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PubMed1993

Comparison of two tests useful in situations where treatment is expected to increase variability relative to controls.

The type I error and power characteristics of the modified t test were compared with those of the generalized t test. Results suggested that, in contrast to the generalized t test, the modified t test can be seriously non-robust to departures from population normality, with such departures often producing anti-conservative results. Neither test held an absolute power advantage over the other when responses were from normal distributions, but the modified t test was generally more powerful for these conditions. In comparison with the pooled samples t test, both tests were usually much more efficient when treatment caused increases both in mean response and between-subject variance, and suffered only small disadvantages when between-subject variance was unchanged by treatment. Given these results and other considerations, recommendations for use of these recently devised tests are given.

Bias↗

PubMed1985

Characteristics of the optic disc cup.

The frequency distribution of the optic cup/optic disc ratio (CDR) and the optic cup depth (OCD) were investigated using clinical data. The mean CDR is 0.30 (SD = 0.13), and the mean OCD is 2.10 D (SD = 0.89 D). Seventy-four percent of 1352 eyes had a CDR of 0.3 or less, and 68% of 1168 eyes had an OCD of 2 D or less. The distribution of the CDR's differs from a normal distribution, but that of the OCD's is nearly normal.

Adolescent↗

PubMed1998

A comparison of Tc-99m HMPAO brain SPECT images of young and aged normal individuals.

The purpose of this study was to examine the normal distribution patterns of 99mTc-HMPAO (HMPAO) in young and aged normal individuals and to clarify differences between the distribution patterns of the two groups by means of an anatomical standardization technique. The tracer distribution was measured with HMPAO and SPECT in 18 normal subjects; age range 20-81 yrs. SPECT images were globally normalized by averaging whole brain radioactivity counts to 100 counts/voxel. The SPECT images for each subject were transformed into the standard brain anatomy by means of a computerized brain atlas, together with each subject's CT images. Mean and SD images for young (28.8 +/- 6.4 yrs) and aged groups (62.3 +/- 10.2 yrs) were then calculated on a voxel-by-voxel basis. Statistically significant differences between young and aged groups were observed in the relative tracer distribution patterns. In the aged group, relative decreases were found in the cortical areas of the frontal and temporal lobes, limbic areas and basal ganglia regions. The results, as visualized changes in tracer distribution patterns with aging, may contribute to more accurate clinical diagnosis.

Adult↗

PubMed2005

Sampling size in the verification of manufactured-supplied air kerma strengths.

Quality control mandate that the air kerma strengths (S(K)) of permanent seeds be verified, this is usually done by statistics inferred from 10% of the seeds. The goal of this paper is to proposed a new sampling method in which the number of seeds to be measured will be set beforehand according to an a priori statistical level of uncertainty. The results are based on the assumption that the S(K) has a normal distribution. To demonstrate this, the S(K) of each of the seeds measured was corrected to ensure that the average S(K) of its sample remained the same. In this process 2030 results were collected and analyzed using a normal plot. In our opinion, the number of seeds sampled should be determined beforehand according to an a priori level of statistical uncertainty.

Air↗

PubMed1991

Actual and predicted word-recognition performance of elderly hearing-impaired listeners.

Word-recognition scores in quiet and in noise were obtained from both ears of 101 elderly listeners demonstrating sensorineural hearing loss. These performance scores were compared to word-recognition scores predicted using Articulation Index analysis procedures. Negative difference scores (actual performance less predicted performance) would reflect aspects of the hearing impairment and/or the aging process that extend beyond the simple speech audibility constraints imposed by the hearing loss and masking noise. The distributions for both the left and right ears of difference scores in quiet revealed the majority of scores to be grouped near 0. In contrast, both distributions of difference scores in noise were normally distributed around means of approximately -25. These results suggest that the typical elderly hearing-impaired listener should be expected to demonstrate word-recognition performance in quiet similar to that of a normally hearing listener, given the same level of audibility of the speech material. On the other hand, in noise, this typical listener may be expected to demonstrate some word-recognition performance decrement, even after accounting for the audibility constraints of the hearing loss and noise.

Aged↗

PubMed1995

Binary regression with continuous outcomes.

