Count data

Mixture modeling within the context of pharmacokinetic (PK)/pharmacodynamic (PD) mixed effects modeling is a useful tool to explore a population for the presence of two or more subpopulations, not explained by evaluated covariates. At present, statistical tests for the existence of mixed populations have not been developed. Therefore, a simulation study was undertaken to evaluate mixture modeling with NONMEM and explore the following questions. First, what is the probability of concluding that a mixed population exists when there truly is not a mixture (false positive significance level)? Second, what is the probability of concluding that a mixed population (two subpopulations) exists when there is truly a mixed population (power), and how well can the mixture be estimated, both in terms of the population parameters and the individual subject classification. Seizure count data were simulated using a Poisson distribution such that each subject's count could decrease from its baseline value, as a function of dose via an Emax model. The dosing design for the simulation was based on a trial with the investigational anti-epileptic drug pregabalin. Four hundred and forty seven subjects received pregabalin as add on therapy for partial seizures, each with a baseline seizure count and up to three subsequent seizure counts. For the mixtures, the two subpopulations were simulated to differ in their Emax values and relative proportions. One subpopulation always had its Emax set to unity (Emax hi), allowing the count to approach zero with increasing dose. The other subpopulation was allowed to vary in its Emax value (Emax lo=0.75, 0.5, 0.25, and 0) and in its relative proportion (pr) of the population (pr=0.05, 0.10, 0.25, and 0.50) giving a total of 4 ⋅ 4=16 different mixtures explored. Three hundred data sets were simulated for each scenario and estimations performed using NONMEM. Metrics used information about the parameter estimates, their standard errors (SE), the difference between minimum objective function (MOF) values for mixture and non-mixture models (MOF(δ)), the proportion of subjects classified correctly, and the estimated conditional probabilities of a subject being simulated as having Emax lo (Emax hi) given that they were estimated as having Emaxlo (Emax hi) and being estimated as having Emaxlo (Emax hi) given that they were simulated as having Emax lo (Emax hi). The false positive significance level was approximately 0.04 (using all 300 runs) or 0.078 (using only those runs with a successful covariance step), when there was no mixture. When simulating mixed data and for those characterizations with successful estimation and covariance steps, the median (range) percentage of 95% confidence intervals containing the true values for the parameters defining the mixture were 94% (89–96%), 89.5% (58–96%), and 95% (92–97%) for pr, Emax lo, and Emax hi, respectively. The median value of the estimated parameters pr, Emax lo (excluding the case when Emax lo was simulated to equal 0) and Emax hi within a scenario were within ±28% of the true values. The median proportion of subjects classified correctly ranged from 0.59 to 0.96. In conclusion, when no mixture was present the false positive probability was less than 0.078 and when mixtures were present they were characterized with varying degrees of success, depending on the nature of the mixture. When the difference between subpopulations was greater (as Emax lo approached zero or pr approached 0.5) the mixtures became easier to characterize.

Chandra, S., Chhetri, P. and J. Corcoran (2009).Spatial patterns of urban compactness in Melbourne: an urban myth or a reality. In: Ostendorf B., Baldock, P., Bruce, D., Burdett, M. and P. Corcoran (eds.), Proceedings of the Surveying & Spatial Sciences Institute Biennial ...

Several long-term mark recapture studies have been conducted on box turtles (Terrapene c. carolina) providing valuable information on life span, basic demography, home range, and apparent effects of environmental changes on box turtle survival. One of the longest studied populations was first marked in 1942 on the Patuxent Wildlife Research Center in Maryland, and has been surveyed every 10 years

