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PubMed1993

Exploring the energy landscape in proteins.

We present two methods to probe the energy landscape and motions of proteins in the context of molecular dynamics simulations of the helix-forming S-peptide of RNase A and the RNase A-3'-UMP enzyme-product complex. The first method uses the generalized ergodic measure to compute the rate of conformational space sampling. Using the dynamics of nonbonded forces as a means of probing the time scale for ergodicity to be obtained, we argue that even in a relatively short time (< 10 psec) several different conformational substrates are sampled. At longer times, barriers on the order of a few kcal/mol (1 cal = 4.184 J) are involved in the large-scale motion of proteins. We also present an approximate method for evaluating the distribution of barrier heights g(EB) using the instantaneous normal-mode spectra of a protein. For the S-peptide, we show that g(EB) is adequately represented by a Poisson distribution. By comparing with previous work on other systems, we suggest that the statistical characteristics of the energy landscape may be a "universal" feature of all proteins.

Amino Acid Sequence↗

PubMed2007

A score test for overdispersion in zero-inflated poisson mixed regression model.

Count data with extra zeros are common in many medical applications. The zero-inflated Poisson (ZIP) regression model is useful to analyse such data. For hierarchical or correlated count data where the observations are either clustered or represent repeated outcomes from individual subjects, a class of ZIP mixed regression models may be appropriate. However, the ZIP parameter estimates can be severely biased if the non-zero counts are overdispersed in relation to the Poisson distribution. In this paper, a score test is proposed for testing the ZIP mixed regression model against the zero-inflated negative binomial alternative. Sampling distribution and power of the test statistic are evaluated by simulation studies. The results show that the test statistic performs satisfactorily under a wide range of conditions. The test procedure is applied to pancreas disorder length of stay that comprised mainly same-day separations and simultaneous prolonged hospitalizations.

Adult↗

PubMed2001

The application of Poisson units to the determination of median lethal cell culture dose.

The median lethal cell culture dose (CCLD(50)) and its 95% confidence interval were determined using the Behrens and Kärber area method with subsequent regression analysis by the action of methylmercury iodide (CH(3)HgI; MMI) on monolayer cultures of HeLa cells. The concentrations of MMI were 0.45, 0.9, 1.8, 3.65, 7.3 and 14.6 microM/l. The duration of MMI action was 24 h. All the calculations were performed with means of sample cell numbers derived from Poisson units. The basis for deriving the Poisson units is the Poisson distribution property on the equality mean to variance or, which is the same, on the equality standard deviation to the root square of mean. Because the size of Poisson unit is predetermined, it is a simple task to find the mean. The outcome of any single count of discrete random objects in the definite area or time interval is divided by the number of Poisson units. The Poisson unit for counting cultured cells was derived by us in relation to Gorjaev's net. In this case it is appropriate to count the cells on the square equal to two Gorjaev's nets. The corresponding Poisson unit is equal to 1/5 of Gorjaev's net (45 big squares). Near-coincidence of CCLD(50) as well as its 95% confidence intervals by use of logarithmic and linear models was observed. However, the former approach was better than the second. CCLD(50) and its 95% confidence interval values, obtained with the aid of the logarithmic model in three series of experiments, were 2.56+/-0.33, 2.09+/-0.37 and 2.31+/-0.37 microM/l.

Cell Count↗

PubMed2000

Misconceptions and false expectations in neutral evolution.

