗
Relationship between phospholipid transfer protein activity and HDL level and size among inbred mouse strains.
Because of the paucity of data on phospholipid transfer protein (PLTP) activity and lipoprotein phospholipid in mouse strains, plasma PLTP activity (PLTA), plasma phospholipid and cholesterol, HDL phospholipid and cholesterol, and HDL size distribution were determined in 15 inbred mouse strains. The 15 inbred mouse strains differed in their relatedness to one another and consisted of six largely unrelated groups: Castaneus, Swiss, C57BL, AKR, DBA, and NZB. Lipid and PLTA analyses were performed on plasma pools from male and female mice that had fasted for 4 h prior to blood draw. Among the representative unrelated strains fed the chow diet, there was a highly significant relationship between PLTA and plasma phospholipid (r(s) = 0.727, P < 0.01), HDL phospholipid (r(s) = 0.762, P < 0.01), HDL cholesterol (r(s) = 0.699, P < 0.02), percentage of large HDL particles (r(s) = 0.699, P < 0.02), and HDL peak size (r(s) = 0.776, P < 0.01). Similar results were obtained among these strains fed a high fat, high cholesterol diet. PLTA increased in all strains fed the high fat diet (chix = 94%, range 6 to 221%). Strain SM having relatively low PLTA and HDL was crossed with strain NZB having high PLTA and HDL. The F1 progeny from this cross were backcrossed to strain SM and 41 male backcross progeny collected. Among these individual backcrossed animals, PLTA was highly correlated with plasma phospholipid (r(s) = 0.508, P = 0.001), HDL phospholipid (r(s) = 0.566, P < 0.001), HDL cholesterol (r(s) = 0.532, P < 0.001), and percentage of large HDL particles (r(s) = 0.446, P = 0.020). Therefore, we conclude that PLTP is a determinant of HDL level and size in mice.-Albers, J. J., W. Pitman, G. Wolfbauer, M. C. Cheung, H. Kennedy, A-Y. Tu, S. M. Marcovina, and B. Paigen. Relationship between phospholipid transfer protein activity and HDL level and size among inbred mouse strains.
Animals↗
Effects of resolution reduction on data analysis.
BACKGROUND: There is often a need in flow cytometry to display and analyze histograms at resolutions lower than those native to the data. It is common, for example, to analyze DNA histograms at 256-channel resolution, even though the data were acquired at 1,024 channels or more. The most common method for reducing resolution, referred to as the consecutive summation (CS) method, can introduce distortions into the shape of histograms. Peaks that were symmetric in the original data can become skewed in the reduced-resolution histogram. Data analysis can be negatively affected by the distortions produced by reducing the histogram resolution. An alternative technique for reducing histogram resolution, the unbiased summation (US) method, minimizes shape distortion. This paper describes the US method and examines the benefits it provides in the analysis of DNA histograms. METHODS: Reduced chi-square (RCS) was used to measure the response to three experimental variables in the least-squares analysis of simulated DNA histograms. For each variable (the percentage of coefficient of variation [%CV], number of events, and mean position of the G1 distribution), a test data set of 1,000 histograms was generated at 1,024-channel resolution. Histogram resolutions were reduced with each method and then analyzed with ModFit LT cell-cycle analysis software (Verity Software House, Topsham, ME). S-phase error and processor computation time of each method also were evaluated. A Monte Carlo experiment was performed to compare CS and US methods to theoretically correct reductions. RESULTS: CS method analysis results were negatively affected by changes in %CV, number of events, and G1 peak position. The US method produced consistently lower RCS values (more accurate results) within the tested ranges. The US method eliminated bias in S-phase error and had negligible impact on analysis processing speed. It improved RCS values 44.50% on average (P < 0.0002) with actual DNA histograms. Whereas the CS method became less accurate (chi-square test) as the amount of reduction increased, the US method was unaffected, producing consistently better results. CONCLUSIONS: The US method is recommended for reducing histogram resolution in modeling applications such as DNA cell-cycle analysis. It may have implications in other areas of flow cytometric data analysis.
Algorithms↗
Data exploration in meta-analysis with smooth latent distributions.
Meta-analysis with discrete outcomes is interpreted as the estimation (in one or two dimensions) of a non-parametric smooth latent distribution of event probabilities (or rates). A simple but efficient EM algorithm is presented. A fine grid is used and fast smoothing is done by penalized least squares. Data exploration is the primary goal, but the estimated distribution can also be used to compute useful statistics of treatment effects.
Algorithms↗
A statistical analysis of the distribution of a larval nematode (Anisakis sp.) in the musculature of chum salmon (Oncorhynchus keta-Walbaum).
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Animals↗
The use of Chi-square maps in the analysis of census data.
"This paper addresses itself to one of the problems inherent in any spatial analysis of census data, namely the variable size of the enumeration units. This variation renders some proportions unstable, due to the small numbers involved. Attempts to overcome this, using visual methods, can be unsatisfactory, whilst doing nothing to aid statistical analysis. Chi-square maps are suggested as a satisfactory alternative in both contexts, and data for Reading, Berkshire are displayed to illustrate this. These maps suggest that some inferences, based upon indicators derived from proportions, may be unsound."
Censuses↗
A statistical analysis of the distribution characteristics of cholera within Ibadan City, Nigeria (1971).
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Cholera↗
Testing experimental data for univariate normality.
BACKGROUND: Many experimentally-derived data sets are generated in the practice of clinical chemistry. Graphical presentation is essential to assess the data distribution. The distribution must also be assessed quantitatively. These approaches will determine if the data is Normal or not. Finally the results of these tests of Normality must be shown to be free of sample size effects. METHODS: Four experimentally-derived data sets were used. They represented normal, positive kurtotic, positive- and negatively-skewed distributions. These data sets were examined by graphical techniques, by moment tests, by tests of Normality, and monitored for sample size effects. RESULTS: The preferred graphical techniques are the histogram and the box-and-whisker plots that may be supplemented, with advantage, by quantile-quantile or probability-probability plots. Classical tests of skewness and kurtosis can produce conflicting and often confusing results and, as a consequence, the alternative use of the newer L-moments is advocated. Normality tests included the Kolmogorov-Smirnov (Lilliefors modification), Cramér-von Mises and Anderson-Darling tests (empirical distribution function statistics) and the Gan-Koehler, Shapiro-Wilk, Shapiro-Francia, and Filliben tests (regression/correlation techniques). Of these only the Anderson-Darling, Shapiro-Wilk, and Shapiro-Francia tests correctly classified all four test samples. The effect of sample size on the resulting p-value was investigated using Royston's V'/v' graphical test. CONCLUSIONS: A systematic approach to Normality testing should follow the route of graphical presentation, the use of L-moments, the use of Anderson-Darling, Shapiro-Wilk, or Shapiro-Francia testing, and Royston's sample size monitoring.
Algorithms↗