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PubMed1976

[Logarithmo-normal distributions of relative and absolute values of human lymphocytes forming spontaneous rosettes in presence of sheep and mouse erythrocytes in normal adult].

The percentages and absolute numbers of peripheral blood lymphocytes forming rosettes with sheep and mouse red blood cells were established in 135 normal human beings. We found SRFC values almost similar to the proportion of so called "active" rosettes, whereas the values of MRFC were low. SRFC and MRFC values had a logarithmico-normal distribution. The absolute number of the two types of rosettes was decreased in the subjects more than 70 years old.

Age Factors↗
PubMed1975

[Disaccharidases of the small intestine mucosa in infants and children. "Normal values", log normal distribution and age dependence].

In 63 infants and children with a histological normal mucosa of the duodenum, without an isolated defect of enzyme and with a normal increase of xylose and glucose in serum after a combined xylose-lactose loading test the activities of disaccharidases were log normal distributed. The asymmetric distributions were transformed into symmetric ones and the geometric mean (x) as well as the range (+/- 2 s) of maltase, saccharase, isomaltase, lactase and trehalase were calculated. Only the activity of lactase shows a significant dependency on age. In the first year of age the lower limit (x -- 2 s) of this enzyme is much higher than later.

Age Factors↗
PubMed1989

Class II MHC antigens in the rat digestive system. Normal distribution and induced expression after interferon-gamma treatment in vivo.

The normal and interferon-gamma induced expression of class II MHC antigens was investigated immunohistologically in the digestive system of LEW rats. In the normal state class II molecules were present in interstitial dendritic cells, B lymphocytes and epithelial cells. Epithelial class II expression was restricted to enterocytes in certain portions of the small intestine and to some duct epithelia in salivary glands. After continuous intravenous infusion of interferon-gamma (IFN-gamma) for 3 days, class II MHC antigens were induced in large vessel endothelium and in the surface epithelia of the tongue, oesophagus and proventricle. In the gastric glands class II molecules appeared in mucous neck cells and in parietal cells, while adjacent mucous surface cells and chief cells did not acquire class II reactivity. All enterocytes, including the previously negative colonic epithelium, were induced to express class II antigens. In the salivary glands class II antigens appeared in all duct epithelia. Serous acinar cells were induced in the parotids, but in the submandibular glands and in the pancreas the serous gland epithelium stayed negative. Our study thus shows that the effects of IFN-gamma on class II MHC antigen expression in vivo depend on the differentiation pathway of the individual cell. The normal distribution in rats suggest that class II MHC antigens may play a role in peptide transport across specialized epithelia. It remains to be determined whether such a function is enhanced after IFN treatment.

Animals↗
PubMed1997

Common noncompartmental pharmacokinetic variables: are they normally or log-normally distributed?

We investigated the hypothesis that distributions of continuous pharmacokinetic variables are positively skewed in nature and that logarithmic transformation of these variables restores normality. The distributions of common continuous noncompartmental pharmacokinetic variables were investigated for four different Glaxo Wellcome compounds, administered by three different routes of administration: ranitidine (po), sumatriptan (sc), ondansetron (iv), and bismuth, from ranitidine bismuth citrate (po). The distributions of all the investigated noncompartmental pharmacokinetic variables were adequately described by a log-normal distribution, whereas statistically significant departures from normality occurred in the majority of cases. Thus, unless there is strong and consistent evidence for a departure from log-normality, the parametric statistical analysis of common noncompartmental pharmacokinetic variables should be carried out after a priori log transformation.

Bismuth↗
PubMed1995

Observations on the normal distribution of quantitative traits.

Two experiments are assumed, which show that group equal assortment of genes produces a centripetal effect and group unequal assortment of genes produces a centrifugal effect. The normal distribution of quantitative traits is intermediate between group equal assortment of genes and group unequal assortment of genes, which means the reduction division and the assortment of genes are relatively equal (not completely equal). From the experiments, we find that individual equal assortment of genes produces a centrifugal effect and the individual unequal assortment of genes produces a centripetal effect. The centrifugal effect of individual equal assortment of genes leads to the result that the F2 generation is considerably more variable than the F1 in the Emerson-East experiment with sweet corn (1). Group assortment interacts with individual assortment. The centrifugal effect interacts with the centripetal effect. These interactions affect the stability of inheritance and variation.

Epistasis, Genetic↗
PubMed2000

Setting specifications for non-normally distributed data.

