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PubMed1990

A comparison of multivariable mathematical methods for predicting survival--I. Introduction, rationale, and general strategy.

This paper and the two following papers (Parts I-III) report an investigation of performance variability for four multivariable methods: discriminant function analysis, and linear, logistic, and Cox regression. Each method was examined for its performance in using the same independent variables to develop predictive models for survival of a large cohort of patients with lung cancer. The cogent biologic attributes of the patients had previously been divided into five ordinal stages having a strong prognostic gradient. With stratified random sampling, we prepared seven "generating" sets of data in which the five biologic stages were arranged in proportional, uniform, symmetrical unimodal, decreasing exponential, increasing exponential, U-shaped, or bi-modal distributions. Each of the multivariable methods was applied to each of the seven generating distributions, and the results were tested in a separate "challenge" set, which had not been included in any of the generating sets. The research was intended not merely to compare the performance of the multivariable methods, but also to see how their performance would be affected by different statistical distributions of the same cogent biologic attributes. The results, which are presented in the second and third papers, were compared for selection of independent variables and coefficients, and for accuracy in fitting the generating sets and the challenge set.

Cohort Studies↗

PubMed1992

Mass isotopomer distribution analysis: a technique for measuring biosynthesis and turnover of polymers.

Mass isotopomer distribution analysis (MIDA) is a technique for measuring biosynthesis and turnover of polymers in vivo. A stable isotopically enriched precursor is administered, and the relative abundances of different mass isotopomers in the polymer of interest are measured by mass spectrometry (MS). By comparison of statistical distributions predicted from the binomial or multinomial expansion to the pattern of excess isotopomer frequencies observed in the polymer, the enrichment of the biosynthetic precursor subunits (p) for newly synthesized polymers is calculated. MIDA thereby provides a solution to the problem of determining the isotope content in the actual precursor molecules that entered a particular polymeric product (the "true" precursor). The fraction of polymer molecules in a mixture that were newly synthesized during an isotopic experiment (fractional synthesis) can then be calculated. We describe some mathematical characteristics of MIDA and point out certain advantageous features. For example, mathematical estimates of p remain valid even if there does not exist a single anatomic or functional precursor pool. The interpretation of decay curves of endogenously labeled polymers may be improved by the use of higher mass isotopomers, which better fulfill the assumption of flash labeling. By combining fractional synthesis values with rate constants of decay, absolute endogenous synthesis rates can be calculated. Thus, by using probability logic combined with MS analysis, MIDA allows dynamic measurements to be made through analyses on a polymer alone during both isotopic incorporation and decay phases. The method has been applied to fatty acids, cholesterol, and glucose and is potentially applicable to nucleic acids, porphyrins, perhaps proteins, and many other classes of polymers.

Indicator Dilution Techniques↗

PubMed1977

Two-dimensional probabilistic images discrimination. I. Simultaneously presented pairs of patterns.

Reaction time and judgment of similarity or dissimilarity were studied in an experiment on two-dimensional probabilistic images (TDPIs) composed of rectangular black and white cells with statistical distribution of these elements 0.5-0.5. The subjects were asked to report verbally whether pairs of TDPIs, presented for 700 ms, appeared to them similar or not. Three sets of TDPIs differed as to the size of their "grain". Within the pairs "physically identical patterns", "statistically same patterns" or "different patterns" have been used. The statistically same patterns pairs reached the lowest (39 percent) judgment correctness. Reaction times for these pairs were generally longer than for others. In the case of identical patterns and statistically same patterns pairs the results indicated a general increase of the processing time as the size of grain had increased. There was a general tendency of reaction time shortening in successive sessions. These results suggest that correct discrimination of TDPIs does not depend primarily upon their grain.

Adult↗

PubMed1980

Development and distribution of proximal caries in 303 9-20-year-old individuals in a Copenhagen suburb.

The purpose of the present study was to establish a theoretical basis for the practice of screening for identification of caries risk groups. Longitudinal data concerning the development of proximal caries in 303 persons from the age of 9 to the age of 20 were examined with regard to statistical distribution. Data from each year and from the entire period showed a close fit to the negative binomial distribution. This distribution can be the result of independent random occurrences, but varying susceptibility. Thus the consistent existence of a caries risk group is illustrated by this analysis, but no prediction is made. It is suggested that future evaluations of preventive measure directed toward caries risk groups should express the degree to which the similarity between the distribution of proximal caries and the negative binomial distribution can be eliminated.