To investigate the reliability and validity of measures obtained from a portable electronic device used to monitor changes in plantar pressure, temperature, and humidity that occur within the shoe during prolonged activity. Descriptive study comparing electronic sensor output with criterion values. Indoor level walkway for pressure data; uncontrolled, outdoor environment for step count data; enclosed environmental control chamber for humidity and temperature data. Convenience sample of 4 healthy, sensate subjects. Not applicable. Correlations between sensor output and criterion measures were determined for pressure and temperature data. The absolute differences between sensor output and criterion values of temperature, humidity, and step count were also determined. Pressure measurements from electronic sensors correlated highly with criterion values (r > or =.82), both before and after prolonged use. Relative humidity sensor output were within 5% of hygrometer values. In-shoe temperature data correlated highly with criterion values (r > or =.99), and differed from known temperatures by.50 degrees +/-.84 degrees C and.96 degrees +/- 1.56 degrees C at the forefoot and heel, respectively. Electronic step counts recorded at the central forefoot were within 1 step of visual step counts. Pressure tracings obtained from the device during different weight-bearing activities revealed qualitatively distinct pressure patterns. The device provides valid and reliable measures of in-shoe plantar pressures, temperature, and humidity during prolonged activity.

In this paper we develop a dynamic model for integer counts to capture fundamental properties of financial prices at the transaction level. Our model relies on an autoregressive multinomial component for the direction of the price change and a dynamic count data component for the size of the price changes. Since the model is capable of capturing a wide range of discrete price movements it is particularly suited for financial markets where the trading intensity is moderate or low. We present the model at work by applying it to transaction data of two shares traded at the NYSE traded over a period of one trading month. We show that the model is well suited to test some theoretical implications of the market microstructure theory on the relationship between price movements and other marks of the trading process. Based on density forecast methods modified for the case of discrete random variables we show that our model is capable to explain large parts of the observed distribution of pr...

This paper provides a survey of count regression models in SAS®, which incorporates various count data modeling strategies. Our estimation procedure allows for a wide variety of count data distributions which can be used to model both under- and over-dispersed count data. We also provide estimation procedures that estimate count data that has excess zeros (zero-inflated) in the sample. A

Software reliability models (SRMs) are very important for estimating and predicting software reliability in the testing/debugging phase. The contributions of this paper are as follows. First, a historical review of the Gompertz SRM is given. Based on several software failure data, the parameters of the Gompertz software reliability model are estimated using two estimation methods, the traditional maximum likelihood and the least square. The methods of estimation are evaluated using the MSE and R-squared criteria. The results show that the least square estimation is an attractive method in term of predictive performance and can be used when the maximum likelihood method fails to give good prediction results.

BACKGROUND: Encouraging cycling is an important way to increase physical activity in the community. The Cycling Connecting Communities (CCC) Project is a community-based cycling promotion program that included a range of community engagement and social marketing activities, such as organised bike rides and events, cycling skills courses, the distribution of cycling maps of the area and coverage in the local

The control chart based on the Poisson residuals has been shown to be competitive for monitoring the number of nonconforming in an industrial process. The Poisson regression model is the most popular used by Generalized Linear Models, which is used to model the event count data. Even so being useful, the Poisson regression model has an assumption that the variance is equal the mean. But does not always happen, as in many situations, it has been found that the variance is greater than the mean, this phenomenon is referred as overdispersio n. This paper shows the identification of the mean-variance relationship and shows the test to verify the overdispersion. But, the main theme here proposed is to investigate the acting and the adaptation of the traditional use of the statistical control of process methods in no-stationary processes, and to discuss the use of Poisson regression model to work with correlated observations.

This article investigates the determinants of foreign direct investment (FDI) location across Italian provinces. Specifically it examines the relationship between industry-specific local industrial systems and the location of inward FDI. This extends previous analysis beyond the mere density of activity, to illustrate the importance of the specific nature of agglomerations in attracting inward investment. The article develops a model of

A variety of methods of modelling overdispersed count data are compared. The methods are classified into three main categories. The first category are ad hoc methods (i.e. pseudo-likelihood, (extended) quasi-likelihood, double exponential family distributions). The second category are discretized continuous distributions and the third category are observational level random effects models (i.e. mixture models comprising explicit and non-explicit continuous mixture models