In this paper, we focus on estimating an upper specification for non-normally distributed data. Cornish-Fisher expansions were exploited for derivations of the method. The method was applied for upper specification calculations of two particle-size data sets, and simulation studies were also performed to demonstrate the accuracy of the approximations. The method was also used to calculate the critical values for delta(min) for the Anderson-Hauck test for equivalence using bootstrap samplings. The main advantage of the method is in calculating specifications with limited data.

Chemistry, Pharmaceutical↗
PubMed1987

Logarithmic normal distribution of incubation times for canine diseases (Sartwell's model).

The distribution of incubation periods for most infectious diseases follows a logarithmic normal distribution (Sartwell's model). The same is true for human neoplastic diseases of known cause and for genetic diseases, when the age at onset of the disease was used as a surrogate measure of the incubation period. In this study, a similar distribution was observed when Sartwell's model was applied to canine diseases of known genetic cause, but not to diseases of an environmental cause. The model was also applied to canine diseases of suspected multifactorial causes for the purpose of distinguishing between the relative importance of genetic and environmental factors that act before or after birth. Limitations of this method were discussed.

Animals↗
PubMed1999

Sample size determination for proving equivalence based on the ratio of two means for normally distributed data.

Equivalence trials aim to demonstrate that two treatments do not differ by more than a prespecified clinically irrelevant amount. We consider the problem when equivalence is defined in terms of the ratio of population means and the original (untransformed) data are normally distributed. Application of the intersection-union principle to the test proposed by Sasabuchi results in a two one-sided tests procedure of size alpha. We give the associated 100 (1-2 alpha) per cent confidence interval and derive the exact methods for calculation of power and sample sizes for the parallel group design and the two-period cross-over. We present tables and figures of required sample sizes and achieved power.

Administration, Inhalation↗
PubMed2004

Log-normal distribution of pulse amplitudes due to Raman cross talk in wavelength division multiplexing soliton transmission.

The effect of delayed Raman response on soliton collisions in wavelength division multiplexing (WDM) transmission systems is investigated. Taking into account the stochastic nature of pulse sequences in different frequency channels and the Raman-induced cross talk, it is shown that the soliton amplitude is a random variable with a log-normal distribution. Moreover, the Raman-induced self-frequency shift and cross-frequency shift are also random variables with log-normal-like distributions. These results imply that fluctuations in soliton amplitude and frequency induced by soliton collisions in the presence of delayed Raman response play an important role in massive WDM transmission.

Journal Article↗
PubMed1982

Transformations towards the normal distribution of broad band spectral parameters of the EEG.

In this report transformations are evaluated for obtaining normally distributed broad band spectral parameters (both for absolute and relative power) in a sample of healthy individuals. This problem leads automatically to the question of defining a normative sample, both in terms of sampling and recording conditions; as to the latter, the electro-oculogram proved to be crucial. For relative power the transformation log(x/(1-x)) was excellent in all regards, whereas the best transformation for absolute power--log(x)--was not fully satisfactory for all bands.

Adolescent↗
PubMed2004

Small-sample inference for the comparison of means of log-normal distributions.

We propose a likelihood-based test for comparing the means of two or more log-normal distributions, with possibly unequal variances. A modification to the likelihood ratio test is needed when sample sizes are small. The performance of the proposed procedures is compared with the F-ratio test using Monte Carlo simulations.

Biometry↗
PubMed1987

Mixed-model analysis of a censored normal distribution with reference to animal breeding.

A mixed-model procedure for analysis of censored data assuming a multivariate normal distribution is described. A Bayesian framework is adopted which allows for estimation of fixed effects and variance components and prediction of random effects when records are left-censored. The procedure can be extended to right- and two-tailed censoring. The model employed is a generalized linear model, and the estimation equations resemble those arising in analysis of multivariate normal or categorical data with threshold models. Estimates of variance components are obtained using expressions similar to those employed in the EM algorithm for restricted maximum likelihood (REML) estimation under normality.

Analysis of Variance↗
PubMed1999

A Wald test comparing medical costs based on log-normal distributions with zero valued costs.

Medical cost data often exhibit strong skewness and sometimes contain large proportions of zero values. Such characteristics prevent the analysis of variance (ANOVA) F-test and other frequently used standard tests from providing the correct inferences when the comparison of means is of interest. One solution to the problem is to introduce a parametric structure based on log-normal distributions with zero values and then construct a likelihood ratio test. While such a likelihood ratio test possesses excellent type I error control and power, its implementation requires a rather complicated iterative optimization program. In this paper, we propose a Wald test with simple computation. We then conduct a Monte Carlo simulation to compare the type I error rates and powers of the proposed Wald test with those of the likelihood ratio test. Our simulation study indicates that although the likelihood ratio test slightly outperforms the Wald test, the performance of the Wald test is also satisfactory, especially when the sample sizes are reasonably large. Finally, we illustrate the use of the proposed Wald test by analysing a clinical study assessing the effects of a computerized prospective drug utilization intervention on in-patient charges.

