SEARCH · PubMed Health

Results for “Normal Distribution”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,405 records · Page 78Linked to original sources

PubMed2004

Experimental validation of a statistical model for evaluating the past or future magnetic field exposures of a population living near power lines.

This study was designed to provide an experimental validation for a statistical model predicting past or future exposures to magnetic fields (MF) from power lines. The model estimates exposure, combining the distribution of ambient MF in the absence of power lines with the distribution of past or future MF produced by power lines. In the study, validation is carried out by comparing exposures predicted by the model with the actual measurements obtained from a large-scale epidemiological study. The comparison was made for a group of 220 women living near a 735 kV power line. Knowing that the individual arithmetic means of MF exposures follow a log-normal distribution, the Pearson correlation between the log-transformed measured means and the calculated ones was determined and found to be 0.77. Predicted values of MF exposures were slightly lower than measured values. The calculated geometric mean of the group was 0.33 microT, compared to 0.38 microT for the measured geometric mean. The present study shows good agreement between the measured MF exposure of an individual inside a house near a 735 kV line and the MF exposure calculated using a statistical model.

Adult↗

PubMed1986

Primary pulmonary hypertension: radiographic and scintigraphic patterns of histologic subtypes.

The chest radiograph and perfusion lung scans were evaluated in 39 consecutive patients with primary pulmonary hypertension to see if these noninvasive methods could distinguish among the histologic subtypes. Chest radiographs were categorized as having either normal lung fields or increased bronchovascular markings. Blood flow on lung scans was graded as normal or as having diffuse, nonsegmental, patchy abnormalities. These patterns were then correlated against pathologic specimens obtained from 19 patients, which were graded on vascular changes and microthrombi. Plexogenic arteriopathy was characterized by a normal chest radiograph and normal distribution of tracer on lung scan. Thromboembolism was characterized by a normal chest radiograph but patchy distribution of tracer on lung scan. Pulmonary veno-occlusive disease was characterized by increased bronchovascular markings on chest radiograph as well as patchy distribution of tracer on lung scan. Distinguishing patients on the basis of their histologic characteristics may be important so that vasodilators or anticoagulants can be selected as therapy.

Adult↗

PubMed1991

Nonparametric analysis of covariance for comparing change in randomized studies with baseline values subject to error.

Change from baseline to a follow-up examination can be compared among two or more randomly assigned treatment groups by using analysis of variance on the change scores. However, a generally more sensitive (powerful) test can be performed using analysis of covariance (ANOVA) on the follow-up data with the baseline data as a covariate. This approach is not without potential problems, though. The assumption of ordinary ANCOVA of normally distributed errors is speculative for many variables employed in biomedical research. Furthermore, the baseline values are inevitably random variables and often are measured with error. This report investigates, in this situation, the validity and relative power of the ordinary ANCOVA test and two asymptotically distribution-free alternative tests, one based on the rank transformation and the other based on the normal scores transformation. The procedures are illustrated with data from a clinical trial. Normal and several nonnormal distributions, as well as varying degree of variable error, are studied by Monte Carlo methods. The normal scores test is generally recommended for statistical practice.

Analysis of Variance↗

PubMed2006

Imputation strategies for blood pressure data nonignorably missing due to medication use.

BACKGROUND: Underlying or untreated blood pressure (BP) is often an outcome of interest, but is unobservable when study participants are on anti-hypertensive medications. Untreated levels are not missing at random but would be higher among those on such medication. In such cases, standard methods of analysis may lead to bias. PURPOSE: BPs obtained at the private physician's office (out-of-study BPs) at the time of prescription of anti-hypertensive medications were available from Phase II of the Trials of Hypertension Prevention (TOHP) and were used to adjust for the potential bias. METHODS: Observed out-of-study BPs were used to estimate the conditional expectation and variance of the unobserved unmedicated study BPs. For those with no physician data, imputation from bootstrap samples of out-of-study BPs was used. An iterative method based on the EM algorithm was used to estimate the unknown study parameters in a random-effects model using multiple imputations. This was compared to an alternative model for the out-of-study BPs based on a theoretical truncated normal distribution, and to standard analyses, including both multivariate repeated measures and last-observation-carried-forward (LOCF) analyses, using data from Phase II of TOHP. RESULTS: Differences between methods were seen in the decline in BP over time in the reference group, where the changes from baseline to 36 months were 3.0 in univariate analyses, 2.4 using LOCF, and 2.6 in the multivariate analysis, compared to 2.0 or 1.7 in the imputation analyses, depending on the number of physician visits. Estimated intervention effects tended to be slightly larger using the imputation methods. LIMITATIONS: out-of-study measures may not be available for other studies. CONCLUSIONS: Because the proposed strategy was based on an empirically observed distribution for out-of-study BP, fewer assumptions about the missing data were made. These data may be useful in suggesting imputation strategies for other studies.

Blood Pressure↗

PubMed2006

Decision making under uncertainty in case of soil remediation.

Decisions on soil remediation are one of the most difficult management issues of municipal and state agencies. The assessment of contamination is uncertain, the costs of remediation are high, and the impacts on the environment are multiple. This paper presents a general, transparent, and consistent method for decision making among the remediation alternatives. Soil washing, phytoremediation, and no remediation are exemplarily considered. Multi-criteria utility functions including (a) the cost of remediation (b) the impact on human health and agricultural productivity, and (c) the economic gain after remediation are constructed using probability density functions representing contamination for all site coordinates. Herewith, the probability of different types of (i) correct decisions such as a hit or a true rejection and (ii) erroneous decisions such as a false alarm or miss are examined. The decision theoretic model is applied to a case study on heavy metal contaminated soil. This case study reveals the non-linear structure of multi-criteria-decision making. The case study shows that the geostatistical uncertainties of the log-normal distributed soil contamination must be taken into account: When uncertainties are not considered and the utilities are assessed according to the estimated value for a spatial unit, only few (N=26) spatial units result where the utility score of the alternative soil washing are higher than the utility score to the no remediation alternative. However, when taking into account geostatistical uncertainties of the log-normal soil distribution this number is about ten times greater (N=237). Furthermore, the use of 'maximizing expected utility' as decision rule is critical in that it may lead to a high probability of misses.

Cadmium↗

PubMed1991

[Variability of percentile values of body measurements of newborn infants (with special reference to body weight)].

The percentile curves for fetal growth between the 25th and 42nd week of gestation calculated for more than 52,000 newborns in East Germany in 1985 were compared with the rates defined for the same population in 1973-74 and showed a significantly lower mean birth weight. Besides methodological differences (primarily a more precise estimation of gestational age in the new study by using ultrasound fetometry), the differences seem to be mainly the result of changes in the reproductive behaviour of the population over that period (decrease in parity). When comparing different populations independently of ethnic specificities, a number of modifying factors have to be taken into account which significantly influence the birth weight, namely: parity, spacing, age and stature of the mother. These variables have also to be remembered when assessing the maturity of newborns in order to standardize the birth weight in relation to mortality and morbidity. As a basis for calculating percentile curves the cumulative frequency distribution should be preferred, rather than assuming a normal distribution, since fetal diseases or developmental anomalies result in an uneven distribution with an over-representation of small for date fetuses. The selection of data for calculating normal values must be rejected because of the arbitrary decisions which this entails.

Anthropometry↗

PubMed2001

Characterization of the expression ratio noise structure in high-density oligonucleotide arrays.

BACKGROUND: High-density oligonucleotide microarrays provide a powerful tool for assessing differential mRNA expression levels. Characterizing the noise resulting from the enzymatic and hybridization steps, called type I noise, is essential for attributing significance measures to the differential expression scores. We introduce scoring functions for expression ratios, and associated quality measures. Both the PM (Perfect Match) probes and PM-MM differentials (MM is the single MisMatch) are considered as raw intensities. We then characterize the log-ratio noise structure using robust estimates of their intensity dependent variance. RESULTS: We show the relationships between the obtained ratios and their quality measures. The complementarity of PM and PM-MM methods is emphasized by the probe sets signal to noise measures. Using a large set of replicate experiments, we demonstrate that the noise structure in the log-ratios very closely follows a local log-normal distribution for both the PM and PM-MM cases. Therefore, significance relative to the type I noise can be quantified reliably using the local STD. We discuss the intensity dependence of the STD and show that ratio scores >1.25 are significant in the mid- to high-intensity range. CONCLUSIONS: The ratio noise structure inherent to high-density oligonucleotide arrays can be well described in terms of local log-normal ratio distributions with characteristic intensity dependence. Therefore, robust estimates of the local STD of these distributions provide a simple and powerful way for assessing significance (relative to type I noise) in differential gene expression. This approach will be helpful for improving the reliability of predictions from hybridization experiments in general.

DNA Probes↗

PubMed2003

Two bivariate geometrically defined reference regions with applications to male reproductive hormones and human growth.

Two conceptually simple two-dimensional reference charts are described. The charts are characterized analytically, but also by geometric properties that are easily communicated to subject-matter researchers--the users of such charts. For both charts, the proposed estimators are non-parametric, so no distributional assumptions are needed about the two-dimensional response. An important example that will serve to motivate and illustrate one of the charts is the study of the human reproductive hormones Inhibin B and FSH. A low Inhibin B concentration combined with a high FSH concentration is an indication that something may be wrong in the seminal cells which produce semen, and such measurements help in the process of distinguishing between different reasons for infertility. The aim in the study of the human reproductive hormones was to give a two-dimensional reference curve for the non-normally distributed hormone measurements while taking into account that some measurements were left-censored because of a detection limit in the assay used to measure the concentrations.

Adolescent↗

PubMed1991

Using a microcomputer to convert percent response values to probits.

Certain relationships between dose/concentration and percent response/binding in various biochemical systems are sigmoidal rather than linear. This sigmoid relationship is considered linear only over the 20-80 percent range. Appropriate analysis of such data over nearly the entire response/binding range requires the conversion of the percent response data to probits or probability units, producing a linear relationship. While tables of probits are available, the author has incorporated the probability function for probit conversion into a commercially available spreadsheet program. Also included is the Rohlf and Sokal approximation for the area under the normal distribution curve (conversion of probits to cumulative percent). These functions allow use of a spreadsheet to automate the creation of dose-response curves, or standard curves as part of chemical assays (i.e., radioimmunoassay).

Dose-Response Relationship, Drug↗

PubMed1991

Familial amyotrophic lateral sclerosis, 1850-1989: a statistical analysis of the world literature.

We present clinical and pathologic data on four previously unreported familial ALS pedigrees and review and analyze by descriptive and exploratory statistical techniques all published cases of familial ALS (1850-1989). In contrast to the age-dependent incidence of sporadic ALS, the age of onset of familial ALS is normally distributed about a mean of 45.7 years (std. dev. 11.3 years). Survival curves for the familial ALS data also demonstrate a skewed distribution with a median survival time of 24 months with 74% surviving at 12 months, 48% at 24 months and 23% surviving at 60 months. The patient characteristics of age at onset of disease, sex and focus of disease onset are unrelated variables and age at onset of disease is the only predictor of survival (Cox's proportional hazard model, chi-square 14.74, p = 0.0001). By applying accelerated failure time models with a log-normal baseline distribution, estimated probabilities for survival adjusted by age at onset were calculated. It was found that the older the age at disease onset, the shorter the survival.

Adult↗

PubMedDate not supplied

Descriptive statistics, Part II: Most commonly used descriptive statistics.

Descriptive measures can reveal a great deal of information about any variable of interest, whether the data be clinical, administrative, educational, or research data. To make best use of a descriptive statistic, it is important to know what levels of measurement should be used with the statistic, and what information the statistic can provide. To find out about the most typical case, measures of central tendency are appropriate. To discover whether the variable has a normal distribution, measures of shape should be applied. And to discover the variability about the mean of the variable, measures of dispersion should be used. Finally, percentiles and quartiles are useful for describing the placement of a single case in a population.

Analysis of Variance↗

PubMed2004

Impact of noise on retinal coding of visual signals.

Neural noise introduces uncertainty about the signals encoded in neural spike trains. Because of the uncertainty neurons can reliably transmit a limited amount of information. This amount is difficult to quantify for neurons that combine signals and noise in a complex manner, as many trials would be needed to estimate the joint probability distribution of stimulus and neural response accurately. The task is experimentally tractable, however, for neurons that combine signals with additive Gaussian noise. For such neurons, the joint probability distribution is well defined and information transmission rates can be computed from estimates of signal-to-noise ratio. Here we use power spectral analysis to specify the contributions of signal and noise to retinal coding of visual information. We show that in the spike trains of cat ganglion cells noise power is minimal and constant at temporal frequencies from 0.3 to 20 Hz and that it increases at higher frequencies to a plateau level that generally depends on stimulus contrast. We also show that trial-to-trial fluctuations in noise amplitude at different frequencies are uncorrelated and normally distributed. Although the contrast dependence indicates that noise at high temporal frequencies contributes nonlinearly to ganglion cell spike trains, cells in the primary visual cortex are not known to respond to stimulus modulations >20 Hz. Hence, noise in the retinal output would appear additive, white, and Gaussian from their perspective. This greatly simplifies analysis of information transmission from the eye to the primary visual cortex and perhaps other regions of the brain.

