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PubMed1989

Genetic determination of plasma apolipoprotein AI in a population-based sample.

Apolipoprotein AI (apo AI) is the major protein of high-density lipoprotein (HDL). Using radioimmunoassay, we measured plasma apo AI levels in 1,880 individuals in 283 pedigrees randomly selected from the population with respect to disease status and risk factors for coronary artery disease. Apo AI levels were first adjusted for date of assay (6.8% of apo AI variation) and then adjusted for variability in age and body mass index (an additional 6.6%, 20.4%, and 23.0% of apo AI variations for males, females not using exogenous hormones, and females using exogenous hormones, respectively). A mixture of two normal distributions fit the adjusted data better than did a single normal distribution. Genetic and environmental models that could explain the mixture of normal distributions were investigated using complex segregation analysis. Heterogeneous etiologies for individual differences in adjusted apo AI levels were suggested by the data in the 283 pedigrees. In a subset of 126 pedigrees, there is evidence for the major effect of a nontransmitted environmental factor that explains the mixture of distributions as well as polygenic loci that influence apo AI levels within each distribution. The environmental factor and polygenic loci account for 32% and 65% of the adjusted variation, respectively. In the other 157 pedigrees there is strong support for a single locus with a major effect that accounts for 27% of the adjusted variation. The effect of the polygenic loci is not different from zero in these 157 pedigrees. This is the first study to present evidence for the segregation of a single unmeasured locus with a major effect on levels of apo AI in a population-based sample of pedigrees.

Adolescent↗
PubMed1999

Use of the generalised linear model with Poisson distribution to compare caries indices.

In dental epidemiological studies, an analysis of variance assuming a normal distribution is commonly used to compare caries indices, which are often not normally distributed. As these indices represent discontinuous data, it would be preferable to use the negative binomial or the Poisson distribution. In this study, in order to compare the DMFS indices of adults working in the confectionery manufacturing industry in France, the results of the generalised linear model obtained using the normal and the Poisson distribution with identity or log built-in link function were compared. The negative binomial distribution was not used because it is very often unavailable in the most used statistical software. Analysis of the caries indices showed that the use of the normal distribution could lead to an incorrect interpretation of the data. Therefore it is concluded that the generalised linear model with Poisson distribution and over dispersion is to be preferred when comparing caries levels.

Adult↗
PubMed1976

Caliber and distribution of normal coronary arterial anatomy.

Selective coronary arteriograms of 125 patients with normal coronary arteries were reviewed to establish the caliber and distribution of normal coronary arterial anatomy. Measurements established the following normal values for coronary arterial caliber in right (R), (M), and left (L) inferior emphasis systems expressed in mm (+/-SEM): (See article). Significant differences in the caliber of right coronary arterial systems and left circumflex coronary arterial systems validate the separation of coronary arterial anatomy into right, mixed, and left inferior emphasis systems, depending upon the blood supply to the inferior wall of the left ventricle. Classification of the anatomical pattern into right, mixed, and left inferior emphasis systems is useful in the cardiac catheterization laboratory at the time of selective coronary arteriography. If the expected distribution of the coronary vessels is not found, then missing vessels must be sought out. A knowledge of the range of normal size for the coronary arterial tree should be of value in defining the severity of coronary arterial narrowing.

Arteries↗
PubMed2006

Simulations of large acoustic scintillations in the straits of Florida.

Using a full-wave acoustic model, Monte Carlo numerical studies of intensity fluctuations in a realistic shallow water environment that simulates the Straits of Florida, including internal wave fluctuations and bottom roughness, have been performed. Results show that the sound intensity at distant receivers scintillates dramatically. The acoustic scintillation index SI increases rapidly with propagation range and is significantly greater than unity at ranges beyond about 10 km. This result supports a theoretical prediction by one of the authors. Statistical analyses show that the distribution of intensity of the random wave field saturates to the expected Rayleigh distribution with SI= 1 at short range due to multipath interference effects, and then SI continues to increase to large values. This effect, which is denoted supersaturation, is universal at long ranges in waveguides having lossy boundaries (where there is differential mode attenuation). The intensity distribution approaches a log-normal distribution to an excellent approximation; it may not be a universal distribution and comparison is also made to a K distribution. The long tails of the log-normal distribution cause "acoustic intermittency" in which very high, but rare, intensities occur.