Neutral evolution results from random recurrent mutation and genetic drift. A small part of random evolution, that which is related to protein or DNA polymorphisms, is the subject of the Neutral Theory of Evolution. One of the foundations of this theory is the demonstration that the mutation rate (m) is equal to the substitution rate. Since both rates are independent of population size, they are independent of drift, which is dependent upon population size. Neutralists have erroneously equated the substitution rate with the fixation rate, despite the fact that they are antithetical conceptions. The neutralists then applied the random walk stochastic model to justify alleles or bases that were fixated or eliminated. In this model, once the allele or base frequencies reach the monomorphic states (values of 1.0 or 0.0), the absorbing barriers, they can no longer return to the polymorphic state. This operates in a pure mathematical model. If recurrent mutation occurs (as in biotic real systems) fixation and elimination are impossible. A population of bacteria in which m = 10(-8) base mutation (or substitution)/site/generation and the reproduction rate is 1000 cell cycle/year should replace all its genome bases in approximately 100,000 years. The expected situation for all sites is polymorphism for the four bases rather than monomorphism at 1.0 or 0.0 frequencies. If fixation and elimination of a base for more than 500,000 years are impossible, then most of the neutral theory is untenable. A new complete neutral model, which allows for recurrent substitutions, is proposed here based on recurrent mutation or substitution and drift alone. The model fits a binomial or Poisson distribution and not a geometric one, as does neutral theory.

Bacteria↗

PubMed1996

Detection of overall space-time clustering in a non-uniformly distributed population. DiMe Study Group.

We developed a test statistic based on an approach of Whittemore et al. (1987) to detect space-time clustering for non-infectious diseases. We extended the spatial test of Whittemore et al. by deriving conditional probabilities for Poisson distributed random variables. To combine spatial and time distances we defined a distance matrix D, where dij is the distance between the ith and jth cell in a three-dimensional space-time grid. Spatial and temporal components are controlled by a weight. By altering the weight, both marginal tests and the intermediate test can be reached. Allowing a continuum from a pure spatial to a pure temporal test, the best result will be gained by trying different weights, because the occurrence of a disease might show some temporal and some spatial tendency to cluster. We examined the behaviour of the test statistic by simulating different distributions for cases and the population. The test was applied to the incidence data of insulin-dependent diabetes mellitus in Finland. This test could be used in the analysis of data which are localized according to map co-ordinates, by addresses or postcodes. This information is important when using the Geographical Information System (GIS) technology to compute the pairwise distances needed for the proposed test.

Child↗

PubMed2003

The structure of self-reported emotional experiences: a mixed-effects Poisson factor model.

Multivariate count data are commonly analysed by using Poisson distributions with varying intensity parameters, resulting in a random-effects model. In the analysis of a data set on the frequency of different emotion experiences we find that a Poisson model with a single random effect does not yield an adequate fit. An alternative model that requires as many random effects as emotion categories requires high-dimensional integration and the estimation of a large number of parameters. As a solution to these computational problems, we propose a factor-analytic Poisson model and show that a two-dimensional factor model fits the reported data very well. Moreover, it yields a substantively satisfactory solution: one factor describing the degree of pleasantness and unpleasantness of emotions and the other factor describing the activation levels of the emotions. We discuss the incorporation of covariates to facilitate rigorous tests of the random-effects structure. Marginal maximum likelihood methods lead to straight-forward estimation of the model, for which goodness-of-fit tests are also presented.

Arousal↗

PubMed1990

A statistical method for evaluating suicide clusters and implementing cluster surveillance.

The absence of any standard definition of suicide cluster events hinders understanding of the prevalence of the problem, hinders the development of appropriate public health responses to observed clusters, and ultimately hinders investigation of the mechanisms underlying contagious communication of suicidal behavior. The authors introduce a Poisson mixture model for assessing potential clusters of adolescent suicide, apply that model to the monthly incidence rates of adolescent suicide for one populous US county over the last 11 years, and generate 99% tolerance limits with 95% confidence for the number of suicides which may occur by chance within specific intervals of time in that county. The suicide incidence data showed a remarkable fit to a single Poisson distribution, suggesting it is not unreasonable to consider the cases as randomly-distributed and independent events. The authors conclude that there is no evidence that adolescent suicides occurred in clusters in the place and in the time frame under study, and recommend the Poisson mixture model for ascertaining clusters as well as implementing cluster surveillance.

Adolescent↗

PubMed1992

[Chiasma distribution in the lampbrush chromosomes of the chicken Gallus gallus domesticus: hot spots of recombination and their possible role in proper dysjunction of homologous chromosomes at the first meiotic division].