Adolescent↗

PubMed1992

The effect of neglecting correlations when propagating uncertainty and estimating the population distribution of risk.

Interest in examining both the uncertainty and variability in environmental health risk assessments has led to increased use of methods for propagating uncertainty. While a variety of approaches have been described, the advent of both powerful personal computers and commercially available simulation software have led to increased use of Monte Carlo simulation. Although most analysts and regulators are encouraged by these developments, some are concerned that Monte Carlo analysis is being applied uncritically. The validity of any analysis is contingent on the validity of the inputs to the analysis. In the propagation of uncertainty or variability, it is essential that the statistical distribution of input variables are properly specified. Furthermore, any dependencies among the input variables must be considered in the analysis. In light of the potential difficulty in specifying dependencies among input variables, it is useful to consider whether there exist rules of thumb as to when correlations can be safely ignored (i.e., when little overall precision is gained by an additional effort to improve upon an estimation of correlation). We make use of well-known error propagation formulas to develop expressions intended to aid the analyst in situations wherein normally and lognormally distributed variables are linearly correlated.

Analysis of Variance↗

PubMed1991

Distribution of time to first postpartum estrus in beef cattle.

The function of a distribution that describes postpartum interval (PPI) under any experimental treatment is useful for simulation modeling, understanding the effects of stimuli on the endocrine system, and estimating the average PPI in experiments terminated before all animals have expressed estrus. This study was undertaken to compare the fit of three statistical distributions, the Weibull, the log-normal, and the linear hazard rate (LHR), to the empirical distribution of PPI for five treatment regimens: no bull exposure postpartum, bull exposure from 53 d postpartum, bull exposure from 3 d postpartum, and bull exposure from an average of 63 d postpartum for 2-yr-old cows and for mature cows. The Weibull and the log-normal distributions deviated considerably from the empirical distribution. The LHR distribution with parameters changing over three different regions gave an excellent fit. The resulting hazard rate (instantaneous probability of a cow expressing her first estrus at time t postpartum) revealed a low probability of expressing estrus within 27 d postpartum (43 d for 2-yr-olds). For cows not exposed to bulls, the hazard rate increased slowly with time. For cows exposed to bulls after 3 d postpartum, the hazard rate increased rapidly between d 27 and d 50. For cows exposed to bulls after 53 d postpartum, the hazard rate increased instantaneously approximately 12 d after initial exposure to bulls. This increase was also seen when cows were exposed to bulls beginning at a constant date (at an average of 63 d postpartum). Because of lack of fit, the Weibull and the log-normal distributions should not be used in survival analysis of PPI.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMed1994

Bioequivalence: performance of several measures of extent of absorption.

The determination of the area under the concentration-time curve (AUC) is the method most commonly used by regulatory agencies to assess extent of drug absorption after single-dose administration of oral products. Using simulations, several approaches toward measuring the actual area, in whole or part, were tested. In addition, the performance of the peak concentration (Cmax), usually taken as a measure of the rate of absorption was assessed evaluating extent. Model scenarios for drugs with typical mean characteristics and statistical distributions were investigated. Using different kinetic models of disposition, the time course of the drug concentration in plasma was simulated. Intraindividual and interindividual variability and assay error were modeled using Monte Carlo techniques. The accuracy, precision, and ease of use of the various measures of extent were evaluated, and statistical power analyses were performed. Among the measures tested, the most reliable were the AUC computed up to the time of the last quantifiable concentration, without extrapolation, and Cmax. However, being also sensitive to rate, Cmax as a measure of extent is of limited potential.

Absorption↗

PubMed1994

Relative effects of left ventricular mass and conduction disturbance on activation in patients with pathological left ventricular hypertrophy.