Acoustics↗
PubMed1986

A proposed method to evaluate brain stem auditory evoked potential amplitude: pilot study.

The distribution and variability of brain stem auditory evoked potentials (BAEP) were studied in 30 guinea pigs under controlled conditions. Coefficient of variation showed amplitude variables to have a greater intersubject variability than latency variables. However, amplitude variables were not found to be normally distributed. Therefore, evaluation of amplitude variables using statistics which assume that the underlying data are normally distributed can be misleading. One must either transform the data so they fit a normal distribution or use statistical methods that do not depend on a normal distribution. A nonparametric analysis study on amplitude variables in humans in recommended to update its clinical applicability.

Animals↗
PubMed1982

Distribution of normal T lymphocytes in tumor-bearing rats.

Changes in distribution properties of T lymphocytes from lymphoid organs of normal rats 3H-uridine labeled in vitro and i. v. injected to tumor-bearing recipients were studied at different stages of tumor growth and rejection. Comparisons were made with T cell migration from normal donors to syngeneic recipients. A temporary decrease in the ability of normal spleen T lymphocytes to migrate into the spleen of tumor-bearing recipients at early stages of tumor growth was in correlation with their enhancement in trapping by the liver of this recipient. At this stage the migrations into tumor-draining lymph nodes and peripheral blood were rather pronounced. The growing tumor evoked an increased migration rate of donor spleen cells into each of the recipient organs studied except for liver. Tumor rejection potentiated the distribution mainly in the draining lymph node and liver. Normal lymph node T lymphocytes migrated at the beginning of tumor growth into spleen, node and liver of tumor-bearing recipients. A sharp decrease of distribution in spleen at the time of maximum tumor growth was compensated by an enhanced migration into draining nodes, peripheral blood and liver. This enhancement was seen also during tumor rejection. Distribution of normal blood T lymphocytes into spleen and peripheral blood of tumor-bearing recipients was equal to normal values. There was only a transitional reduction in their migration rates into draining nodes caused by tumor growth. Migration rates of thymocytes in tumor-bearing recipients remained unaltered. The results presented indicate that the distribution pattern of i. v. injected labeled T lymphocytes from normal donors into lymphoid organs of tumor-bearing recipients was determined by changes in the immune status of the recipients brought about by tumor development.

Animals↗
PubMed1989

Aspects of line-fitting in bivariate allometric analyses.

One of the fundamental problems involved in analyses of the scaling effects of body size (allometric analysis is the choice of an appropriate best-fit line in bivariate logarithmic plots. Following a discussion of some basic aspects of allometric analysis, the tow mai procedures for the determination of a best-fit line - the least-squares regression and the major axis - are examined with respect to their different properties and underlying models. It is important to distinguish intraspecific from interspecific scaling and to recognize the distinction between use of a best-fit line to define a relationship and use of the line for prediction. An alternative model to the bivariate normal distribution, referred to as the 'extruded normal distribution', is presented and its implications are examined with respect to two test cases (scaling of basal metabolic rate in human males; scaling of population density in mammals).

Animals↗
PubMed1985

Determination of reference intervals for 10 serum proteins measured by rate nephelometry, taking into consideration different sample groups and different distribution functions.

Reference intervals were established for 10 serum proteins (IgA, IgG, IgM, transferrin, haptoglobin, complement C3, complement C4, alpha 1-acid-glycoprotein, alpha 1-antitrypsin, alpha 2-macroglobulin) measured by rate nephelometry. The reference individuals - 200 blood donors - were divided into 5 subgroups: men aged 19-39 and 40-60 years, women aged 19-39 and 40-60 years and women aged 19-48 years using oral contraceptives. Where possible, two or more subgroups were combined to give reference sample groups. Criteria for this procedure are given. The reference limits of the sample groups were estimated by parametric methods. Assuming that for a specified serum protein the type of distribution is the same in each subgroup, the data were standardized with estimated group specific parameter values and combined into one big sample. This permitted an improved determination of the underlying type of distribution. As a possible form of distribution we also considered the normal distribution truncated on the left side at c greater than or equal to 0. In some cases, after determination of an optimal c, this unusual distribution fitted the data significantly better than the generally used normal or log-normal distribution.