Clinical research often involves continuous outcome measures, such as blood cholesterol, that are amenable to statistical techniques of analysis based on the mean, such as the t-test or multiple linear regression. Clinical interest, however, frequently focuses on the proportion of subjects who fall below or above a clinically relevant cut-off value, as a measure of the risk of disease. The customary approach to analyse such data is to dichotomize the continuous outcome measure and use statistical techniques based on binary data and the binomial distribution. In this paper, we use a parametric approach and the framework of generalized linear models to fit various regression models, including the logistic, on the basis of the original continuous outcome. We consider the Gaussian and the three-parameter log-normal distributions for the continuous outcome, assessing both precision and bias under various conditions. In simulation analyses, we find that we are unable to fit some of the samples with the 'dichotomous' approach, but we can with the 'continuous' approach, and that the latter yields estimates between 25 and 85 per cent more efficient than the former. We illustrate the method, programmed using GLIM macros, with data from clinical studies of the risk of hypoxaemia during open thoracic surgery and the risk of nocturnal hypoglycaemia among diabetic children.

Diabetes Mellitus, Type 1↗

PubMed1998

Analysis of intracellular Th1 cytokine secretion data using parametric methodology.

Flow cytometric methods are widely used for analyzing cytokine release from immune cell populations. However, difficulties are frequently encountered in the analysis of flow cytometric data from intracellular cytokine staining because the cytokine positive and cytokine negative histograms overlap considerably. This study compares models containing Gaussian, Giddings, Haarhoff-van der Linde (HVL) and Weibull distributions for fitting flow cytometric intracellular cytokine histogram peaks. The results show that flow cytometric data for the Th1 cytokines, interferon-gamma and interleukin-2, in peripheral blood are well described by a model consisting of the sum of two log-normal distributions but the other distributions tested also showed satisfactory fits. The model-based approach may potentially eliminate the need to use markers derived from isotype control staining. The results obtained using peak fitting were also compared to the widely practised 99% division line or marker method. The percent positive calculated using the 99% division line or marker methods correlates poorly with the percent area under the cytokine-positive peak. However, when the model is used to calculate a cytokine-positive percentage analogous to that determined by the 99% division line or marker method, the two methods correlate well.

Flow Cytometry↗

PubMed1993

Construction of age-related reference centiles using absolute residuals.

This paper proposes a simple approach to the parametric derivation of age-related reference ranges which avoids the creation of arbitrary age groups, copes easily with a non-linear relation between variability and age, and is computationally simple. After the mean is modelled as a function of age, the age-specific standard deviation is estimated by regressing the absolute residuals on age. The method assumes that the data are, or can be transformed to be, normal at each age, and uses the properties of the half normal distribution. An example is given using 450 measurements of fetal foot length.

Age Factors↗

PubMed1992

Urinary and blood manganese in occupationally nonexposed populations and in manual metal arc welders of mild steel.

To obtain reference values for blood and serum manganese levels, blood specimens were collected from 29 men and 36 women. Mn in blood showed a normal distribution; its upper 97.5% limit in blood was 0.38 mumol/l. Mn in serum showed a skewed distribution, which did not differ from the normal one after logarithmic transformation. The respective reference limit was 19 nmol/l. In both specimens, the levels of Mn were significantly lower in men than in women. To obtain reference values for Mn in urine, midday urine specimens were collected from 58 men and 96 women. Mn in urine also showed a skewed distribution, and the upper 97.5% limit was 38 nmol/l. The levels of Mn in blood and urine were statistically significantly higher in manual metal arc (MMA) welders of mild steel (MS) than in the reference populations. Five MMA/MS welders were subjected to a further study in which the ambient intramask Mn levels and urinary Mn excretion were monitored throughout a full working week. For two welders the correlation of Mn in urine specimens voided in the afternoon was good with the before noon Mn concentrations in the hygienic measurements; for the rest the correlation was minimal. Mn in diurnal urine specimens collected in six portions showed fluctuation if specific gravity or creatinine in urine was used to standardize for the urinary flow, but it was less evident for urinary Mn excretion rate. Our results seem to indicate that the measurement of Mn in urine or blood may be used for monitoring Mn exposure in MMA/MS welders only at the group level.

Adolescent↗

PubMed2006

Customised birthweight: coefficients for an Australian population and validation of the model.

BACKGROUND: Published birthweight references in Australia do not fully take into account constitutional factors that influence birthweight and therefore may not provide an accurate reference to identify the infant with abnormal growth. Furthermore, studies in other regions that have derived adjusted (customised) birthweight references have applied untested assumptions in the statistical modelling. AIMS: To validate the customised birthweight model and to produce a reference set of coefficients for estimating a customised birthweight that may be useful for maternity care in Australia and for future research. METHODS: De-identified data were extracted from the clinical database for all births at the Mater Mother's Hospital, Brisbane, Australia, between January 1997 and June 2005. Births with missing data for the variables under study were excluded. In addition the following were excluded: multiple pregnancies, births less than 37 completed week's gestation, stillbirths, and major congenital abnormalities. Multivariate analysis was undertaken. A double cross-validation procedure was used to validate the model. RESULTS: The study of 42,206 births demonstrated that, for statistical purposes, birthweight is normally distributed. Coefficients for the derivation of customised birthweight in an Australian population were developed and the statistical model is demonstrably robust. CONCLUSIONS: This study provides empirical data as to the robustness of the model to determine customised birthweight. Further research is required to define where normal physiology ends and pathology begins, and which segments of the population should be included in the construction of a customised birthweight standard.