Chiasma distribution in the lambrush chromosomes of the chicken Gallus gallus domesticus was studied. The data of the authors show that the general pattern of chiasmata in the interstitional region of chromosomes corresponds to the Poisson distribution. However, in the telomeric and subtelomeric regions of all chicken macrochromosomes one can see chiasma as a rule. In the half of 140 microchromosomes from 24 different oocytes, there are also the telomeric chiasmata. On the basis of this observation, it may be predicted that there are hot spots of recombination near or into the telomeric GC-rich heterochromatic bands of chicken chromosomes. We suggest that these hot spots of recombination near the telomeres are a necessary facility for not only macrochromosomes but all microchromosomes as well to have at least one chiasma. The constant presence of at least one chiasma in a bivalent in needed for correct disjunction of homologous chromosomes at the first meiotic division.

Animals↗

PubMed2003

Benign essential blepharospasm among residents of Olmsted County, Minnesota, 1976 to 1995: an epidemiologic study.

PURPOSE: To describe the incidence, patient demographics, and response to treatment of benign essential blepharospasm (BEB) in a population-based cohort. METHODS: In this epidemiologic study, we searched the Rochester Epidemiology Project database for patients diagnosed with blepharospasm or related disorders between 1976 and 1995. The incident rate denominator was based on a linear interpolation of decennial census data from Olmsted County. The 95% confidence interval for the incidence rate was based on the Poisson distribution. RESULTS: Olmsted County residents (n = 295) were diagnosed with blepharospasm or related disorders between 1976 and 1995. Of these, 8 patients met the criteria for BEB. The calculated incidence rate of BEB is 1.2 persons per 100,000 population per year (95% CI, 0.37 to 2.02). At the time of BEB diagnosis, the median patient age was 61.5 years, and symptoms had been present for a median of 24 months. Four patients were men and 4 were women. Four of the 8 patients had Meige syndrome. Three of 4 patients treated with oral medications reported symptomatic improvement. Botulinum toxin injection was offered to all patients, but only 4 elected treatment. All who were treated with botulinum toxin had temporary symptomatic improvement. No patient underwent surgical treatment for BEB. Two patients had resolution of symptoms within the follow-up period. CONCLUSIONS: BEB is a rare disorder. In this small, population-based sample, women and men were affected with equal frequency, and half of patients had lower facial dystonia (Meige syndrome). Only half of patients with BEB elected botulinum toxin injections, and none required surgery. Disease remission occurred in 2 of 8 patients.

Adult↗

PubMed2006

Bayesian analysis of the differences of count data.

Paired count data usually arise in medicine when before and after treatment measurements are considered. In the present paper we assume that the correlated paired count data follow a bivariate Poisson distribution in order to derive the distribution of their difference. The derived distribution is shown to be the same as the one derived for the difference of the independent Poisson variables, thus recasting interest on the distribution introduced by Skellam. Using this distribution we remove correlation, which naturally exists in paired data, and we improve the quality of our inference by using exact distributions instead of normal approximations. The zero-inflated version is considered to account for an excess of zero counts. Bayesian estimation and hypothesis testing for the models considered are discussed. An example from dental epidemiology is used to illustrate the proposed methodology.

Algorithms↗

PubMed1999

Suppression of positional errors in biological development.

Cells in developing embryos behave according to their positions in the organism, and therefore seem to be receiving 'positional information'. A widespread view of the mechanism for this is that each cell responds locally to the concentration level of some extracellular chemical which is distributed in a spatial gradient. For molecules conveying and receiving the positional signal, concentrations are likely to be low enough that, per individual cell, only a few thousand molecules may be involved. Fluctuations to be expected in these numbers (Poisson distribution) could readily lead to errors up to a few percent of embryo length in the reading of position. This is an intolerable level of error for some developmental pattern-forming events. Embryos must have means of suppressing such errors. We maintain that this requires communication between cells, and illustrate this by using the reaction part of two well-known Turing-type reaction-diffusion models as the local gradient reader. We show that switching on diffusion in these models leads to adequate suppression of positional errors.

