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PubMed1999

Stochastic nature of precisely timed spike patterns in visual system neuronal responses.

It is not clear how information related to cognitive or psychological processes is carried by or represented in the responses of single neurons. One provocative proposal is that precisely timed spike patterns play a role in carrying such information. This would require that these spike patterns have the potential for carrying information that would not be available from other measures such as spike count or latency. We examined exactly timed (1-ms precision) triplets and quadruplets of spikes in the stimulus-elicited responses of lateral geniculate nucleus (LGN) and primary visual cortex (V1) neurons of the awake fixating rhesus monkey. Large numbers of these precisely timed spike patterns were found. Information theoretical analysis showed that the precisely timed spike patterns carried only information already available from spike count, suggesting that the number of precisely timed spike patterns was related to firing rate. We therefore examined statistical models relating precisely timed spike patterns to response strength. Previous statistical models use observed properties of neuronal responses such as the peristimulus time histogram, interspike interval, and/or spike count distributions to constrain the parameters of the model. We examined a new stochastic model, which unlike previous models included all three of these constraints and unlike previous models predicted the numbers and types of observed precisely timed spike patterns. This shows that the precise temporal structures of stimulus-elicited responses in LGN and V1 can occur by chance. We show that any deviation of the spike count distribution, no matter how small, from a Poisson distribution necessarily changes the number of precisely timed spike patterns expected in neural responses. Overall the results indicate that the fine temporal structure of responses can only be interpreted once all the coarse temporal statistics of neural responses have been taken into account.

Action Potentials↗
PubMed1999

Annual variation in birth rate of people who subsequently develop schizophrenia.

BACKGROUND: Previous attempts to decide whether there is significant year-to-year variation in the birth rate of people who subsequently develop schizophrenia have given conflicting results, probably because of differences in the statistical methods employed. AIMS: To determine whether there is significant year-to-year variation in the birth rate. METHOD: Variation in the birth rate for the period 1921-1960 was studied in three separate national data sets--English, Danish and Scottish--using cubic splines to smooth the distribution curve before calculating residuals from a Poisson distribution. RESULTS: Over-dispersion was found in all three data sets, particularly in the Danish and Scottish data. However, the correlation between the sets of standardised residuals derived from the three data sets was only statistically significant for Denmark v. England. CONCLUSIONS: There was statistically significant year-to-year variation in the birth rate of people who subsequently developed schizophrenia in three countries in north-west Europe in the years 1921-1960. This is potentially a clue to the nature of the environmental determinants of schizophrenia, but better data will be needed before useful explanatory hypotheses can be generated and tested.

Adult↗
PubMed2001

A stochastic model for the self-similar heterogeneity of regional organ blood flow.

The theory of exponential dispersion models was applied to construct a stochastic model for heterogeneities in regional organ blood flow as inferred from the deposition of labeled microspheres. The requirements that the dispersion model be additive (or reproductive), scale invariant, and represent a compound Poisson distribution, implied that the relative dispersion (RD = standard deviation/mean) of blood flow should exhibit self-similar scaling in macroscopic tissue samples of masses m and m(ref) such that RD(m) = RD(m(ref)). (m/m(ref))(1-D), where D was a constant. Under these circumstances this empirical relationship was a consequence of a compound Poisson-gamma distribution that represented macroscopic blood flow. The model also predicted that blood flow, at the microcirculatory level, should also be heterogeneous but obey a gamma distribution-a prediction supported by observation.

Blood Flow Velocity↗
PubMed2003

Neural population codes.

In many regions of the brain, information is represented by patterns of activity occurring over populations of neurons. Understanding the encoding of information in neural population activity is important both for grasping the fundamental computations underlying brain function, and for interpreting signals that may be useful for the control of prosthetic devices. We concentrate on the representation of information in neurons with Poisson spike statistics, in which information is contained in the average spike firing rate. We analyze the properties of population codes in terms of the tuning functions that describe individual neuron behavior. The discussion centers on three computational questions: first, what information is encoded in a population; second, how does the brain compute using populations; and third, when is a population optimal? To answer these questions, we discuss several methods for decoding population activity in an experimental setting. We also discuss how computation can be performed within the brain in networks of interconnected populations. Finally, we examine questions of optimal design of population codes that may help to explain their particular form and the set of variables that are best represented. We show that for population codes based on neurons that have a Poisson distribution of spike probabilities, the behavior and computational properties of the code can be understood in terms of the tuning properties of individual cells.

