Method for decreasing the statistical variance of stereological estimates

Three methods are described for decreasing the statistical variance of stereological estimates. Methods 1 uses profile boundaries and surface densities of nuclear membranes, measured in thin sections, to estimate the mean diameter, surface area, and numerical density of spherical and nonspherical nuclei. For the guinea pig pancreas (number(m) = 4), the standard deviations (s.d.) as a percent of the mean for the estimates of the diameters of the exocrine, duct, and endothelial cell nuclei were 1.5%, 3.3% and 1.4%. The estimate for the mean diameter of exocrine nuclei (6.4 ± 0.1 μm) was based on a spherical model, whereas the estimates for the diameters of the nonspherical (and nonconvex) nuclei of the duct (6.4 ± 0.2 μm) and endothelial (6.7 ± 0.1 μm) cells were calculated from the numerical density of the exocrine cells and the relative frequenceis of the three cell types (determined from serial reconstructions). In an average cubic centimeter, there were 6.17 × 10⁸ ± 0.32 × 10⁸ (s.d. 5.1% of mean) exocrine cells, 1.64 × 10⁸ ± 0.18 × 10⁸ (10.9%) duct cells, and 0.803 × 10⁸ ± 0.13 × 10⁸ (16.6%) endothelial cells. In contrast to method 1, conventional stereological approaches were found to have standard deviations two-to eightfold larger. Method 2 uses a mean nuclear surface area and a ratio of surface densities to estimate the surface area of a membrane compartment in an average cell. A s.d. equal to 6.5% of the mean was found for the surface are of the outer mitochondrial membrane in an average exocrine cell (672 ± 43.6 μm²), which represented an almost fourfold reduction in the s.d. compared with an earlier estimate (Bolender, 1974). Method 3 relates the surface area of a membrane compartment to a standard number of cells. Referenced to 10⁶ cells, for example, the surface area of the inner nuclear membrane of endothelial cells had a s.d. equal to 2.9% of the mean, whereas the surface density of the same membrane compartment—referenced to a cm³ to cells—had a s.d. at 19.1% of the mean. In this case, method 3 produced almost a sevenfold reduction in the standard deviation. Similar results were found for exocrine and duct cells. The results of the study indicate that the standard deviation of a stereological estimate can be reduced to a miniumum by using a mean nuclear profile boundary to generate an estimate for a nuclear numerical density, which, in turn, can be combined with a surface density to obtain average cell information.     

An EM algorithm for obtaining maximum likelihood estimates in the multi-phenotype variance components linkage model

In recent years variance components models have been developed for localising genes that contribute to human quantitative variation. In typical applications one assumes a multivariate normal model for phenotypes and estimates model parameters by maximum likelihood. For the joint analysis of several correlated phenotypes, however, finding the maximum likelihood estimates for an appropriate multivariate normal model can be a difficult computational task due to complex constraints among the model parameters. We propose an algorithm for computing maximum likelihood estimates in a multi-phenotype variance components linkage model that readily accommodates these parameter constraints. Data simulated for Genetic Analysis Workshop 10 are used to demonstrate the potential increase in power to detect linkage that can be obtained if correlated phenotypes are analysed jointly rather than individually.     

A comparison between stereological estimates of mean nuclear volume and DNA flow cytometry in bladder tumours

The correlation between stereological estimate of mean nuclear volume and DNA-content was studied in 55 human urinary bladder tumours. The DNA-content was determined by flow cytometry on isolated nuclei stained with ethidium bromide. Trout erythrocytes were used as a biological internal standard providing an accurate determination of the DNA-histogram. An unbiased estimate of the mean nuclear volume (vv) was obtained after standard formaline fixation, paraffin-embedding, sectioning and hematoxylin-eosin staining using the equation vv = pi/3.l3(0). Here l0 is the length of an intercept measured in a random direction through a test point, which hit a nucleus. A highly significant correlation was found between vv and mean DNA-content of nuclei (2p = 0.0004). A highly significant correlation was also found between vv and the highest DNA-content present in tumours having cell populations with different DNA content (2p = 0.0016). The mean nuclear volume and the DNA-content also correlated well with the pathologic grade. Although significant the correlations were far from perfect, which indicates that DNA content and mean nuclear volume may provide partly independent biological information. The methods provide objective, unbiased and reproducible data which may improve the possibility of grading and predicting the disease course of human urinary bladder tumours.     

Use of cryostat sections from snap-frozen nervous tissue for combining stereological estimates with histological, cellular, or molecular analyses on adjacent sections

Adequate tissue preparation is essential for both modern stereological and immunohistochemical investigations. However, combining these methodologies in a single study presents a number of obstacles pertaining to optimal histological preparation. Tissue shrinkage and loss of nuclei/nucleoli from the unprotected section surfaces of unembedded tissue used for immunohistochemistry may be problematic with regard to adequate stereological design. In this study, frozen cryostat sections from hippocampal and cerebellar regions of two rat strains and cerebellar and cerebral regions from a human brain were analyzed to determine the potential impact of these factors on estimates of neuron number obtained using the optical disector. Neuronal nuclei and nucleoli were clearly present in thin sections of snap-frozen rat (3 microm) and human (6 microm) tissue, indicating that neuronal nuclei/nucleoli are not unavoidably lost from unprotected section surfaces of unembedded tissue. In order to quantify the potential impact of any nuclear loss, optical fractionator estimates of rat hippocampal pyramidal cells in areas CA1-3 and cerebellar granule and Purkinje cells were made using minimal (1 microm) upper guard zones. Estimates did not differ from data reported previously in the literature. This data indicates that cryostat sections of snap-frozen nervous tissue may successfully be used for estimating total neuronal numbers using optical disectors.     

New stereological method for obtaining unbiased and efficient estimates of total nerve cell number in human brain areas. Exemplified by the mediodorsal thalamic nucleus in schizophrenics

Using a new stereological technique, the total number of nerve and glia cells can be estimated in selected brain regions. The method is completely independent of precise knowledge of nerve cell size, section thickness and of dimensional changes in brain tissue induced by histological procedures. It therefore provides an unbiased estimate of total nerve cell number. As an example, the total neuron number from the mediodorsal nucleus of thalamus in brains from schizophrenic patients is compared to control cases. The total neuron number was reduced by 40% in the brains from chronic schizophrenic patients.     

Planimetric grids for macroscopic and microscopic stereological investigations

A type of grid for plamimetric investigations of macroscopic and microscopic objects with equidistant nodal points of zero thickness is suggested. The method of performing the stereological investigation is described. Formulas are suggested for determining the necessary number of counts of points in order to enable representative data to be obtained for the quota of a structural component in the specimen studied with 95% confidence limits. Formulas for calculating the bulk density of a structural formation in a macroscopic and microscopic object with calculation of statistical indices are given.Central Pathological-Anatomical Laboratory, Institute of Human Morphology, Academy of Medical Sciences of the USSR. Departments of Operative Surgery and Topographical Anatomy, M. Gor'kii Donetsk Medical Institute. (Presented by Academician of the Academy of Medical Sciences of the USSR A. P. Avtsyn.) Translated from Byulleten' Éksperimental'noi Biologii i Meditsiny, Vol. 83, No. 1, pp. 93–95, January, 1977.     

Analysis of variance is easily misapplied in the analysis of randomized trials: a critique and discussion of alternative statistical approaches

Analysis of variance (ANOVA) is a statistical method that is widely used in the psychosomatic literature to analyze the results of randomized trials, yet ANOVA does not provide an estimate for the difference between groups, the key variable of interest in a randomized trial. Although the use of ANOVA is frequently justified on the grounds that a trial incorporates more than two groups, the hypothesis tested by ANOVA for these trials--"Are all groups equivalent?"--is often scientifically uninteresting. Regression methods are not only applicable to trials with many groups, but can be designed to address specific questions arising from the study design. ANOVA is also frequently used for trials with repeated measures, but the consequent reporting of "group effects," "time effects," and "time-by-group interactions" is a distraction from statistics of clinical and scientific value. Given that ANOVA is easily misapplied in the analysis of randomized trials, alternative approaches such as regression methods should be considered in preference.     

A stereological study of the differentiation process inTrypanosoma cruzi

When epimastigote forms ofTrypanosoma cruzi grown in a rich medium (LIT) are transferred to a simple, chemically defined medium (TAU3AAG, containing Ca²⁺, Mg²⁺, K⁺, Na⁺,l-proline,l-glutamate, andl-aspartate in phosphate buffer, they transform into trypomastigote forms. Morphometric analysis of transmission electron micrographs of thin sections of parasites collected at different steps of the transformation process showed that no changes occurred in the volume density of mitochondria and cytoplasmic vacuoles. However, a significant increase in the volume density of the kinetoplast DNA network as well as the lipid inclusions and a decrease in that of the reservosome (a special type of endosome) was observed. These observations suggest that during differentiation,T. cruzi accumulates lipids and uses molecules contained in the reservosome as its main energy source.     

Estimation of the variance components for dermal ridge count

Refinements of the scoring algorithm to estimate variance components from pedigree data are developed. Subsequent to these modifications, heritability estimates were readily obtained from data for over 50 traits, including total finger ridge count reported here. A significant contribution to the total variance of ridge count could be attributed to the effects of dominance, a finding not previously reported for this dermatoglyphic trait.     

A stereological study of the human ovarian surface epithelium.

The surface of the ovary has been found to be composed of two types of epithelial cells called A and B cells which are found in their own respective zones, the A and B zones. A quantitative study was undertaken to determine the mean cell volumes and cell ultrastructure. Ovarian biopsies were taken from six women and A and B zones, having been identified by scanning electron microscopy, were re-embedded for transmission electron microscopy. Stereological measurements using point sampled intercepts were made on vertical sections and showed that B cells are significantly larger than A cells. The volume weighted mean cell volumes of the A and B cells were 237.3 microns 3 and 676.8 microns 3 respectively. The volume fractions of the nucleus and mitochondria were similar in the two cell types. Although the vesicle content of each type was similar, a large variation between cases made the interpretation difficult. The stereological tools used in this study proved to be easy and efficient estimators of surface cell ultrastructure and give an important direction for ultrastructural research.     

Admixture estimates for the population of Havana City

Background: The Cuban population is essentially a result of the admixture between Spanish, West African and, to a lesser degree, Amerindian tribes that inhabited the island.

Aim: The study analysed the genetic structure of the three principal ethnic groups from Havana City, and the contribution of parental populations to its genetic pool.

Subjects and methods: According to genealogical information and anthropological traits, 206 subjects were classified as Mulatto, of Spanish decent or of African descent. Seventeen Ancestry Informative Markers, with high difference in frequency between parental populations, were selected to estimate individual and group admixture proportions. The statistical analyses were performed using the ADMIX, ADMIX95 and STRUCTURE 2.1 packages.

Results: The results demonstrate a high level of European and African admixture in Mulattos (57–59% European; 41–43% West African). The European contribution was higher in those of Spanish descent (85%) while in those of African descent, the West African contribution ranged between 74% and 76%. Genetic structure was only detected in Mulattos and those of African descent. An Amerindian contribution was not detectable in the studied sample.

Conclusion: Our findings indicate the existence of admixture and genetic structure in the population of Havana City. This study represents one of the first steps towards understanding Cuban population admixture in order to produce successful experimental designs for admixture mapping.     

Methods of testing for a deficit in single-case studies: Evaluation of statistical power by Monte Carlo simulation

Testing for the presence of a deficit by comparing a case to controls is a fundamental feature of many neuropsychological single-case studies. Monte Carlo simulation was employed to study the statistical power of two competing approaches to this task. The power to detect a large deficit was low to moderate for a method proposed by Crawford and Howell (1998; ranging from 44% to 63%) but was extremely low for a method proposed by Mycroft, Mitchell, and Kay (2002; ranging from 1% to 13%). The effects of departures from normality were examined, as was the effect of varying degrees of measurement error in the scores of controls and the single case. Measurement error produced a moderate reduction in power when present in both controls and the case; the effect of differentially greater measurement error for the single case depended on the initial level of power. When Mycroft et al.'s method was used to test for the presence of a classical dissociation, it produced very high Type I error rates (ranging from 20.7% to 49.3%); in contrast, the rates for criteria proposed by Crawford and Garthwaite (2005b) were low (ranging from 1.3% to 6.7%). The broader implications of these results for single-case research are discussed.     

Methods of testing for a deficit in single-case studies: Evaluation of statistical power by Monte Carlo simulation

Testing for the presence of a deficit by comparing a case to controls is a fundamental feature of many neuropsychological single-case studies. Monte Carlo simulation was employed to study the statistical power of two competing approaches to this task. The power to detect a large deficit was low to moderate for a method proposed by Crawford and Howell (1998; ranging from 44% to 63%) but was extremely low for a method proposed by Mycroft, Mitchell, and Kay (2002; ranging from 1% to 13%). The effects of departures from normality were examined, as was the effect of varying degrees of measurement error in the scores of controls and the single case. Measurement error produced a moderate reduction in power when present in both controls and the case; the effect of differentially greater measurement error for the single case depended on the initial level of power. When Mycroft et al.'s method was used to test for the presence of a classical dissociation, it produced very high Type I error rates (ranging from 20.7% to 49.3%); in contrast, the rates for criteria proposed by Crawford and Garthwaite (2005b) were low (ranging from 1.3% to 6.7%). The broader implications of these results for single-case research are discussed.     

Ultrastructural stereological analysis of the lungs of monkeys with Ebola fever

Ebola virus replicates in mononuclear phagocytes, endotheliocytes, and, rarely, in bronchial epitheliocytes in the lungs of subcutaneously infected green monkeys, rhesus macaques,Papio hamadryas, andMacaca iris. Quantitative analysis demonstrates specific features in infection of different cells, depending on the disease duration and dose of infection. Translated from Byulleten’Eksperimental’noi Biologii i Meditsiny, Vol. 123, No. 2, pp. 205–208, February, 1997     

Components of variance

Components of variance have a long history and find application in all areas of scientific investigation. This review introduces components of variance and their importance firstly by examples on blood pressure, proteomic data, breath analysers and esophageal pH monitoring devices. We then present an intuitive geometric representation of analysis of variance and explain how the components of variance can be estimated from the analysis of variance table. We conclude by suggesting practice points for studies which incorporate components of variance, and recommend commonly used statistical software to undertake such analysis.