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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↗

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↗

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↗

PubMed1999

[Clinical reference values for laboratory hematology tests calculated using the iterative truncation method with correction: Part 2, Reference values for white blood cell (WBC) count, WBC differential including segmented neutrophil, band neutrophil, lymphocyte, monocyte, eosinophil, basophil, platelet count and mean platelet volume].

Age and sex dependent differences in the clinical reference values for white blood cell(WBC) count, WBC differential including segmented neutrophils(SEG), band neutrophils(BAND), lymphocytes (LYMPH), monocytes(MONO), eosinophils(EOSINO), basophils(BASO), platelet count(PLT) and mean platelet volume(MPV) were calculated by the iterative truncation method with correction(Usui's method) using the result from tests on 6,300 patient specimens obtained at Kyoto University Hospital. WBC counts exhibited log-normal distribution in all age either in male and female. PLT counts and MPV showed normal or log-normal distribution. WBC differential (SEG, BAND, LYMPH, MONO, EOSINO, BASO) usually showed log-normal distribution. As to the reference value for WBC, high limit values gradually decreased in the age range of 5-14 year old in males and females. After 15 year old, it gradually increased and reached adult's level. Low limit values for WBC gradually decreased with age both in males and females. The reference value for SEG showed similar change to WBC. The reference value for LYMPH gradually decreased age both in males and females. The reference values for BAND, MONO, EOSINO, BASO were generated by the percentile method instead of the iterative truncation method because of the strong deviation in the distribution pattern. BAND, MONO and BASO values were very stable for all ages in males and females. High limit values for EOSINO in the age range of 5-10 year old in males and females remained constant, and gradually decreased in 10-20 year old, and were stable at ages above 20 year old. PLT counts gradually decreased with age, and the MPV remained constant in all age populations both in male and female.

Adolescent↗

PubMed1996

Haemoglobin and ferritin concentrations in infants at 8 months of age.

AIM: To identify the optimum age to screen for iron deficiency, the normal distribution of haemoglobin and ferritin in a representative population sample was investigated. METHODS: Normal values for haemoglobin and ferritin were measured from heel prick capillary samples obtained from a representative cohort of 1175 infants at 8 months old who were randomly selected from children taking part in the Avon Longitudinal Study of Pregnancy and Childhood (ALSPAC). RESULTS: Haemoglobin was normally distributed: mean (SD) 117 (11) milligrams, 95% confidence interval (CI) 116 to 118, and range 72-153 milligrams. Ferritin was log normally distributed: geometric mean 38.5 micrograms/l, 95% CI 37.0 to 39.9, range 7.1-224 micrograms/l. The 5th centile for haemoglobin was 97 milligrams and for ferritin 16.9 micrograms/l. No correlation was found between haemoglobin and ferritin. Multiple regression analysis showed ferritin concentrations to be positively related to birth weight (p < 0.0001) and the sex of the child (girls with higher concentrations) (p < 0.0001) but negatively with the child's weight at 8 months (p < 0.0001). Haemoglobin concentrations were positively related to the child's weight at 8 months (p = 0.04). Neither haemoglobin nor ferritin concentrations were related to social class as measured by maternal education level. CONCLUSION: These data define the normal range for haemoglobin and ferritin in capillary samples in the UK population, and suggest that anaemia is common in infancy. Using current recommendations, 23% of infants would be identified as anaemic. For British infants at 8 months of age, a more representative 'cut off' for anaemia would be haemoglobin concentration < 97 milligrams and for iron deficiency ferritin < 16 micrograms/l.

Age Factors↗

PubMed1995

Analysis of tomato root initiation using a normal mixture distribution.

We attempt to identify the number of underlying physical phenomena behind tomato lateral root initiation by using a normal mixture distribution coupled with the Box-Cox power transformation. An initial analysis of the data suggested the possibility of two (possibly more) subpopulations, but upon taking reciprocals, the data appear to be very nearly Gaussian. A simulation study explores the possibility of erroneously detecting a second subpopulation by fitting data which are improperly scaled. A power calculation suggests that only unrealistically large sample sizes can detect the unbalanced mixtures one might expect with data of this type.

Biometry↗

PubMed1990

Fibronectin distribution in normal and malignant urothelium.

Fibronectin is a glycoprotein that mediates the attachment of BCG to the murine bladder. To assess the potential role of fibronectin on bladder cancer cells as a specific substrate for BCG binding in man, a semi-quantitative method was employed to evaluate the presence of fibronectin on normal urothelium and bladder cancer. Monoclonal anti-fibronectin binding to normal and malignant urothelial tissues was evaluated by an immunoperoxidase assay. Human tumor cell lines were evaluated with mixed hemadsorption and immunoperoxidase assays. In both systems, immunoreactive fibronectin had low expression on unfixed normal and malignant urothelium. With fixation, immunoreactive fibronectin decreased on supporting stroma and increased in normal and malignant urothelium. Fibronectin distribution did not show tumor specificity either with fixed or unfixed specimens.

BCG Vaccine↗

PubMed1991

Development of pragmatic exposure-control concentrations based on packaging regulation risk phrases.