OBJECTIVE: To investigate the relative effects of left ventricular mass and conduction disturbance on the duration and axis of the QRS complex in patients with left ventricular hypertrophy and a normal cavity size. STUDY DESIGN: Retrospective and prospective study of 42 patients with pathological left ventricular hypertrophy and 17 normal controls by electrocardiography, echocardiography, and pulsed Doppler recordings. SETTING: Tertiary cardiac referral centre. PATIENTS: 42 patients (mean (SD) age 58(16)) with left ventricular hypertrophy and normal cavity size. 17 had stenotic or replaced aortic valves, 14 had hypertension, 9 had hypertrophic cardiomyopathy and 2 had left ventricular hypertrophy without obvious cause. 17 normal people (mean (SD) age 47(20)) were used as controls. RESULTS: The values of QRS duration segregated into two normally distributed populations, with a cut off point at 135 ms. When patients with QRS duration of < 135 ms (n = 30) were compared with those with QRS duration of > or = 135 ms (n = 12), there were no significant differences in age, heart rate, left ventricular size, shortening fraction, left ventricular mass and total QRS amplitude. Both the PR and QT intervals were, however, longer in patients with a QRS duration of > or = 135 ms, and the extent of incoordinate left ventricular wall motion during the preejection period was greater. When it was < 135 ms the QRS duration was strikingly correlated with left ventricular mass (r = 0.81, p < 0.01). The onsets of transverse septal motion and of posterior wall thickening were normal, as were the onsets of the longitudinal motion of left, septal, and right atrioventricular junctions. When the QRS duration was > or = 135 ms the onset of transverse septal motion and of the longitudinal right atrioventricular junction were both normal, but that of the posterior wall thickening (p < 0.01) and the longitudinal motion of the septum (p < 0.05) and lateral left ventricular wall (p < 0.01) were significantly delayed. Peak rates of left ventricular dimension decrease (p < 0.01) and increase (p < 0.01) were both reduced, as were the peak rates of the long axis shortening of the septum (p < 0.01) and left atrioventricular junction (p < 0.05), whereas the peak rates of posterior wall thickening and thinning did not differ between the two groups. Mean isovolumic relaxation time was longer (p < 0.05) in patients with QRS duration of > or = 135 ms and the peak velocity of the A wave and thus the A to E ratio was greater than in patients with a QRS duration of < 135 ms and that of the E wave was similar in the two groups. CONCLUSION: In patients with left ventricular hypertrophy the values of QRS duration are bimodally distributed, with a cut off point at 135 ms. When QRS duration is < 135 ms, left ventricular mass seems to be closely related to QRS duration, making it the dominant factor determining the activation time. Once QRS duration reaches > or = 135 ms the correlation with mass no longer exists. The statistical distribution, electrocardiographic characteristics, and incoordination pattern of left ventricular wall motion all suggest the development of a proximal left bundle branch block.

Adolescent↗

PubMed1977

Some quantitative results on Golgi impregnated axons in rat visual cortex using a computer assisted video digitizer.

Axonal fiber distributions of pyramidal cells in the visual cortex of the albino rat have been investigated using the rapid Golgi method and modern data collecting techniques. Three dimensional coordinate information was extracted from Golgi-impregnated axonal networks using a computer-assisted video digitizer. Computer programs used this data to generate various statistical distributions. In particular, angular distributions of the initial collateral segments and their endpoints were examined and found to reveal anisotropies. Inspection of the spatial distributions of the endpoints indicated a clustering at two distinct levels with respect to the pyramidal cell from which they originate. Dynamic graphic displays of the three dimensional data have been obtained and presented in the form of computer tracings of various orthogonal projections.

Animals↗

PubMed1980

The random character of protein evolution and its effects on the reliability of phylogenetic information deduced from amino acid sequences and compositions.

Because evolution occurs by random events, the actual number of substitutions that occur in any period is not exactly equal to the number expected from the mean rate of substitution, but is statistically distributed about it. In consequence, even if rates of evolution are constant in different lineages, 'trees' deduced from descendant protein sequences contain random errors. When there are fewer than about eight differences between the sequences of the most distantly related pair from a set of proteins, this random effect is very large. It can then render trivial the statistical disadvantage inherent in using a crude measure of protein difference, such as amino acid composition or immunological cross-reactivity, in preference to a measure based the sequences of the most distantly related pair from a set of proteins, this random effect is very large. It can then render trivial the statistical disadvantage inherent in using a crude measure of protein difference, such as amino acid composition or immunological cross-reactivity, in preference to a measure based the sequences of the most distantly related pair from a set of proteins, this random effect is very large. It can then render trivial the statistical disadvantage inherent in using a crude measure of protein difference, such as amino acid composition or immunological cross-reactivity, in preference to a measure based on amino acid sequence. In some cases, such as classification of mammals on the basis of cytochrome c structure, it appears to make little difference to the reliability of the results whether the sequences of the protein concerned are known or not. It may also be possible to obtain more reliable phylogenetic information from composition measurements on several kinds of protein than one could obtain from sequence measurements on a single kind of protein.

Amino Acid Sequence↗

PubMed1990

The distribution of physical, chemical and conformational properties in signal and nascent peptides.

Signal peptides play a major role in an as-yet-undefined way in the translocation of proteins across membranes. The sequential arrangement of the chemical, physical and conformational properties of the signal and nascent amino acid sequences of the translocated proteins has been compiled and analysed in the present study. The sequence data of 126 signal peptides of length between 18 and 21 residues form the basis of this study. The statistical distribution of the following properties was studied hydrophobicity, Mr, bulkiness, chromatographic index and preference for adopting alpha-helical, beta-sheet and turn structures. The contribution of each property to the sequence arrangement was derived. A hydrophobic core sequence was found in all signal peptides investigated. The structural arrangement of the cleavage site was also clearly revealed by this study. Most of the physical properties of the individual sequences correlated (correlation coefficient approximately 0.4) very well with the average distribution. The preferred occupancy of amino acid residues in the signal and nascent sequences was also calculated and correlated with their property distribution. The periodic behaviour of the signal and nascent chains was revealed by calculating their hydrophobic moments for various repetitive conformations. A graphical analysis of average hydrophobic moments versus average hydrophobicity of peptides revealed the transmembrane characteristics of signal peptides and globular characteristics of the nascent peptides.

Amino Acid Sequence↗

PubMed1980

[Effects of molecular parameters of galacturonan substrate on the activity of a polygalacturonase from tomatoes].

The activity of a major form of the tomato polygalacturonase (EC 3.2.1.15) depends of the origin of the galacturonan substrates (apple, citrus) as well as upon the molecular mass, the degree of esterification and the distribution of the ester methoxyl groups. Optimal substrates are citrus pectic acids with a degree of esterification < 1% and a molecular mass corresponding to a viscosity number [eta] = 90 ml/g galacturonan. In the [eta] range from 16 to 474 ml/g, the Km values decrease to constant amount of 15.6 mM galacturonic acid units, which corresponds to 0.27% galacturonan. In a statistical distribution of the ester methoxyl groups, the activity reaches zero in the range of the degree of esterification from 80 to 90%. Enzymatically de-esterified pectins with a degree of esterification < 32% and a block-like distribution of the ester methoxyl groups behave as comparable pectic acids. In summary, there is a good agreement between these enzymesubstrate interactions and those of endopolygalacturonases from Aspergillus spec. Differentiations manifested themselves only in the transition range between macromolecular galacturonan substrates and oligomeric substrates below the established critical molecular mass.

Glycoside Hydrolases↗

PubMed1972

Statistical analysis of the bioassay of continuous carcinogens.

In an experiment consisting of the continuous constant application of various carcinogenic regimens to a pure strain of experimental animals for a long period, the cancer incidence rates so caused may be studied and compared by the fit of an appropriate class of statistical distributions. In this paper we show that a Weibull distribution in which the age-specific cancer incidence rate rises as a power of time since first risk is more appropriate than a lognormal distribution. If the Weibull family of distributions is used, more information can be extracted from the data, and differences of toxicity between various regimens will not bias the comparison of their carcinogenic forces.

Animals↗

PubMed1986

[Statistical patterns of the anomalous staining of 5-bromodeoxyuridine-substituted chromosomes].

Five large chromosome segments showing sometimes an abnormal staining were found in the genome of Chinese hamster (clone 237). Three types of abnormal staining were recorded. After one round of replication in the presence of BrdUrd these segments showed a hetero-staining, whereas after two rounds of replication the same segments showed iso-dark or iso-light staining. Pulse labeling with 3H-thymidine showed that all these segments were the late-replicating ones. The labeling proceeded according to all-or-none principle; in a given cell all five segments showed either presence or absence of the label. On the contrary, the abnormal staining was statistically distributed among these segments. These results are in disagreement with the current view that the abnormal staining is associated with asymmetrical distribution of thymine among two strands of DNA duplex. The above regularities are considered as an argument for the two-stranded model of chromosome.

Animals↗

PubMed1984

Estimation of cumulative exposures to ethylene oxide associated with hospital sterilizer operation.

The statistical distribution of exposures to ethylene oxide was estimated for a task involving transfer of materials from a hospital sterilizer. The exposure data are consistent with either a normal or log-normal distribution. It is shown how the single-task distribution and the number of task repetitions can be used to determine the minimum differences in task repetitions necessary to distinguish for epidemiological purposes between worker groups on the basis of cumulative exposure.

Environmental Exposure↗

PubMed1994

A statistical analysis of side-chain conformations in proteins: comparison with ECEPP predictions.

A comparison of the statistical distributions of side-chain conformations of 17 amino acids (Gly, Ala, and Pro excluded), observed in 63 nonhomologous globular proteins (covering 10,832 residues), is made with similar distributions calculated from the low-energy conformational states for the same amino acids (blocked with acetyl and N-methylamide groups at the N- and C-termini, respectively) obtained by Vásquez et al. [(1983), Macromolecules 16, 1043-1049] using the ECEPP/2 force field. Those residues (i) with linear side chains (Arg, Lys, Met, Cys, Ser), or those that are unbranched through the gamma-carbon atom (Glu, Gln) show good agreement, whereas (ii) those with side chains that are branched at C beta or C gamma show poor agreement with ECEPP calculations. A possible explanation for this is shown to be the greater tendency for side-chain atoms in class (ii) to interact with the backbone and/or adjacent side chains. Accordingly, ECEPP/3 calculations, carried out after elongating the backbone chain of the model peptide unit (by adding three Ala residues on each side of the central residue, and then blocking the termini as before), result in distributions that are often closer to the observed side-chain distributions. The implications of these results for the relative importance of short-range versus long-range interactions in determining protein structure are discussed.

Amino Acids↗

PubMed1987

The galactose-specific receptor system in rat liver during development.

The number and distribution of galactose-specific binding sites were investigated in rat liver cells during perinatal development. Ligand binding to hepatocytes, macrophages and endothelial cells was followed with in vitro and in situ experiments by electron microscopy, using lactosylated bovine serum albumin adsorbed onto 5 nm colloidal gold particles as ligand. Binding capacity, starting at a late stage of fetal development, is very low both on the hepatocyte and on the macrophage surface, which show single particles statistically distributed. By contrast, bound particles are absent from fetal endothelial cells, which also lack the typical coated regions. In vivo, experiments at 37 degrees C show that endocytosis occurs to some extent in prenatal life. These results indicate that the expression of galactose-specific receptors' activity on the different liver cell types follows different developmental patterns, which are independently modulated.

Animals↗

PubMed1989

Marked regional heterogeneity in blood flow within a single skeletal muscle at rest and during exercise hyperaemia in the rabbit.

In 1985 both Pendergast et al. and Piiper et al. described a major regional heterogeneity in blood flow within single skeletal muscles both at rest and during exercise. Based on the microsphere method they described large variations in blood flow between muscle samples as large as 1 g each. The aims of the present study were: (1) To test this notion of regional heterogeneity in microsphere deposition within single skeletal muscles both at rest and during exercise. (2) To compare the distribution of microspheres with other blood flow tracers. (3) To test whether or not any heterogeneity was due to vasomotion in small arteries or arterioles. Microspheres were infused into anaesthetized rabbits over either 10, 30 or 120 s, or 10 min. Exercise was mimicked by tetanic contractions obtained by electrical stimulation of the motor nerves. Three hindleg muscles were divided into samples of 0.25 g each. Regional heterogeneity was expressed as the coefficient of variation corrected for statistical distribution of microspheres (CVc). The CVc at rest was about 0.34. The CVc was unaffected by the various infusion periods and did not change during exercise. Simultaneous infusions of microspheres and 86Rb+ or antipyrine gave high correlations between the two blood flow tracers, with all r values exceeding 0.83 (n = 18). We conclude that the microsphere method provides reliable estimates for regional blood flow within single skeletal muscles. The distribution of blood flow was markedly heterogeneous both at rest and during exercise. The heterogeneity in blood flow was apparently not a result of vasomotion.

Animals↗