Australia↗

PubMed1995

Pyramidal tract fiber spectrum in rats, with comments on cats and man.

Most CNS fiber spectrums are unimodal and strongly positively skewed, with many small and few large fibers. This study shows that the pyramidal tract (PT) fiber spectrum of a rat can be calculated as the sum of three distributions of myelinated axons, each derived by normal Gompertzian growth from three normal distributions of protoaxons. Histological measurement of the rat PT determined the values entered into the model, thus forcing a unique solution. The model was generalized to cats and man by assuming values for which no experimental data was available; the simulated PT fiber spectrums closely matched the observed PT fiber spectrums, in both species. It is concluded that normal Gompertzian growth is sufficient to account for the specific shape of the fiber spectrum, with no recourse to morphogenetic sculpting. The overproduction of cells during growth, and death of cells during development, may regulate the total number of neurons in different areas of cortex, but plays no role in determining the specific shape of the PT fiber spectrum.

Animals↗

PubMed1987

Genotypic distribution at the limits to natural and artificial selection with mutation.

A general procedure for analysing the change of genotypic distributions under stabilizing and truncation selection is described here and used to investigate the genotypic distribution at the limits to selection. For comparison, a simple approximate procedure using a normal distribution is also presented. It is clear that in the long term truncation introduces departures from normality mainly through gene frequency change, rather than through the generation of linkage disequilibrium under random mating. The Gaussian approximation performs reasonably well for additive gene effects unless the mean gene frequency is very extreme (say, outside the range of 0.05 to 0.95) and the number of loci is small (say, less then 50) regardless of the type of selection in operation. The genotypic distribution at the limits to selection largely depends on the type of limit reached. If a limit is obtained due to the action of natural selection before the exhaustion of existing variation, the distribution will normally not be very skew, but if a limit is reached at which mutation plays a central role in the maintenance of genetic variability, it could have high coefficients of skewness and kurtosis. The role of mutation on the long-term response is also discussed.

Gene Frequency↗

PubMed1997

Long-term precision of glomerular filtration rate measurements using 51Cr-EDTA plasma clearance.

The long-term precision of chromium-51 ethylenediamine tetraacetic acid (51Cr-EDTA) measurements of glomerular filtration rate (GFR) was evaluated in a retrospective study of data obtained over a 12 year period. Each GFR measurement was derived from plasma samples taken at 2, 3 and 4 h following injection of 3 MBq 51Cr-EDTA. The records of 7507 patients were reviewed, from which 55 subjects were identified as having had studies on 10 or more occasions. The mean number of studies per patient was 12.9 (range 10-23) over a mean period of 9.4 years (range 4.3-11.8 years). Plots of GFR, clearance half-life, (T1/2) and volume of distribution (VD) were drawn for each patient and used to identify subjects showing linear changes with time that could be fitted using linear regression. Each residual was expressed as a percentage of the expected value calculated from the regression line and all the residuals combined to give histograms for GFR, T1/2 and VD. Each histogram was fitted with a normal distribution between the -3 S.D. and +3 S.D. limits using weighted least squares. Final results for the coefficient of variation were: GFR 9.8%, T1/2 6.7%, VD 9.4%. The precision errors were used to calculate the smallest statistically significant change measurable by the 51Cr-EDTA technique. With 10% significance and 80% power, the smallest measureable change was 30% for GFR and 20% for T1/2. Unless there are clinical grounds for thinking that a patient's volume of distribution has changed, T1/2 is the optimal parameter for identifying real changes in renal function.

Chromium Radioisotopes↗

PubMed1998

Statistical significance of ungapped sequence alignments.

Statistical significance of a local sequence alignment depends not only on the similarity score and on the sequence lengths, but also on a length of the alignment. Dependence of the alignment significance on the length of the sequences has been analyzed earlier, and is based on the idea that the longer sequences have more chances to share a local similarity with a bigger score. To the best of our knowledge, a dependence of the statistical significance on the length of an alignment has not been used in selecting the best alignments. We have applied to real proteins formulas for assessing the statistical significance of ungapped local alignments. Let L be a length of the alignment, then the expected value of a similarity score is Sexp = * L, where is the expected similarity between two randomly chosen residues. Value of can be calculated from a similarity (substitution) matrix M and amino acid frequencies P. = sigma ij pi*pj*mij. The probability of observing a score S greater than or equal to x for an alignment of length L is given by the normal distribution: Prob(S > or = x) = 1-integral of N ((S-Sexp)/sigma) = 1-integral of N((S- *L)/sigma m square root of L), where sigma m is a standard deviation of m. From these formula, we conclude, that we should select the best alignment using a normalized value of the similarity score as follows: S' = max ¿(S- *L)/ sigma m square root of L¿. The proposed normalization of the similarity score has been tested on the representative benchmark. To evaluate a performance of the normalization, we have calculated several measures of the recognition quality. Our normalization has improved all these measures. This procedure is important for choosing the correct alignment for homology modelling as well as for selecting distantly related sequences in databases.