Animals↗

PubMed1991

CANEST: a microcomputer program for estimating cancer in a cohort.

Certain diseases and symptoms carry an overrepresentation of cancer. To be able to measure the strength of such an association it is necessary to be able to predict cancer development in the group being observed. A computer program for computers running under the MS DOS operating system has been developed for this purpose. The program is written in the CLIPPER programming language. The estimates are based on incidence and prevalence data from the Swedish Cancer Registry for the years 1958 to 1986. The program also computes confidence intervals based on the Poisson distribution. The results can be printed out or exported to other programs for further analysis.

Cohort Studies↗

PubMed1991

An empirical Bayes formulation of cohort models in cancer epidemiology.

This paper concerns the incidence rates of malignant skin melanoma for several age-sex groups and time periods in three geographic regions, uses a method of cohort analysis and employs a two-stage random effects model. The first stage entails the assumption that the within-region variation in the frequency of disease incidence for a fixed age-sex-cohort group has a Poisson distribution with mean proportional to the population at risk. The second stage, after adjusting for age and sex, entails the assumption that the between-region geographic variation in the logarithm of the true incidence rate has a prior distribution with parameters estimated by the method of maximum likelihood. After adjusting for age effects, we estimate random geographic-specific cohort effects for each sex with use of an empirical Bayes method and compare the results with the usual multiplicative Poisson model that assumes fixed geographic-specific cohort effects for each sex. This comparison shows that the method presented here provides more stable estimates of geographic-specific cohort effects, and in addition the random effects model describes these data more adequately.

Adult↗

PubMedDate not supplied

[Trends in the incidence of hepatic tumors in childhood].

OBJECTIVE: To evaluate the incidence trends of hepatic tumors among children living in Mexico City. MATERIAL AND METHODS: A cross-sectional hospital survey was conducted to yield two databases. The first database contains the registry of all the cases of hepatic tumors occurring during the period 1982-1991, in public hospitals of Mexico City. The second database contains all hepatic tumor cases found between 1996 and 1999 in Hospital de Pediatría del Centro Médico Nacional "Siglo XXI" and in Hospital General del Centro Médico La Raza, both hospitals pertaining to Instituto Mexicano del Seguro Social (Mexican Institute of Social Security). The average annual incidence rates (AAIR) were calculated for each type of hepatic tumor. The rates were standardized with the direct method, using as standard the world population under 15 years of age. The trends were evaluated with the annual incidence rates and the average rate of change assuming a Poisson distribution. RESULTS: The AAIR for hepatoblastoma during the period 1982-1991 was three times higher for men than for women, with a value of 0.6 x 10(6). The group of 1-4 years of age was the most affected. For hepatocarcinomas the AAIR was two-fold for women (0.14) as compared to men. Between 1996-1999 the AAIR for hepatoblastoma was 5.11 in women and 1.85 in men. The age group with the highest rate was women under one year of age. The AAIR for hepatocarcinoma was 0.64 for males and 1.23 for females. The most affected age group was males aged 10 to 14 years. No significant upward or downward trend was found in the incidence of hepatoblastomas. A non-significant change rate of 10% was found for hepatocarcinoma. CONCLUSIONS: No significant trends were observed in the incidence of hepatic tumors in children of Mexico City aged under 15 years, during the periods 1982-1991 and 1996-1999. The English version of this paper is available at: http://www.insp.mx/salud/index.html.

Adolescent↗

PubMed1996

Improved models of tumour cure.

