Inpatient length of stay: a finite mixture modeling analysis

Length of stay (LOS) in hospital for inpatient treatment is a measure of crucial recovery time. Using nationwide data on inpatient healthcare in India, a three-component finite mixture negative binomial model was found to provide a reasonable fit to the heterogeneous LOS distribution. Associated risk factors for short-stay, medium-stay and long-stay subgroups were identified from the respective negative binomial components. In addition, significant heterogeneities within each group were also found.

Clustered mixed nonhomogeneous Poisson process spline models for the analysis of recurrent event panel data

A flexible semiparametric model for analyzing longitudinal panel count data arising from mixtures is presented. Panel count data refers here to count data on recurrent events collected as the number of events that have occurred within specific follow-up periods. The model assumes that the counts for each subject are generated by mixtures of nonhomogeneous Poisson processes with smooth intensity functions modeled with penalized splines. Time-dependent covariate effects are also incorporated into the process intensity using splines. Discrete mixtures of these nonhomogeneous Poisson process spline models extract functional information from underlying clusters representing hidden subpopulations. The motivating application is an experiment to test the effectiveness of pheromones in disrupting the mating pattern of the cherry bark tortrix moth. Mature moths arise from hidden, but distinct, subpopulations and monitoring the subpopulation responses was of interest. Within-cluster random effects are used to account for correlation structures and heterogeneity common to this type of data. An estimating equation approach to inference requiring only low moment assumptions is developed and the finite sample properties of the proposed estimating functions are investigated empirically by simulation.

Minimum Hellinger distance estimation for k-component poisson mixture with random effects

The k-component Poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations. However, the residual maximum likelihood estimation (REML) of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination. In the literature, the minimum Hellinger distance (MHD) estimation has been investigated to obtain robust estimation for finite Poisson mixtures. This article aims to develop a robust MHD estimation approach for k-component Poisson mixtures with normally distributed random effects. By applying the Gaussian quadrature technique to approximate the integrals involved in the marginal distribution, the marginal probability function of the k-component Poisson mixture with random effects can be approximated by the summation of a set of finite Poisson mixtures. Simulation study shows that the MHD estimates perform satisfactorily for data without outlying observation(s), and outperform the REML estimates when data are contaminated. Application to a data set of recurrent urinary tract infections (UTI) with random institution effects demonstrates the practical use of the robust MHD estimation method.

Mixture Model Framework Facilitates Understanding of Zero-Inflated and Hurdle Models for Count Data

In this note, we comment on the zero-inflated and hurdle models for count data presented by Rose et al., 2006, J. Biopharma. Stat. 16:463-481. By viewing these models as finite mixture models, one gains a better understanding of the components of the models, including assumptions about the latent variable(s) in the finite mixture models. Deciding whether a zero-inflated or hurdle model is appropriate for a given data set requires close collaboration with subject matter experts. For instance, in modeling vaccine adverse event count data, the pharmacokinetic rationale for the occurrence of an adverse event and the likelihood of detecting or reporting the adverse event are important considerations for mixture model development.

Testing approaches for overdispersion in poisson regression versus the generalized poisson model

Overdispersion is a common phenomenon in Poisson modeling, and the negative binomial (NB) model is frequently used to account for overdispersion. Testing approaches (Wald test, likelihood ratio test (LRT), and score test) for overdispersion in the Poisson regression versus the NB model are available. Because the generalized Poisson (GP) model is similar to the NB model, we consider the former as an alternate model for overdispersed count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes a score test for overdispersion based on the GP model and compares the power of the test with the LRT and Wald tests. A simulation study indicates the score test based on asymptotic standard Normal distribution is more appropriate in practical application for higher empirical power, however, it underestimates the nominal significance level, especially in small sample situations, and examples illustrate the results of comparing the candidate tests between the Poisson and GP models. A bootstrap test is also proposed to adjust the underestimation of nominal level in the score statistic when the sample size is small. The simulation study indicates the bootstrap test has significance level closer to nominal size and has uniformly greater power than the score test based on asymptotic standard Normal distribution. From a practical perspective, we suggest that, if the score test gives even a weak indication that the Poisson model is inappropriate, say at the 0.10 significance level, we advise the more accurate bootstrap procedure as a better test for comparing whether the GP model is more appropriate than Poisson model. Finally, the Vuong test is illustrated to choose between GP and NB2 models for the same dataset.

Mixture modeling for the detection of subpopulations in a pharmacokinetic/pharmacodynamic analysis

To be able to estimate accurately parameters entering a non-linear mixed effects model taking into account that one or more subpopulations of patients can exist rather than assuming that the entire population is best described by unimodal distributions for the random effects, we proposed a methodology based on the likelihood approximation using the Gauss-Hermite quadrature. The idea is to combine the estimation of the model parameters and the detection of homogeneous subgroups of patients in a given population using a Gaussian mixture for the distribution of the random effects. As the accuracy of the likelihood approximation is likely to govern the quality of the estimation of the different parameters entering the non-linear mixed effects model, we based this approximation on the use of an adjustable Gauss-Hermite quadrature. Moreover, to complete this methodology, we propose a strategy allowing the detection and explanation of heterogeneity based on the Kullback-Leibler test, which was used to estimate the number of components in the Gaussian mixture. In order to evaluate the capability of the method to take into account heterogeneity, this strategy was performed in a PK/PD analysis using the database and the structural model selected in a previous analysis. In this analysis, non-responders were found out using NONMEM [Beal and Sheiner. NONMEM Users Guides. NONMEM Project Group, University of California, San Francisio, 1992] in a population of diabetic patients treated with a once-a-day new formulation of an antidiabetic drug. The authors looked for a subpopulation of patients for whom the therapeutic effect would vanish. In this paper, we looked for subpopulations of patients exhibiting specificities with respect to different parameters entering the description of the effect. The results obtained with our approach are compared in terms of parameter estimation and heterogeneity detection to those obtained in the previous analysis.