This paper relates United Kingdom and other national Occupational Exposure Limits (OELs) for volatile organic substances to the Risk Phrases (RPs) which they are assigned under EEC Classification, Packaging and Labelling Directives. The OELs for organic volatiles assigned RP 20 ('harmful by inhalation'), RP 23 ('toxic by inhalation') and RP 26 ('very toxic by inhalation') fitted better to the cumulative log-normal distribution than to the cumulative normal distribution and the means for RPs 23 and 26 were not significantly different. The means for RP 20 and RP 23/26 were 100 mg m-3 (or 25 ppm) and 5 mg m-3 (or 1 ppm), respectively. In the absence of any relevant, specific information, it is suggested that these values may be useful as guidelines for pragmatic exposure-control concentrations (PECCs) for the control of exposure by inhalation in workplaces handling substances labelled with these RPs.

Environmental Exposure↗

PubMed1988

Doppler ultrasound waveform indices: A/B ratio, pulsatility index and Pourcelot ratio.

Three different indices, the A/B ratio, the pulsatility index (PI) and the Pourcelot ratio (PR), are in common use for quantitative analysis of umbilical artery Doppler ultrasound waveforms. A detailed examination of the similarities and differences between these indices, together with the expected errors for each, was undertaken to enable informed comparisons and choices to be made. The indices were calculated from 133 last trimester recordings using an objective and very reliable computer analysis technique. The PI is more difficult to calculate than the other two quantities and the extra computation does not provide any extra information. The A/B ratio appears the simplest index to use but the values are not normally distributed. With the PR a normal distribution of values can be assumed. A theoretical consideration of errors showed that none of the indices is intrinsically less error prone for last trimester waveforms overall. The errors in the A/B ratio increase as the value of the index increase, whereas the converse holds for the PI and PR.

Blood Flow Velocity↗

PubMed1978

Comparison of kinetic and end-point diffusion methods for quantitating human serum immunoglobulins.

Proficiency testing results were used to compare the kinetic and end-point versions of the single radial immunodiffusion method for quantitating human serum immunoglobulins. Statistical analysis of the results indicated that the results were not normally distributed but that the log normal distribution gives the best fit of any of the well-known frequency distributions. Consequently, statistical analysis of immunoglobulin results must be log transformed before parametric statistical tests can be appropriately applied. In general, there were no significant differences in level, precision, or interlaboratory comparability for these two methods. However, levels were different for participants using Hyland reagents, and better interlaboratory comparability was achieved by the end-point assay for immunoglobulin M. There were no significant differences in reported levels when compared by manufacturer within the same method.

Humans↗

PubMed1996

Measurement of beta 2-microglobulin in bovine serum and urine by radioimmunoassay.

A radioimmunoassay (RIA) system for quantification of bovine beta 2-microglobulin (beta 2-M) in serum and urine was developed. The protein isolated from bovine colostrum showed a single band in SDS-PAGE, and its molecular weight was approximately 11,600. Amino acid sequences for the first 24 residues and the amino acid composition of the protein were in agreement with those in the bovine beta 2-M of previous research works. In an Ouchterlony test, a single precipitation line was formed between the protein and the antiserum made by the protein. From these results, it was confirmed that the protein isolated from the colostrum was pure bovine beta 2-M. For creation of an RIA calibration curve for urine, a urine void of beta 2-M, as much as possible (beta 2-M-free urine), and a PBS were used as diluents. Intraassay (n = 10) and interassay (n = 3) variances were 1.7-4.6% and 7.1-11.5% in the PBS dilute method, and were 1.4-5.1% and 12.3-13.5% in the beta 2-M-free urine dilute method, respectively. Mean recoveries were 160 +/- 19% (mean +/- SD) and 98.4 +/- 7.9% in PBS and beta-M-free urine, respectively. It was found that the method using the beta 2-M-free urine as a diluent was more accurate than using PBS. The beta 2-M concentrations in serum and urine of healthy Holstein cows measured by this RIA system showed a logarithmic normal distribution for urine and a normal distribution for serum. The mean beta 2-M concentrations were 0.0305(+0.04443)(-0.0210) mg/l (Geometric mean +/- S.D., n = 43) in urine and 2.87 +/- 0.45 mg/l (Arithmetic mean +/- S.D., n = 26) in sera. Further, we could not observe the particular tendency of daily variation in urinary beta 2-M concentrations of healthy cows (Holstein, n = 3 x 2 days).

Amino Acid Sequence↗

PubMed1996

[Normal values of calcium and oxalate excretion in children].

Aim of the study was to establish normal values for calcium/creatinine (Ca/cr) and oxalate/creatinine (Ox/cr) ratio in infants and children. Urine probes of 416 healthy children (25 infants aged 1-7 days and 391 children aged 1 month-14.5 years) were analysed. Oxalate was measured by ion-chromatography. Urinary Ca2+/cr was normally distributed, Ox/cr had log-normal distribution. Ca/cr was the lowest in the first days of life, the highest between 7 month-1.5 years (mean +/- SD = 0.39 +/- 0.28 mmol/mmol), a slight decrease could be observed until 14 years (0.34 +/- 0.18). The highest Ox/cr values were measured during the first month of life (geometric mean/range/ = 133 /61-280 mmol/mmol/), followed by gradual decrease until 14 years (25/6-73/). The measurement of Ca2+/cr and Ox/cr in first morning urine samples is suitable for screening of hypercalciuria and hyperoxaluria. The interpretation of the values requires age specific reference values. Both calcium and oxalate determinations should be the part of the evaluation of patients with hematuria, hypercalciuria or nephrolithiasis.

Adolescent↗