Analysis of Variance↗
PubMedDate not supplied

ROC curves and the areas under them for dichotomized tests: empirical findings for logistically and normally distributed diagnostic test results.

Many measures, including sensitivity and specificity, predictive values, and likelihood ratios, are available for the assessment of diagnostic tests. A drawback of the use of these measures is that continuous test results are often dichotomized, with consequent loss of information. Receiver operating characteristic (ROC) curves do not depend on discrimination thresholds, and therefore the area under the ROC curve (AUC) is one of the preferred measures. Although quantitative test results are often presented dichotomized, it would be convenient still to be able to estimate the ROC curve and the AUC. The authors present equations for such estimates when only one pair of a true- and a false-positive rate is given, for inherently logistically and normally distributed data. Illustrative empirical data are provided for both distributions. In contradiction to earlier reports, the authors also show that differential disease verification may skew the ROC curve. The ROC curve is thus not invariant to selection bias.

Bayes Theorem↗
PubMed1978

Log normal distribution of ovarian and placental steroid values in early human pregnancy.

Concentrations of estradiol, progesterone, 17OH-progesterone were measured by radioimmunoassay in individual serum samples obtained from a group of 304 women with normal gestations between the 4th and 17th week of pregnancy. Values obtained underwent statistical analysis in order to determine the arithmetic mean and the 95% normal range (+/- two standard deviations). It was noted hereby that the spread of values above the mean was greater than that below the mean, and that very often the mean minus two standard deviations was either close to zero or negative. Therefore, the data for each hormone were analyzed for normality of the distributions by the chi-square test. For each hormone the chi-square test was significantly different (p less than 0.001) from the normal distribution (Gaussian). Subsequently, linear transformation by rankit analysis revealed the log-normal distribution of our data. Furthermore, rankit analysis was used as a graphical method to delineate a useful clinical range, which includes the mean and meaningful 95% confidence limits for estradiol, progesterone, and 17OH-progesterone in early normal pregnancies.

Estradiol↗
PubMed1985

[Learning and prototype formation of artificial categories defined by multidimensional normal distributions].

In order to approximate the variety of natural categories, two kinds of stimuli whose attributes vary according to different multivariate normal distributions are generated on CRT screen. Twenty undergraduate and graduate students served as subjects. Subject's task was to discriminate the stimuli. Results revealed that subject's performance can be explained very well by the parameters of the distributions (Exp.1). Although in previous studies prototypes have been assumed to be the mean value or central tendency of category instances, there is another possibility, especially when two or more concepts are simultaneously learned, that they have attributes which are emphasized. This hypothesis was confirmed in Exp.2, using 30 undergraduates as subjects. It was argued that we must distinguish at least two kinds of prototypes: the one formed by the most frequent instances and the other the most discriminate in contrast with the other concepts.

Adolescent↗
PubMed2001

On tests of the overall treatment effect in meta-analysis with normally distributed responses.

For the meta-analysis of controlled clinical trials or epidemiological studies, in which the responses are at least approximately normally distributed, a refined test for the hypothesis of no overall treatment effect is proposed. The test statistic is based on a direct estimation function for the variance of the overall treatment effect estimator. As outcome measures, the absolute and the standardized difference between means are considered. In simulation studies it is shown that the proposed test keeps the prescribed significance level very well in contrast to the commonly used tests in the fixed effects and random effects model, respectively, which can become very liberal. Furthermore, just for using the proposed test it is not necessary to choose between the fixed effects and the random effects approach in advance.

Amlodipine↗
PubMed1983

Recovering the parameters of finite mixtures of normal distributions from a noisy record: an empirical comparison of different estimating procedures.

Three procedures were compared for their ability to estimate the known parameters of mixtures of normal distributions: maximum likelihood estimators (MLE), X2 minimization method and the least-square error procedure. For this purpose a Monte-Carlo study was undertaken to evaluate empirically the performance of the estimators. We chose to investigate their behaviour using closely-positioned mixtures of two or 3 univariate Gaussians. The Monte-Carlo simulations clearly demonstrate the superiority of the MLE and X2 minimum methods. Other reasons why the MLE is to be preferred are discussed. The effect of sample size was also examined. All 3 estimators have also been applied to data derived from different physiological experiments, and the use of the estimators is considered in practical terms. The formulae for all 3 procedures are given in the Appendix.

Animals↗