Amino Acid Sequence↗

PubMed2003

Explaining and controlling regression to the mean in longitudinal research designs.

This tutorial is concerned with examining how regression to the mean influences research findings in longitudinal studies of clinical populations. In such studies participants are often obtained because of performance that deviates systematically from the population mean and are then subsequently studied with respect to change in the trait used for this selection. It is shown that in such research there is a potential for the estimates of change to be erroneous due to the effect of regression to the mean. The source of the regression effect is shown to arise from measurement error and a sampling bias of this measurement error in the process of selecting on extreme scores. It is also shown that regression effects are greater with measures that are less reliable and with samples that are selected with more extreme scores. Furthermore, it is shown that regression effects are particularly prominent when measures of change are based on changes in dichotomous states formed from quantitative, normally distributed traits. In addition to a formal analysis of the regression to the mean, the features of regression to the mean are demonstrated via a simulation.

Humans↗

PubMed2000

Moment expansions in spatial ecological models and moment closure through Gaussian approximation.

We describe the dynamics of competing species in terms of interactions between spatial moments. We close the moment hierarchy by employing a Gaussian approximation which assumes that fluctuations are independent and distributed normally about the mean values. The Gaussian approximation provides the lowest-order systematic correction to the mean-field approximation by incorporating the effect of fluctuations. When there are no fluctuations in the system, the mean equations agree with the Gaussian approximation as the fluctuations are weak. As the fluctuations gain strength, they influence the mean quantities and hence the Gaussian approximation departs from the mean-field approximation. At large fluctuation levels, the Gaussian approximation breaks down, as may be explained by the bimodality and skewness of the fluctuation distribution of the partial differential equation.

Animals↗

PubMed1976

Diacridines: bifunctional intercalators. III. Definition of the general site of action.

Electron microscopy of HeLa cells exposed to spermine diacridine shows nucleolar distortions which disappear after several days despite the persistence of the metabolic changes promoted by spermine diacridine. This compound inhibits ribosomal RNA synthesis and appears to act independently of any particular phase of the cell cycle. The DNA content of the HeLa cells remains unchanged and the cell distribution is not significantly disturbed from its normal distribution in the various phases of the cell cycle. Spermine diacridine and other diacridines inhibit primarily chain initiation but also chain elongation by DNA-directed RNA polymerase of Azotobacter vinelandii.

Acridines↗

PubMed2005

The Calgary Depression Rating Scale for schizophrenia in a healthy control group: psychometric properties and reference values.

BACKGROUND: Assessment of depression in schizophrenia is of great importance as depressive signs and symptoms and suicidality are highly prevalent in patients with schizophrenic disorders. The Calgary Depression Rating Scale (CDSS) is the standard assessment instrument for that purpose due to its proven reliability and validity. However, so far no reference values derived from an adequate healthy sample have been published. METHODS: The present study analyzed CDSS item scores and summary scores in 154 healthy subjects (49% female, mean age 32.8+/-11.7 years) selected from studies as controls for schizophrenic patients. RESULTS: The total CDSS score was 2.6+/-2.7 (range 0-12), about 1/3 of healthy subjects had scores=0. Gender differences were observed with respect to "early awakening" and "suicidal ideation" with higher scores in females. Total CDSS scores (r=-0.17, P=0.03) and single items were slightly negatively correlated with age. The psychometric properties of the CDSS scale were satisfying (corrected item-score correlations r(tc)=0.33-0.61, internal consistency Cronbach's alpha=0.76, one-dimensional factor structure). CDSS total scores showed a skewed distribution fitting the upper part of a normal distribution. Based on the empirical distribution of CDSS values, reference values were listed for the total group of healthy subjects, and for females and males separately. CONCLUSIONS: The results corroborate the favourable psychometric properties of the CDSS found previously in clinical samples in a healthy control group. The reference values reported here can assist the clinical use and interpretation of CDSS values and emphasize the usefulness of the CDSS for a thorough assessment of depression and suicidality in schizophrenia.

Adult↗