On the generalized poisson regression mixture model for mapping quantitative trait loci with count data

Statistical methods for mapping quantitative trait loci (QTL) have been extensively studied. While most existing methods assume normal distribution of the phenotype, the normality assumption could be easily violated when phenotypes are measured in counts. One natural choice to deal with count traits is to apply the classical Poisson regression model. However, conditional on covariates, the Poisson assumption of mean-variance equality may not be valid when data are potentially under- or overdispersed. In this article, we propose an interval-mapping approach for phenotypes measured in counts. We model the effects of QTL through a generalized Poisson regression model and develop efficient likelihood-based inference procedures. This approach, implemented with the EM algorithm, allows for a genomewide scan for the existence of QTL throughout the entire genome. The performance of the proposed method is evaluated through extensive simulation studies along with comparisons with existing approaches such as the Poisson regression and the generalized estimating equation approach. An application to a rice tiller number data set is given. Our approach provides a standard procedure for mapping QTL involved in the genetic control of complex traits measured in counts.

Sensitivity of test for overdispersion in Poisson regression

Overdispersion or extra-Poisson variation is very common for count data. This phenomenon arises when the variability of the counts greatly exceeds the mean under the Poisson assumption, resulting in substantial bias for the parameter estimates. To detect whether count data are overdispersed in the Poisson regression setting, various tests have been proposed and among them, the score tests derived by Dean (1992) are popular and easy to implement. However, such tests can be sensitive to anomalous or extreme observations. In this paper, diagnostic measures are proposed for assessing the sensitivity of Dean's score test for overdispersion in Poisson regression. Applications to the well-known fabric faults and Ames salmonella assay data sets illustrate the usefulness of the diagnostics in analyzing overdispersed count data.

Influence diagnostics for two-component Poisson mixture regression models: applications in public health

In many medical and health applications, Poisson mixture regression models are commonly used to analyse heterogeneous count data. Motivated by two data sets drawn from public health studies, influence diagnostics are proposed for assessing the sensitivity of the fitted two-component Poisson mixture regression models. Under various perturbations of the observed data or model assumptions, influence assessments based on the local influence approach are developed for detecting clusters and/or individual observations that impact on the estimation of model parameters. Results from studies on recurrent urinary tract infections and maternity length of stay illustrate the usefulness of the influence diagnostics.

Minimum Hellinger distance estimation for finite mixtures of Poisson regression models and its applications

Minimum Hellinger distance estimation (MHDE) has been shown to discount anomalous data points in a smooth manner with first-order efficiency for a correctly specified model. An estimation approach is proposed for finite mixtures of Poisson regression models based on MHDE. Evidence from Monte Carlo simulations suggests that MHDE is a viable alternative to the maximum likelihood estimator when the mixture components are not well separated or the model parameters are near zero. Biometrical applications also illustrate the practical usefulness of the MHDE method.

Estimation of infection prevalence from correlated binomial samples

Infection prevalence in a population often is estimated from grouped binary data expressed as proportions. The groups can be families, herds, flocks, farms, etc. The observed number of cases generally is assumed to have a Binomial distribution and the estimate of prevalence is then the sample proportion of cases. However, the individual binary observations might not be independent--leading to overdispersion. The goal of this paper was to demonstrate random-effects models for the estimation of infection prevalence from data which are correlated and in particular, to illustrate a nonparametric random-effects model for this purpose. The nonparametric approach is a relatively recent addition to the random-effects class of models and does not appear to have been discussed previously in the veterinary epidemiology literature. The assumptions for a logistic-regression model with a nonparametric random effect were outlined. In a demonstration of the method on data relating to Salmonella infection in Irish pig herds, the nonparametric method resulted in the classification of herds into a small number of distinct prevalence groups (i.e. low, medium and high prevalence) and also estimated the relative frequency of each prevalence category in the population. We compared the estimates from a logistic model with a nonparametric distribution for the random effects with four alternative models: a logistic-regression model with no random effects, a marginal model using a generalised estimating equation (GEE) and two methods of fitting a Normally distributed random effect (the GLIMMIX macro and the NLMIXED procedure both in SAS). Parameter estimates from random-effects models are not readily interpretable in terms of prevalences. Therefore, we outlined two methods for calculating population-averaged estimates of prevalence from random-effects models: one using numerical integration and the other using Monte Carlo simulation.

Seasonal variation in stroke in the Hunter Region, Australia: a 5-year hospital-based study, 1995-2000

BACKGROUND AND PURPOSE

Seasonal variation in stroke has long been recognized. To date, there are minimal published data on seasonal variations in rates of stroke and subsequent case fatality in the Southern Hemisphere. The aim of this study was to examine stroke seasonality through the use of data from a hospital-based stroke register in the Hunter Region of New South Wales, Australia.

METHODS

From July 1, 1995, to June 30, 2000, 3803 stroke events were registered in residents of the Hunter Region, New South Wales, Australia. We analyzed the trend of seasonal and monthly stroke attack rates and case-fatality rates using Poisson regressions with age and sex as covariates.

RESULTS

Stroke attack rates were highest in the winter and lowest in the summer. From February (summer) to July (winter), there was a significant trend in increasing stroke attack rates (rate ratio, 1.07; 95% confidence interval, 1.05 to 1.10; P<0.001). This increase was seen mainly in those >or=65 years of age. Case-fatality rates showed similar trends with a 1- to 2-month lag compared with attack rates.

CONCLUSIONS

There is an increase in stroke attack rates and case-fatality rate from summer to winter in the Hunter Region, