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PubMed2003

Time to first recurrence as a trial endpoint: time to change?

There has been a rapidly increasing interest in developing new therapies for management of atrial fibrillation. The optimal method for evaluating their efficacy is by measuring changes in outcomes such as mortality, quality of life or cost of care; requiring trials of large sample size. In order to reduce the sample size, there is a need to develop appropriate surrogate endpoints. "Is time to first recurrence of symptomatic atrial fibrillation" an appropriate surrogate endpoint for quality of life? Since a surrogate endpoint must capture the net effect of the treatment, it was assumed (a) that frequency of symptomatic episodes captures the net effect on quality of life and (b) "time to first recurrence" is a measure of the frequency of symptomatic episodes. The effect of frequency of symptomatic episodes or their duration and symptom severity on quality of life has not been evaluated. "Time to first symptomatic recurrence" was proposed because data from a few patients demonstrated that symptomatic atrial fibrillation episodes arose independently and randomly and could be represented mathematically by a Poisson distribution. Recent data from a greater number of patients with implantable devices that detect symptomatic and asymptomatic episodes of atrial tachyarrhythmias indicate that these episodes tend to cluster in time and cannot be well represented by a Poisson distribution. Because all atrial tachyarrhythmia episodes do not follow a Poisson distribution, it is unlikely that only symptomatic episodes would follow the same distribution, although this needs to be proved. A non-Poisson distribution requires a larger sample to detect differences in clinical trials. This should be taken into consideration when designing prospective trials. Alternative methods may include measuring frequency of symptomatic episodes as well their severity and duration. In patients with implanted devices, total duration of time spent in atrial tachyarrhythmias or objective measures of rate control should also be evaluated as surrogate endpoints. If surrogate endpoints cannot be developed, changes in clinical outcomes will need to be demonstrated to evaluate therapeutic efficacy.

Atrial Fibrillation↗

PubMed1993

Estimating the variance of standardized rates of recurrent events, with application to hospitalizations among the elderly in New England.

Usual approaches for estimating the variance of a standardized rate may not be applicable to rates of recurrent events. Where individuals are prone to repeated health events, Greenwood and Yule (J R Stat Soc [A], 1920;83:255-79) advocated use of the negative binomial distribution to account for departures from the assumption of randomness of recurrent events required by the Poisson distribution. In this paper, the authors implemented the negative binomial distribution in the computation of annual hospitalization rates within certain hospital market areas. Data used were from 1,549,915 New England residents aged 65 years or more who were enrolled in Medicare between October 1, 1988, and September 30, 1989, and who had 458,593 hospital admissions during that year. New England was partitioned into 170 hospital market areas ranging in population size from 162 to 70,821 elderly Medicare enrollees. The negative binomial distribution demonstrated substantially better fits than the Poisson distribution to the numbers of hospitalizations within hospital market areas. Estimated standard errors for indirectly standardized rates based on the negative binomial distribution were 25-51 percent higher than estimated standard errors that assumed an underlying Poisson distribution. Using regression analysis to smooth overdispersion parameters across hospital market areas produced similar results. The approach described in this paper may be useful in estimation of confidence intervals for standardized rates of recurrent events when these events do not recur randomly.

Age Factors↗

PubMed1991

Frequency of elevated urinary beta 2-microglobulin levels in relatives of patients with asymptomatic low-molecular-weight proteinuria.

We studied urinary beta 2-microglobulin levels in a total of 29 apparently healthy relatives (aged 0.8-70 years) of 8 male patients with asymptomatic low-molecular-weight proteinuria in six families. The frequency of levels above the age- and sex-associated 95% confidence limit was 7 of 29 (24%), 4 of 12 (33%) in first-degree relatives, 2 of 6 (33%) fathers, and 2 of 6 (33%) mothers. These frequencies were significantly above those in the general population (P less than 0.01, by a normal distribution test, a binomial distribution, and Poisson distribution test for the sample proportion). The increased frequency in fathers argues against an X-linked pattern of inheritance for this entity, suggesting that there is heterogeneity in the inheritance.

Adolescent↗

PubMed2006

How much does band broadening adulterate results deduced from chromatograms measured by size-exclusion chromatography really?

A number of polystyrene samples and standards were measured with several column combinations which differed in their extent of band broadening, sigma(BB). Comparison of the derived chain length distributions showed in some cases good agreement even despite strong distinctions in the determined sigma(BB) values. The calculated number and weight averages of the samples were almost identical in most cases for the column combinations used. Furthermore, the points of inflection of the standards and of multimodale distributions composed of narrow (Poisson like) peaks in microemulsion were examined. When conferred with the theoretical values which were calculated for assumed Poisson distributions the respective deviations from the "true" ones were as high as 10% (almost reaching 20% in unfavorable cases). Simple (correction) procedures were tested in order to obtain the actual average values as well as the effective points of inflection of narrow distributions.

Chromatography, Gel↗

PubMed1957

Sensitivity to light in the sea anemone Metridium senile (L). II. Studies of reaction time variability and the effects of changes in light intensity and temperature.

1. The reaction time of the photosensitive response of Metridium was found to be composed almost entirely of a sensitization period. If a latent period exists, it is too short to be detected by the methods used and is probably less than a second in duration. The length of the reaction time, therefore, was used as a measure of the radiant energy necessary at any intensity to elicit a response. 2. The length of the reaction time was found to vary randomly by a factor of seven under constant environmental and stimulating conditions. Determination of large numbers of reaction times on several anemones, grouped according to length, gave closely similar distributions resembling Poisson distributions. It was suggested that the variability may be caused by the same factor or mechanism in each individual. An experimental scheme was presented for determining the expected error and variation in statistical quantities when groups of ten observations are used. 3. The means of groups of reaction times determined at different intensities formed a hyperbolic relationship when plotted against intensity, suggesting that the animal obeys the Bunsen-Roscoe law of reciprocity. No marked changes were noted of per cent deviation from the mean or of randomness at different intensities. Stimulation of Metridium requires roughly 5 x 10(9) incident quanta/cm.(2) of blue-green light. 4. No temperature effect could be found on either the means, the per cent deviation from the mean, or the degree of randomness of series of about ten observations, studied over a 17 degrees C. range. It was concluded that the variability in reaction time was not due to changes in any complex physiological state such as muscular tone. 5. A possible use of the photosensitive response is suggested and the potentialities of "integrative" photosensitivity are discussed. 6. Possible mechanisms to explain the variability in reaction time are discussed. In the light of evidence presented, the most likely hypothesis appears to be the uncertainty of quantum capture caused by low concentrations of photosensitive pigment. Assuming the validity of this hypothesis, evidence suggests that the anemones responded to less than 10 quanta of absorbed light. Caution, however, is recommended in accepting the hypothesis because of the indirect nature of the supporting evidence.

Animals↗

PubMed1989

[Optimum number of mixed peripheral blood samples by membrane filtration technique for mass blood survey of filariasis].

The membrane filtration technique has been used widely in the evaluation of effect of control and survey of filariasis. The present study was made to explore an optimum number of mixed peripheral blood samples and a mathematical model of work load for this method in surveying filariasis. By analysing the correlation between the microfilaremia rate and the optimum number of mixed peripheral blood samples and applying the theory of Binomial Distribution or Poisson Distribution, the authors reckoned a table for estimating the number of filariasis cases in villages with different microfilarial rates and different population as well as the optimum number of mixed peripheral blood samples.

Animals↗

PubMed1984

[Dynamics of the distribution of variables in morphology].

This paper discusses examples of exponentially distributed, Poisson-distributed, and binomially distributed random variables from morphology and describes secular and historical processes as well as phenomena of aging as factors of the dynamics of such distributions, the major focus being on tests of morphometric variables for the existence of normal distributions. In those cases where hypotheses of the existence of particular distributions of random morphometric variables are established it is necessary that consideration be given to metrological and stereological factors pertaining to the process of measuring and the geometry of the structures being measured, respectively. Karyometric results are used to demonstrate the splitting of a single statistical population into several populations as a result of the process of aging of the human organism.

Aged↗

PubMed2001

Distribution of the number of clonogens surviving fractionated radiotherapy: a long-standing problem revisited.

PURPOSE: A long-standing problem is addressed: what form of the probability distribution for the number of clonogenic tumor cells remaining after fractionated radiotherapy should be used in the analysis aimed at evaluating the efficacy of cancer treatment? Over a period of years, a lack of theoretical results leading to a closed-form analytic expression for this distribution, even under very simplistic models of cell kinetics in the course of fractionated radiotherapy, was the most critical deterrent to the development of relevant methods of data analysis. MATERIALS AND METHODS: Rigorous mathematical results associated with a model of fractionated irradiation of tumors based on the iterated birth and death stochastic process are discussed. RESULTS: A formula is presented for the exact distribution of the number of clonogenic tumor cells at the end of treatment. It is shown that, under certain conditions, this distribution can be approximated by a Poisson distribution. An explicit formula for the parameter of the limiting Poisson distribution is given and sample computations aimed at evaluation of the convergence rate are reported. Another useful limit that retains a dose-response relationship in the distribution of the number of clonogens has been found. Practical implications of the key theoretical findings are discussed in the context of survival data analysis. CONCLUSIONS: This study answers some challenging theoretical questions that have been under discussion over a number of years. The results presented in this work provide mechanistic motivation for parametric regression models designed to analyze data on the efficacy of radiation therapy.

Humans↗

PubMed1981

Application of Poisson's distribution model to the occurrence of acute viral hepatitis in the district of Sokolov.

The possibility of application of the Poisson's model of distribution in the field of epidemiology was analyzed on an example of actual distribution pattern of HBsAg-positive and HBsAg-negative cases of acute viral hepatitis notified weekly in a distinct during a period of 6 years. The results suggest that the distribution pattern of HBsAg-positive AVH is fully compatible with the Poisson's model of distribution, whereas the distribution pattern of HBsAg-negative AVH differs from it quite evidently. The observed Poisson's distribution of HBsAg-positive AVH offers some new theoretical and practical implications concerning the incidence, distribution and prophylaxis of this infection. It is also assumed that HBsAg-positive AVH is not the only one of the communicable diseases the occurrence of which is compatible with the Poisson's model of distribution.

Czechoslovakia↗

PubMed2001

Chromosome aberration analysis in radiotherapy patients and simulated partial body exposures: biological dosimetry for non-uniform exposures.

Chromosome aberration analysis was carried out in peripheral blood lymphocytes of cancer patients following radiotherapy of lungs, cervix and spine. Radiotherapy in the pelvic region involving large doses (6 Gy) showed an overdispersed distribution of dicentrics. However, when the doses were fractionated (three fractions of 2 Gy) distribution was found to be near Poisson. Spine irradiation covering almost all the lymphocytes pools, indicated a Poisson distribution. The data show that depending on the sites of exposure, the distribution of dicentrics in cells varies and hence there is a non-uniform distribution of lymphocytes in the body. The average dose to the lymphocytes was found to be one sixth of the partial body dose. Based on the non-Poisson distribution of aberrations, the fraction of lymphocytes irradiated, mean dose to the fraction and part of the body exposed was calculated in a case of acute 6 Gy pelvic irradiation. The fraction of cells irradiated was calculated to be 4.11% and the portion of the body exposed was approximately 16.8%. The dose to the irradiated fraction was found to be 5.4 Gy, which is in agreement with the given dose of 6 Gy. In simulated exposures the u values increased systematically with the decrease in fraction of irradiated cells and the calculated dose to the fraction was also in good agreement with the true dose.

Chromosome Aberrations↗

PubMed1999

Evidence that most radiation-induced HPRT mutants are generated directly by the initial radiation exposure.

Radiation-induced HPRT mutants are generally assumed to arise directly from DNA damage that is misrepaired within a few hours after X-irradiation. However, there is the possibility that mutations result indirectly from radiation-induced genomic instability that may occur several days after the initial radiation exposure. The protocols that commonly employ a 5-7 day expression period to allow for expression of the mutant phenotype prior to replating for selection of mutants would not be able to discriminate between mutants that occurred initially and those that arose during or after the expression period. To address this question, we performed a fluctuation analysis in which synchronous or asynchronous populations of human bladder carcinoma cells were treated with single doses of X-irradiation. For comparison, radiation was delivered during the expression period, either from an initial dose of 1.0 Gy followed by two 1.0 Gy doses separated by 24 h or from disintegrations resulting from I125dU incorporated into DNA. The mutation frequency observed at the time of replating was used to calculate the average number of mutants in the initial irradiated culture by assuming that the mutants were induced directly at the time of irradiation. Then, this average number was used to calculate the fraction of the irradiated cultures that would be predicted by a Poisson distribution to have zero mutants. There was reasonably good agreement between the predicted poisson distribution and the observed distribution for the cultures that received single doses. Moreover, as expected, when cultures were irradiated during the expression period, the fraction of the cultures having zero mutants was significantly less than that predicted by a Poisson distribution. These results indicate that most radiation-induced HPRT mutations are induced directly by the initial DNA damage, and are not the result of radiation-induced instability during the 5-7 day expression period.

DNA↗

PubMed2000

Justification of statistical overlap theory in programmed temperature gas chromatography: thermodynamic origin of random distribution of retention times.

A specific distribution of compounds' standard-state changes of enthalpy and entropy between mobile and stationary phases in programmed temperature gas chromatography (PTGC) is shown to produce the Poisson distribution of retention times often postulated in statistical-overlap theory (SOT). A three-part model is proposed, in which the enthalpy change is Poisson distributed, the average entropy change depends on the enthalpy change, and the actual entropy change varies in a uniformly random manner about the average entropy change. To test the model, the entropy and enthalpy changes of 350 aliphatic and aromatic hydrocarbons in petroleum were calculated with commercial GC software. These changes are shown to follow the three-part model. The model then was used with Monte Carlo methods to mimic the enthalpy and entropy changes. The substitution of the mimicked enthalpy and entropy changes into an equation for the retention temperature in PTGC is shown to produce a Poisson distribution of retention times that is statistically significant. This finding establishes a scientific link between the thermodynamics governing retention in PTGC and the superficially ad hoc assumption of the Poisson retention time distribution in SOT. Similar thermodynamic distributions are found for flavors and fragrances and for tetrachlorodibenzo-p-dioxins and furans, which follow SOT based on the Poisson distribution, but not for polychloronaphthalenes, which do not follow that SOT.

Journal Article↗

PubMed2002

[Epidemiology of rhegmatogenous retinal detachment in Beijing, China].

OBJECTIVE: To investigate the incidence and epidemiological characteristics of rhegmatogenous retinal detachment (RD) in Beijing, China. METHODS: A prospective population-based study of the incidence of rhegmatogenous RD diagnosed between October 1999 and September 2000 was performed. The study group of Epidemiology of Rhegmatogenous Retinal Detachment in Beijing, China was made-up by the Department of Health Care Epidemiology of Peking University and all 35 hospitals with conditions of diagnosis and treatment for rhegmatogenous RD in Beijing city. Standard questionnaire and diagnostic guidelines for rhegmatogenous RD were adopted. All patients diagnosed for rhegmatogenous RD the first time in this period (included in-patients and out-patients) and resided in Beijing city proper and nearby suburbs were registered and recorded. The record included the age, sex, residing district, month rhegmatogenous RD occurring, refraction, eye or eyes of illness, history of blunt trauma, history of cataract extraction, history of rhegmatogenous RD on the contra-lateral eye, etc. Cases with recurrence, retinal break without retinal detachment and without patient's compliant and subclinical RD were excluded. Exudative RD, tractional RD, secondary detachment of retina after vitrectomy or strabismus operation or excision of ocular tumor and mixed retinal detachment were also excluded. RESULTS: A total of 526 patients were diagnosed in the city proper and the nearby suburbs. The annual incidence of rhegmatogenous RD was 7.98 per 100 000 population [95% confidence interval (CI), 7.3 - 8.7]. The incidence of blunt traumatic, aphakic or pseudophakic, and nontraumatic phakic cases being 0.93/10(5) (95% CI, 0.7 - 1.2), 0.80/10(5) (95% CI, 0.6 - 1.0), and 6.25/10(5) (95% CI, 5.7 - 6.9), respectively. The incidence of traumatic detachment for males was 1.55/10(5) (95% CI, 1.1 - 2.0), which was higher than that for females 0.30/10(5) (95% CI, 0.1 - 0.5), (Z test based on the Poisson distribution, P < 0.001). But there was no significant difference between males and females in the incidences of nontraumatic phakic detachment and aphakic detachment (Z test based on the Poisson distribution, 0.5 < P < 0.7). There were two peak incidences, one occurred in 60 - 69-age-group, and the other occurred in 20 - 29-age-group. No seasonal variations in the occurrence of retinal detachment was found (Z test based on the Poisson distribution, 0.8 < P < 0.9). There was no difference of incidence between the left and the right eye (Z test based on the Poisson distribution, P > 0.05). The proportion of bilateral detachment was 5.82% in that myopia was found in 66.5% of the patients. The proportion of high myopia in bilateral retinal detachment was greater than that of the unilateral retinal detachment (Chi-square test, 0.01 < P < 0.02). CONCLUSIONS: The annual incidence of rhegmatogenous RD in Beijing city proper and its nearby suburbs of China between Oct 1999 and Sept 2000 was 7.98 per 10(5) population (95% CI, 7.3 - 8.7).

Adolescent↗

PubMed1965

RAPID GRAPHICAL METHOD FOR ESTIMATING THE PRECISION OF DIRECT MICROSCOPIC COUNTING DATA.

A graphical method of estimating the 90, 95, or 99% confidence intervals of direct microscopic counting data is presented. Construction of the graphs is based on the assumption that the normal distribution approximates the Poisson distribution. The method, useful on data obtained from dried films or counting chambers, eliminates time-consuming computation of precision. The minimal number of fields which must be counted to maintain a certain level of precision can be readily determined.

Blood Cell Count↗

PubMed1998

Patterns of macroparasite aggregation in wildlife host populations.

Frequency distributions from 49 published wildlife host-macroparasite systems were analysed by maximum likelihood for goodness of fit to the negative binomial distribution. In 45 of the 49 (90%) data-sets, the negative binomial distribution provided a statistically satisfactory fit. In the other 4 data-sets the negative binomial distribution still provided a better fit than the Poisson distribution, and only 1 of the data-sets fitted the Poisson distribution. The degree of aggregation was large, with 43 of the 49 data-sets having an estimated k of less than 1. From these 49 data-sets, 22 subsets of host data were available (i.e. host data could be divided by either host sex, age, where or when hosts were sampled). In 11 of these 22 subsets there was significant variation in the degree of aggregation between host subsets of the same host-parasite system. A common k estimate was always larger than that obtained with all the host data considered together. These results indicate that lumping host data can hide important variations in aggregation between hosts and can exaggerate the true degree of aggregation. Wherever possible common k estimates should be used to estimate the degree of aggregation. In addition, significant differences in the degree of aggregation between subgroups of host data, were generally associated with significant differences in both mean parasite burdens and the prevalence of infection.

Animals↗

PubMed1996

Establishment probability in fluctuating environments: a branching process model.

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.

Demography↗

PubMed2001

Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations.

The maximum-likelihood (ML) expectation-maximization (EM) [ML-EM] algorithm is being widely used for image reconstruction in positron emission tomography. The algorithm is strictly valid if the data are Poisson distributed. However, it is also often applied to processed sinograms that do not meet this requirement. This may sometimes lead to suboptimal results: streak artifacts appear and the algorithm converges toward a lower likelihood value. As a remedy, we propose two simple pixel-by-pixel methods [noise equivalent counts (NEC)-scaling and NEC-shifting] in order to transform arbitrary sinogram noise into noise which is approximately Poisson distributed (the first and second moments of the distribution match those of the Poisson distribution). The convergence speed associated with both transformation methods is compared, and the NEC-scaling method is validated with both simulations and clinical data. These new methods extend the ML-EM algorithm to a general purpose nonnegative reconstruction algorithm.

Algorithms↗

PubMed1988

Neurofilaments are spaced randomly in the radial dimension of axons.

The organization of the cytoskeleton is compared in the large myelinated parasympathetic and somatic motor axons of the avian oculomotor system. Electron microscopic studies demonstrate that neurofilaments are the chief structural elements in these axons, and quantitative analyses of the distribution of neurofilaments in axonal cross-sections found that the average neurofilament packing density is 25% greater in the parasympathetic axons than in the somatic motor axons. In both types of axon the distributions of neurofilaments matched a randomly generated (Poisson) distribution. In axoplasm, a Poisson distribution could arise if the neurofilaments were distributed in the cross-sectional plane by stochastic forces operating randomly and without significant neurofilament-neurofilament interactions. Thus, in these axons, the neurofilaments behave as if they are inert 'molecules' in a dilute solution-subject to non-specific stochastic forces that tend to distribute them at random. We propose that neurofilaments normally are relatively free to move apart from each other and to fill the available space within the axon.

Animals↗