Action Potentials↗
PubMed2006

Methods for analysing recurrent events in health care data. Examples from admissions in Ebeltoft Health Promotion Project.

BACKGROUND: Evaluation of health care contacts from first events alone often misses large amounts of potentially important data and may produce different results than evaluation of all data including recurrent events. OBJECTIVE: We aim to bring the different methodological approaches for analysing longitudinal health care data to the attention of researchers in primary care. METHODS: We used hospital admission data from the Ebeltoft Health Promotion Project, a randomized trial in primary care examining the effect of preventive health checks. Comparisons included three randomized groups: an intervention group receiving health checks, a group where intervention consisted of a health check followed by a health discussion with the GP and one control group. RESULTS: Both intervention groups had approximately 20% fewer hospital admissions than the control group over a 6 year period. If dependence among recurrent events is excluded, such a reduction amounts to a highly significant effect. Use of the standard Poisson distribution for analysing recurrent events and exclusion of their dependent structure causes data interpretation to be incorrect, because the model does not account for the extra variability between persons; the resulting 95% CIs would therefore be too small. CONCLUSION: Analysis of health care contacts should embrace both first and recurrent events and it should use a model appropriate to these data. An individual rate model that includes a parameter of an unspecified individual event distribution frailty may be a natural choice when analysing longitudinal data of contacts to the health care system in broad terms.

Denmark↗
PubMed2006

Description of a new all cause mortality surveillance system in Sweden as a warning system using threshold detection algorithms.

A warning system has been set up to detect unusual weekly clusters of deaths by age group and municipality using all-cause Swedish death registry data. The technique for monitoring deaths by age group (<1, 1-24, 25-44, 45-64 and 65 plus) and week uses a compound smoothing technique, which calculates a baseline of expected events from retrospective data. Due to insufficient baseline data for the geographical component of the system a different algorithm, based on the Poisson distribution, was chosen to calculate expected weekly number of deaths per municipality, adjusting for municipalities with inherently higher mortality rates. This system was designed and tested during 2004 and implemented from the beginning of 2005. Threshold settings have been adjusted to provide a realistic number of weekly alerts. An evaluation of the system will be performed prospectively from the beginning of 2005 due to the lack of a gold standard for retrospective performance evaluation.

Adolescent↗
PubMed2002

Formulation of a soil-pesticide transport model based on a compartmental approach.

A semianalytical soil-pesticide transport model is formulated based on a compartmental approach to determine spatial and temporal variations of pesticide residues across a soil profile. The compartmental model is implemented by drawing an analogy between a series of continuous-flow stirred tank reactors and a soil horizon that consists of multiple perfectly mixed compartments. The analogy is strengthened by exploiting a relation between the compartment series and the conventional convective-dispersive equation (CDE) for vertical transport in the soil. Consequently, the number of compartments in the model formulation is not free, but dictated as a function of transport parameters. The model formulation allows consideration of arbitrary boundary value specifications and also, for some cases, spatially varying initial concentration profiles. Sorption kinetics is represented via a two-site model that involves a linear sorption isotherm and a first-order irreversible sorption or a radial diffusive penetrating model. For these three cases, analysis of the compartmental model allows the resultant concentration profiles to be expressed in terms of the Poisson distribution. When a nonlinear kinetic sorption model is used to simulate the sorption processes, an analytical solution is not found and a numerical approach is required.

Atrazine↗
PubMed2002

An evaluation of spatio-temporal models for the estimation of the mortality relative risk from breast cancer in Galicia, Spain.

BACKGROUND: Disease mapping is now a big focus of interest in the area of Public Health, and the geographical distribution of a disease has an important role in understanding its origin or its causes. The purpose of this work is to review and evaluate different techniques to map the mortality risk of a disease in small geographical areas. METHODS: Three different methods have been studied. The first one is a classical approach consisting of mapping SMRs, which are maximum likelihood estimates of the relative risk under a Poisson model of death counts. In a second step we consider Poisson and negative binomial regression to fit the rates and finally we use a Bayesian approach that assumes a hierarchical model where the death counts follow a Poisson distribution conditioned by the prior information. These methods have been applied to the study of geographical variation in female breast cancer mortality from 1976 to 1999 in the districts of Galicia, Spain. RESULTS: Mapping the SMRs using the first method has important drawbacks and there are difficulties to distinguish the mortality pattern. With the second method we achieved some improvements. The Bayesian methodology produces smoother maps with a clear mortality pattern. DISCUSSION: These methods are powerful tools for identifying areas with elevated risk. The Bayesian methodology has many advantages over the other methods that had been analysed in this work.

Adult↗
PubMedDate not supplied

Spatial variation of natural radiation and childhood leukaemia incidence in Great Britain.

This paper describes an analysis of the geographical variation of childhood leukaemia incidence in Great Britain over a 15 year period in relation to natural radiation (gamma and radon). Data at the level of the 459 district level local authorities in England, Wales and regional districts in Scotland are analysed in two complementary ways: first, by Poisson regressions with the inclusion of environmental covariates and a smooth spatial structure; secondly, by a hierarchical Bayesian model in which extra-Poisson variability is modelled explicitly in terms of spatial and non-spatial components. From this analysis, we deduce a strong indication that a main part of the variability is accounted for by a local neighbourhood 'clustering' structure. This structure is furthermore relatively stable over the 15 year period for the lymphocytic leukaemias which make up the majority of observed cases. We found no evidence of a positive association of childhood leukaemia incidence with outdoor or indoor gamma radiation levels. There is no consistent evidence of any association with radon levels. Indeed, in the Poisson regressions, a significant positive association was only observed for one 5-year period, a result which is not compatible with a stable environmental effect. Moreover, this positive association became clearly non-significant when over-dispersion relative to the Poisson distribution was taken into account.

Air Pollution, Indoor↗
PubMedDate not supplied

The four county study of childhood cancer: clusters in context.

Observations of childhood 'cancer clusters' in small communities in central California prompted us to examine the distribution of childhood cancer in communities throughout the region to see if the overall cancer rate or the distribution of 'cancer clusters' was unusual for agricultural towns where pesticide exposure might be elevated. The distribution of rates was evaluated using a variety of methods: comparison of rates to the regional average, evaluation of the empirical observed versus expected Poisson distribution of events, and multivariate modelling using Poisson regression. These analyses suggest that there were no previously undiscovered communities with excess rates, although the index community which prompted the initial investigation does stand out as unusual. We discuss the impact of a range of forces of morbidity on the likelihood of 'cancer clusters' and the distributions of observed and expected numbers of cancers in a population of locales.

Adolescent↗
PubMed1991

Modeling the overdispersion of parasite loads.

Many epidemic models lead to an approximately Poisson distribution of parasites among hosts. This is at variance with observation, where heavy overdispersion is the rule. A simple model is proposed that, while treating individuals alike, nonetheless gives rise to highly variable parasite loads.

Animals↗
PubMed1993

[Analysis of the geographic distribution of the incidence of diabetes mellitus type I in Catalonia].

BACKGROUND: The aim of the present study was to evaluate the geographic distribution of the incidence of diabetes mellitus type I (DMI) in Catalonia from 1987-1990. METHODS: The base of the study is the Catalonian registry of incidence of DMI in the period from 1987-1990. The definition criteria were: diagnostic criteria of diabetes (WHO norms 1985), age of diagnosis under 30 years, residence in Catalonia in the period of diagnosis and exclusion of other types of diabetes. The population at risk was estimated according to the general census of the population of 1986. The total incidence of Catalonia was calculated by provinces and counties according to the Poisson distribution. RESULTS: The incidence of DMI observed in Catalonia was of 11.5/100,000 inhabitants per year (CI 95%, 10.6-12.4) in the age group from 0-14 years and 10.7/100,000 inhabitants per year (CI 95% 10.1-11.3) in the age group from 0-29 years. The exhaustivity in the detection of the cases was of 90.3%. No differences were found in interprovincial incidence in the 0-14 age group: Barcelona 11.6 (10.6-12.7), Girona 10.2 (7.2-13.4), Lleida 11.7 (7.7-15.8), Tarragona 10.5 (7.6-13.5). In the 15-29 age group a lower incidence was observed in Tarragona. The incidence by counties varied between 2.9 and 15.0/100,000 inhabitants per year with those of greatest incidence being observed in the Vallés Oriental (15.0/100,000 inhabitants/years), Alt Penedés (14.5/100,000 inhabitants/year), Segrià (15.0/100,000 inhabitants/year) and the Priorat (13.7/100,000 inhabitants/year). CONCLUSIONS: No differences were found in the incidence of diabetes mellitus type I in the four Catalonian provinces. Distribution by counties was more heterogeneous without defining zones with a much higher incidence to that observed in the whole of Catalonia.

Adolescent↗
PubMed2007

Optimal designs for radiation retention with poisson correlated response.

In this paper we describe a non-linear model with correlated observations which accounts for the elimination rate of radiation in the lung of individuals who have been exposed to an accidental intake at some time. The response is then modelled as a conditional Poisson distribution. When the leak is moderate or the size of the particles is large a theoretical justification of this assumption is given and D-optimal designs are computed.

Dose-Response Relationship, Radiation↗
PubMed1992

An inferential procedure for the Poisson intervention parameter.

To describe a health chance mechanism whose incidence rate is altered in the middle of a data collection period due to preventive treatments taken by health service agencies, a model called Intervened Poisson Distribution (cf. Shanmugam, 1985, Biometrics 41, 1025-1029) was introduced. In this article, we derive a statistic to test the hypothesis concerning the effectiveness of such preventive treatments, and compare its power with another suggested test (cf. Streit, 1987, Biometrics 43, 999-1000).

Health Services↗
PubMedDate not supplied

Prevalence of tetraploid metaphases in semidirect and cultured chorionic villi.

OBJECTIVE: Investigation of the normal frequency of tetraploid metaphases in semidirect (STC) and cultured (LTC) chorionic villi. METHODS: Fifty metaphases in STC- and in LTC-villi slides of 100 women of advanced maternal age were screened for tetraploidy. RESULTS: Up to three tetraploid metaphases were encountered in 27% of the STC-villi preparations; the scores fitted a Poisson distribution. In all LTC-villi preparations tetraploid cells were seen; the scores fitted a log-Gaussian distribution. CONCLUSIONS: On the basis of these distributions, we propose a protocol for the management of tetraploid metaphases in chorionic villi, strongly reducing the number of prenatal follow-up investigations.

Cells, Cultured↗
PubMed1994

Sample size requirements for evaluating heart valves with constant risk events.

A method is described for computing sample size requirements for a clinical study of a new heart valve, according to the guidance document recently revised by the FDA. The FDA requirements specify a one-sample hypothesis test in which the complication rates for the study valve are compared to fixed values determined from previous experience with approved devices. These values, which can differ for different complications and for mechanical or tissue valve types, are called OPC's (Objective Performance Criteria). The method described, using the Poisson distribution, provides a simple formula for computing the valve-years required corresponding to any OPC. At the OPC level required by the FDA guidelines (1.2%/year), the minimum follow-up necessary is about 800 valve-years.

Guidelines as Topic↗
PubMed2005

Duality of fatigue failures of materials caused by Poisson defect statistics of competing failure modes.

The statistical nature of failures of components subjected to fatigue loading is a major challenge in engineering applications. Here, we report an interesting fatigue phenomenon in which there is a 'duality' of the S-N fatigue data (S is stress and N is cycles to failure)--the grouping of data into two distinct S-N curves as a result of two competing failure modes. The proportions of failure by either mode are about the same and one cannot predict which failure mode will eventually dominate. This means that fatigue lives may be unpredictable in materials under certain application conditions and the consequences can be disastrous. Based on Poisson defect statistics and Monte Carlo simulations, we show that this phenomenon can arise from the Poisson distribution of low populations of microscale defects. An unexpected finding is that there should be a combination of average defect density and specimen area at which this phenomenon is observable in materials having sparsely populated defects.

Algorithms↗