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Use of overlapping normal distributions in genetic counselling.

If a numerical variable can be assumed to be normally, but differently, distributed in each of two or more populations, then for an 'unknown' individual whose numerical value is known the relative probability of his belonging to each of the populations can be simply calculated. We briefly review the method and its application in genetic counselling.

Genes↗

Regional cerebral blood flow as assessed by principal component analysis and (99m)Tc-HMPAO SPET in healthy subjects at rest: normal distribution and effect of age and gender.

The increasing implementation of standardisation techniques in brain research and clinical diagnosis has highlighted the importance of reliable baseline data from normal control subjects for inter-subject analysis. In this context, knowledge of the regional cerebral blood flow (rCBF) distribution in normal ageing is a factor of the utmost importance. In the present study, rCBF was investigated in 50 healthy volunteers (25 men, 25 women), aged 31-78 years, who were examined at rest by means of single-photon emission tomography (SPET) using technetium-99m d, l-hexamethylpropylene amine oxime (HMPAO). After normalising the CBF data, 27 left and 27 right volumes of interest (VOIs) were selected and automatically outlined by standardisation software (computerised brain atlas). The heavy load of flow data thus obtained was reduced in number and grouped in factors by means of principal component analysis (PCA). PCA extracted 12 components explaining 81% of the variance and including the vast majority of cortical and subcortical regions. Analysis of variance and regression analyses were performed for rCBF, age and gender before PCA was applied and subsequently for each single extracted factor. There was a significantly higher CBF on the right side than on the left side ( P<0.001). In the overall analysis, a significant decrease was found in CBF ( P=0.05) with increasing age, and this decrease was particularly evident in the left hemisphere ( P=0.006). When gender was specifically analysed, CBF was found to decrease significantly with increasing age in females ( P=0.037) but not in males. Furthermore, a significant decrease in rCBF with increasing age was found in the brain vertex ( P=0.05), left frontotemporal cortex ( P=0.012) and temporocingulate cortex ( P=0.003). By contrast, relative rCBF in central structures increased with age ( P=0.001). The ability of standardisation software and PCA to identify functionally connected brain regions might contribute to a better understanding of the relationships between rCBF at rest, anatomically defined brain structures, ageing and gender.

Adult↗

Normal distribution of melanocytes in the mouse heart.

We report the consistent distribution of a population of pigmented trp-1-positive cells in several important septal and valvular structures of the normal mouse (C57BL/6) heart. The pigmented cell population was first apparent by E16.5 p.c. in the right atrial wall and extended into the atrium along the interatrial septum. By E17.5, these cells were found along the apical membranous interventricular septum near or below the surface of the endocardium. The most striking distribution of dark pigmented cells was found in the tricuspid and mitral valvular leaflets and chordae tendineae. The normal distribution of pigmented cells in the valvuloseptal apparatus of C57BL/6 adult heart suggests that a premelanocytic lineage may participate in the earlier morphogenesis of the valve leaflets and chordae tendineae. The origin of the premelanocyte lineage is currently unknown. The most likely candidate populations include the neural crest and the epicardially derived cells. The only cell type in the heart previously shown to form melanocytes is the neural crest. The presence of neural crest cells, but not melanocytes, in some of the regions we describe has been reported by others. However, previous reports have not shown a contribution of melanocytes or neural crest derivatives to the atrioventricular valve leaflets or chordae tendineae in mouse hearts. If these cells are of neural crest origin, it would suggest a possibly greater contribution and persistence of neural crest cells to the valvuloseptal apparatus than has been previously understood.

Animals↗

A completion simulator for the two-sided truncated normal distribution.

This paper presents simulation formulae of two-sided truncated normal random variables using a completion distribution and its two corresponding conditionals generated via a Gibbs sampler. This procedure extends formulae given by Robert and Casella for the one-sided case.

Journal Article↗

A comparison of methods of normalizing a discrete distribution.

Normal distributions are the foundation of modern statistical procedures, which differ in their sensitivity to violation of the assumption of normality. This paper reports on the effectiveness of two different methods of normalizing distributions of discrete test score data. The scores of 971 Ontario high school students on the 22 scales of PRF-E (Jackson, 1974) were normalized using two variants of the cumulative proportions method and by a rank method. Neither cumulative procedure appreciably altered the modality or skewness of the distributions. The rank method succeeded in normalizing all the distributions, except for an occasional case of platykurtosis. It was concluded that normalization by ranks is to be preferred over cumulative methods for use in situations in which a statistical procedure is sensitive to violations of normality.

Adolescent↗

Plasma glycoprotein V levels in the general population: normal distribution, associated parameters and implications for clinical studies.

Soluble glycoprotein V (sGPV) is a new plasma marker of thrombosis released from the platelet surface by thrombin. sGPV levels are increased in patients with atherothrombotic diseases, but the determinants of sGPV levels are unknown in the general population. Identification of these potential confounding factors is needed for correct design and analysis of clinical studies on cardiovascular diseases. The aim of this study was to determine the normal range of plasma values and the factors controlling sGPV levels in a population of normal individuals. Three hundred blood donors were recruited at the Etablissement Français du Sang-Alsace for the measurement of plasma levels of sGPV, platelet factor 4 (PF4), thrombin-antithrombin complexes (TAT) and D-dimers. The plasma level of sGPV was (median [interquartile range]) 27.5 [23.5-34.4] microg/l and displayed a Gaussian distribution. sGPV had a lower interindividual coefficient of variation (33%) than PF4 (176%), TAT (87%) or D-dimers (82%). sGPV levels were independent of age and sex but sensitive to red cell (r = 0.412; p < 0.0001) and platelet counts (r = 0.267; p = 0.001), total cholesterol (r = -0.313; p < 0.0001), food intake (r = 0.184; p = 0.0014) and smoking (r = -0.154; p = 0.039). Contrary to PF4 and TAT, sGPV did not differ between venous and arterial blood samples of 12 healthy individuals. Red cell and platelet counts, total cholesterol, current smoking and recent food intake are important determinants of sGPV levels and must be taken into account in clinical studies using sGPV as a thrombosis marker. Normal distribution of sGPV levels in the general population supports its use in clinical applications.

Adult↗