Action Potentials↗

PubMed1995

Linear rank tests for doubly censored data.

This paper establishes the asymptotic properties of the non-parametric maximum likelihood estimator of the survival function based on data censored both from the left and the right. We show that the sample mean based on the survival estimator converges to a normal distribution, and we derive non-parametric tests for the differences in survival functions. The methods are applied to a study of dementia associated with Parkinson's disease.

Adult↗

PubMed1999

Group sequential designs for phase II trials with historical controls.

Two-step tests based on historical control data are proposed for detecting different means when experimental and control populations are normally distributed with possibly different known variances. The results readily extend to the case where the control and experimental data are dichotomous. Provisions for early acceptance and early rejection are included.

Analysis of Variance↗

PubMed1990

Potential prenatal predictions of Down syndrome: a statistical analysis.

To determine the feasibility of combining several screening tests for the prenatal detection of Down syndrome, we evaluated the potential relationship among three proposed predictors. We determined the concentration of chorionic gonadotropin in frozen serum samples from women of known maternal age and weight, fetal biparietal diameter, and femur length, and alpha-fetoprotein concentration. When corrected for gestational age and maternal weight, the potential predictors were independent, except for a slight correlation (r = 0.10) between maternal serum alpha-fetoprotein and maternal serum human chorionic gonadotropin. Both maternal serum human chorionic gonadotropin and biparietal diameter/femur length demonstrated an approximately log-normal distribution similar to maternal serum alpha-fetoprotein. Therefore it is scientifically sound to use any or all of these variables in combination for the identification of pregnancies at increased risk for Down syndrome.

Body Weight↗

PubMedDate not supplied

Variation in semen parameters derived from computer-aided semen analysis, within donors and between donors.

The development of computer-aided semen analysis (CASA) has made it possible to study sperm motility characteristics objectively and longitudinally. In this 2-year study of 8 sperm donors, we used CASA to measure 7 semen parameters (concentration, percentage of motile spermatozoa, curvilinear velocity, average path velocity, straight-line velocity, amplitude of lateral head displacement, and beat/cross frequency). The frequency distributions of the 7 parameters in the semen samples of each donor were investigated. All parameters but one were normally distributed; concentration was distributed log-normally. Variation within individual donors and between donors was studied. Analysis of variance demonstrated that variation between donors was not explained by the longitudinal variation within individual donors. Variations in motility characteristics between donors were substantial, which may make motility characteristics of limited value as a tool for establishing fertility. Strong correlations were found between the 7 parameters, partly because by definition, motility characteristics are interdependent. Fisher's discriminant analysis demonstrated that each donor appeared to have his own set of semen characteristics and, more specifically, his own motility signature. From this data set it can be predicted that in order to find population means among sperm, it may be more efficient to measure more subjects than to increase the number of samples per subject.

Humans↗

PubMed1998

The female/male ratio of anthropometric dimensions.

A great many anthropometric studies contain the data of either males or females. Instead of presenting single-sex data, this study presents a method of using the female/male (F/M) ratio to estimate the dimensions of unknown body parts. Several studies that include the data for both sexes are used to develop the ratio. Statistical analysis is performed, including fitting to normal distribution. Stature, sitting shoulder height, shoulder breadth, and hip breadth are used in the study. The result of the analysis reveals the importance of using a different F/M ratio for each body part instead of adopting a single value for estimation.

Africa↗

PubMed2003

Bayesian techniques for sample size determination in clinical trials: a short review.

The aim of this paper is to review some key techniques of Bayesian methods of sample size determination. The approach is to cover a small number of simple problems, such as estimating the mean of a normal distribution. The methods considered are in two groups: inferential and decision theoretic. In the inferential Bayesian methods of sample size determination, we are solely concerned with the inference about the parameter(s) of interest. The fully Bayesian or decision theoretic approach treats the problem as a decision problem and employs a loss or utility function.

Bayes Theorem↗