Adult↗
PubMed1993

An investigation of the distribution of the protein content of samples of corn, meat and bone meal, and soybean meal.

This study examines the critical assumption of a normal distribution for protein content in feedstuffs. Data were collected from broiler feed mills on the nutrient content of corn, meat and bone meal, and soybean meal. Tests of normality for protein within each feedstuff were performed by each of two methods: 1) the Shapiro-Wilk test (n < 50) or Kolmogorov-Smirnov test (n > 50); and 2) the D'Agostino-Pearson K2 test. Results indicate that protein is non-normally distributed in corn and in meat and bone meal, but protein is normally distributed in soybean meal.

Animal Feed↗
PubMed1991

The genetic and environmental sources of body mass index variability: the Muscatine Ponderosity Family Study.

The role of genetic and environmental factors in determining the variability in body mass index (BMI; kg/m2) was investigated in 1,302 relatives identified through 284 schoolchildren from Muscatine, IA. BMI levels were first adjusted for variability in age, by gender and by relative type. There was significant familial aggregation of adjusted BMI in the pedigrees, as indicated by inter- and intraclass correlation coefficients significantly different from zero. A mixture of two normal distributions fit the adjusted BMI data better than did a single normal distribution. Genetic and environmental models that could explain both the familial aggregation and the mixture of normal distributions were investigated using complex segregation analysis. There was strong support for a single recessive locus with a major effect that accounted for almost 35% of the adjusted variation in BMI. Polygenic loci accounted for an additional 42% of the variation. Approximately 23% of the adjusted variation was not explained by genetic factors. For spouses living in the same household, their shared environment accounted for 12% of their variation. For siblings living in the same household, their shared environment accounted for 10% of their variation. While shared environments contributed to variation in adjusted BMI, more than 75% of the variation was explained by genetic factors that include a single recessive locus. Approximately 6% of the individuals in the population from which these pedigrees were sampled are predicted to have two copies of the recessive gene, while 37% of the individuals are predicted to have one copy of the gene.

Adolescent↗
PubMed2000

Brownian Coagulation of Fractal Agglomerates: Analytical Solution Using the Log-Normal Size Distribution Assumption.

An analytical solution to Brownian coagulation of fractal agglomerates in the continuum regime that provides time evolution of the particle size distribution is presented. The theoretical analysis is based on representation of the size distribution of coagulating agglomerates with a time-dependent log-normal size distribution function and employs the method of moments together with suitable simplifications. The results are found in the form that extends the spherical particle solution previously obtained by K. W. Lee (J. Colloid Interface Sci. 92, 315-325 (1983)). The results show that the mass fractal dimension has a significant effect on the size distribution evolution during coagulation. When the obtained solution was compared with numerical results, good agreement was found. The self-preserving size distribution of nonspherical agglomerates is discussed. Copyright 2000 Academic Press.

Journal Article↗
PubMed2004

Comparison of preprocessing procedures for oligo-nucleotide micro-arrays by parametric bootstrap simulation of spike-in experiments.

OBJECTIVE: Due to scarcity of calibration data for microarray experiments, simulation methods are employed to assess preprocessing procedures. Here we analyze several procedures' robustness against increasing numbers of differentially expressed genes and varying proportions of up-regulation. METHODS: Raw probe data from oligo-nucleotide microarrays are assumed to be approximately multivariate normally distributed on the log scale. Chips can be simulated from a multivariate normal distribution with mean and variance-covariance matrix estimated from a real raw data set. A chip effect induces strong positive correlations. In reverse, sampling from a normal distribution with strong correlation variance-covariance matrix generates data exhibiting a chip effect. No explicit model of chip-effect is needed. Differences can be artificially spiked-in according to a given distribution of effect sizes. Thirty preprocessing procedures combining background correction, normalization, perfect match correction and summarization methods available from the BioConductor project were compared. RESULTS: In the symmetrical setting "50% differentially expressed genes, 50% of which up-regulated" background correction reduces bias, but inflates low intensity probe variance as well as the mean squared error of the estimates. Any normalization reduces variance and increases sensitivity with no clear winner. Asymmetry between up and down regulation causes bias in the effect-size estimate of non-differentially expressed genes. This markedly inflates the false positive discovery rates. Variance stabilizing normalization (VSN) behaved best. CONCLUSION: A simple parametric bootstrap was used to simulate oligo-nucleotide micro-array raw data. Current normalization methods inflate the false positive rate when many genes show an effect in the same direction.