The standard mechanistic model for the probability of tumour cure (the "Poisson model') is based on the assumption that the number of surviving clonogens at the end of treatment follows a Poisson distribution from tumour to tumour. This assumption is not correct, however, if proliferation of tumour clonogens occurs during treatment, as would be expected in general during a fractionated course of radiotherapy. In the present study, the possible magnitude of the error in the Poisson model was investigated for tumours treated with either conventional fractionation or split-course therapy. An example is presented in which the Poisson model has an absolute error of nearly 100%, predicting a cure rate of 0% when in fact the cure rate was close to 100%. The largest errors in the Poisson model found in this study were for very small tumours (approximately 100 clonogens), but for larger tumours (> or = 10(6) clonogens), the Poisson model may still be highly inaccurate, predicting a cure rate that differs from the actual cure rate by as much as 40%. Three new tumour-cure models are proposed (the GS, PS, and GS+ models), and their accuracy is also investigated. Two of these (the GS and PS models) are better than the Poisson model for the clinically relevant cases tested here. The third model, the GS+ model, consistently produced the most accurate estimate of the tumour cure rate, but has more limited use than the GS and PS models because it is more highly parametrized. It is demonstrated here that no tumour-cure model based on the effective clonogen doubling time will be perfectly accurate in all cases, since the cure rate depends on the details of the cell kinetics contributing to the effective doubling time.

Clone Cells↗

PubMedDate not supplied

A planning model for requirement of emergency beds.

In-patient bed requirement (or number of beds required to cope with the workload) is of prime importance for hospital management because of its direct implication for manpower requirement and therefore the costs. In-patient beds could be divided into emergency beds and elective beds, where the requirement for emergency beds will be affected by both patient length of stay distributions and the random patterns in which patients arrive. In this paper, the author extends the early results by Pike et al. (1963, Br. J. Prev. Soc. Med. 17, 172) so that day-of-week effect is introduced into the queuing model to evaluate the requirement of emergency beds. It is demonstrated that emergency bed occupancy on any specific day of the week follows a Poisson distribution.

Emergency Service, Hospital↗

PubMedDate not supplied

Spontaneous and induced micronuclei and UDS in peripheral lymphocytes.

We have examined the distributions both of spontaneous and X-ray-induced micronuclei (MN) and of spontaneous and UV-induced unscheduled DNA synthesis (autoradiographic grains; UDS) in cultures of peripheral blood lymphocytes from normal, healthy human volunteers. While the spontaneous MN and UDS do not differ significantly from the expected Poisson distributions, both the induced MN and UDS are strongly overdistributed (i.e., variance much greater than mean). This not only must be allowed for in statistical tests used for population monitoring, but offers suggestive evidence that there are large differences in radiation response from sample to sample, some of which may reflect true differences among normal, healthy subjects.

Adult↗

PubMed2002

Risk of second cancers in patients with colorectal carcinoids.

INTRODUCTION: It is often stated that patients with colorectal carcinoid tumors have an increased risk of developing other malignancies. However, this risk has not been conclusively documented. A comprehensive evaluation is needed to more thoroughly assess the risk of second cancers in patients with colorectal carcinoids. METHODS: A search of the National Cancer Institute Surveillance, Epidemiology, and End Result database from 1973 to 1996 revealed 2,086 patients with colorectal carcinoids. This subset of patients was examined for occurrence of second cancers. The observed incidence of cancer for each site was compared with the expected incidence based on the gender-adjusted and age-adjusted cancer rates in the remaining Surveillance, Epidemiology, and End Result file. A Poisson distribution probability was used to determine the significance of these comparisons. RESULTS: Patients with colorectal carcinoids had an increased rate of cancer in the colon and rectum (P < 0.001), small bowel (P < 0.001), esophagus/stomach (P = 0.02), lung/bronchus (P < 0.001), urinary tract (P = 0.005), and prostate (P < 0.001), when compared with a control population. Most of the gastrointestinal tract cancers were synchronous cancers, whereas lesions outside the gastrointestinal tract were most commonly metachronous tumors. CONCLUSIONS: A significantly increased risk of synchronous colorectal, small-bowel, gastric, and esophageal cancers and metachronous lung, prostate, and urinary tract neoplasms is clearly demonstrated. After the diagnosis of colorectal carcinoid tumors, patients should undergo appropriate screening and surveillance for cancer at these sites.

Age Distribution↗