Computer Simulation↗
PubMed2006

Statistical characterisation of bacterial wild-type MIC value distributions and the determination of epidemiological cut-off values.

MIC distribution data were obtained from a variety of international sources, and pooled after selection by a defined criterion. Sixty-seven of these datasets were subjected to a range of statistical goodness-of-fit tests. The log-normal distribution was selected for subsequent modelling. Cumulative counts of MIC distribution data were fitted to the cumulative log-normal distribution using non-linear least squares regression for a range of data subsets from each antibiotic-bacterium combination. Estimated parameters in the regression were the number of isolates in the subset, and (the log(2) values of) the mean and standard deviation. Optimum fits for the cumulative log-normal curve were then used to determine the wild-type MIC range, determined by calculating the MICs associated with the lower and upper 0.1% of the distribution, rounding to the nearest two-fold dilution, and calculating the probabilities of values higher and lower than these values. When plotted logarithmically, histograms of MIC frequencies appeared normal (Gaussian), but standard goodness-of-fit tests showed that the two-fold dilution grouping of MICs fits poorly to a log-normal distribution, whereas non-linear regression gave good fits to population (histogram) log-normal distributions of log(2) MIC frequencies, and even better fits to log-normal cumulative distributions. Optimum fits were found when the difference between the estimated and true number of isolates in the fitted subset was minimal. Sixteen antibiotic-bacterium datasets were fitted using this technique, and the log(2) values of the means and standard deviations were used to determine the 0.1% and 99.9% wild-type cut-off values. When rounded to the nearest two-fold dilution, > or = 98.5% of MIC values fall within the cut-off value range. Non-linear regression fitting to a cumulative log-normal distribution is a novel and effective method for modelling MIC distributions and quantifying wild-type MIC ranges.

Anti-Infective Agents↗
PubMed1988

Change in attachment level.

Attachment level or pocket depth measurements are used to detect change in periodontal attachment. However, measurement error limits their usefulness for this purpose. The aims of this study are twofold. The first aim was to test the assumption, used in previous reports of measurement error, that attachment level measurements are normally distributed. The second aim was to estimate error rates encountered when assessing periodontal attachment level change with attachment level or pocket depth measurements. Two simulation methods are compared in their ability to reproduce the distribution of differences in replicated measurements. A simulation method based on a normal distribution was not able to reproduce the actual distribution of differences between replicate measurements. In contrast simulations based on resampling recreated the distribution of differences in replicated attachment level measurements. Due to the inability of simulations based on the normal distribution to reproduce the distribution of differences in replicated measurements, simulations based on the resampling procedure were used to estimate error rates. Determining change in attachment level or pocket depth by either single or paired measurements resulted in low Type I error rates for both single and paired measurements. For single measurements of attachment level, the Type I error rate was 0.0074 for a 3-mm change. Paired measurements of attachment level had a Type I error rate of 0.0014 for a 3-mm change. However, false-positive rates were found to be much higher. For single measurements of attachment level, the false-positive rate was 0.32 for a 3-mm change.(ABSTRACT TRUNCATED AT 250 WORDS)

Diagnostic Errors↗
PubMed2003

Normality of oligonucleotide microarray data and implications for parametric statistical analyses.

MOTIVATION: Experimental limitations have resulted in the popularity of parametric statistical tests as a method for identifying differentially regulated genes in microarray data sets. However, these tests assume that the data follow a normal distribution. To date, the assumption that replicate expression values for any gene are normally distributed, has not been critically addressed for Affymetrix GeneChip data. RESULTS: The normality of the expression values calculated using four different commercial and academic software packages was investigated using a data set consisting of the same target RNA applied to 59 human Affymetrix U95A GeneChips using a combination of statistical tests and visualization techniques. For the majority of probe sets obtained from each analysis suite, the expression data showed a good correlation with normality. The exception was a large number of low-expressed genes in the data set produced using Affymetrix Microarray Suite 5.0, which showed a striking non-normal distribution. In summary, our data provide strong support for the application of parametric tests to GeneChip data sets without the need for data transformation.

Algorithms↗
PubMed1976

Enzyme loading of electrically homogeneous human red blood cell ghosts prepared by dielelctric breakdown.

Human red blood cell ghosts were prepared by electrical haemolysis at 0 degrees C in isotonic solutions using a discharge chamber which was part of a high voltage circuit. The size distribution of the ghosts was normally distributed, the modal (=mean) volume was approx. 115 mum3, performing the electrical haemolysis in the following solution: 105 mM KCI, 20 mM NaCL, 4mM MgCl2, 7.6 mM Na2HPO4, 2.94 mM NaH2PO4, 10 mM glucose, pH 7.2. Resealing was carried out at o degrees C for 10 min (after the haemolytic step) and then for further 20 min at 37 degrees C. The mean volume of the ghost preparation could be changed by variation of the phosphate concentration in the above solution replacing a part of NaCl by phosphate (5 mM phosphate: 94 mum3, 15 mM phosphate: 135 mum3). The breakdown voltage of the ghost cell membranes measured with a hydrodynamic focusing Coulter Counter depends on the mean volume (94 mum3 = 1.04 V, 134 mum3 = 1.36 V). On the other hand, the breakdown voltage is constant throughout each size distribution pointing to an "electrically homogeneous" ghost preparation. The sensitiviity of the Coulter Counter to detect electrical inhomogeneities in the membranes of a ghost population is demonstrated by dielectric breakdown measurements of an apparently normally distributed ghost preparation containing two different "electrically homogeneous" ghost population i.e. with two different breakdown voltages. The ghost cells obtained by electrical haemolysis in the above solution containing 10mM phosphate were fairly impermeable to sucrose and behave like an ideal osometer. It is further demonstrated that ghost cells can be loaded with enzymes (e.g. urease) and drugs using this technique and that these loaded ghost cells can be used as bioactive capsules for clinical application.

Biological Transport↗
PubMed1978

[Evaluation of the clinical effectiveness of paradentosis therapy (author's transl)].

The x2 test of goodness of fit was used to assess the correlation between empirically determined distributions of a number of characteristics used in parodontology and the model of normal distribution. There was found a more or less pronounced asymmetry in the statistical distributions of some clinical and biochemical tests. It is recommended to use 10g X or square root of x in order to achieve approximation to the normal distribution. Inaccuracies in interpretation of clinical data due to neglect of variations from normal distribution are pointed out.

Diagnostic Errors↗
PubMed1977

Frequency dependence of ventilation distribution in normal and obstructed lungs.

Differences in regional pulmonary time constant may cause ventilation distribution to vary with breathing frequency and frequency-dependent changes in regional ventilation per unit volume might be expected. We measured the regional distribution of inhaled xenon-133 (133Xe) at 10 and 60 breaths/min in normal subjects and in patients with a clinical diagnosis of chornic bronchitis or asthma. Breathing frequency had no siqnificant effect on ventilation distribution in normals but in patients with chronic bronchitis ventilation decreased in the lower lung regions at 60 breaths/min compared with 10 breaths/min. In six asthmatic patients the lung regions demonstrating the greatest frequency-dependent reductions in ventilation, which were assumed to have the greatest time constants, also showed decreased ventilation-perfusion ratios (V/Q) measured by standard 133Xe techniques. Bronchodilator increased ventilation more than perfusion in these regions and thus V/Q ratio increased toward the normal range. These results imply that measurement of the frequency dependence of regional ventilation provides information about the relative distribution of airway obstruction, and that airway function in the most obstructed lung regions in asthmatics is improved following bronchodilator therapy.

Asthma↗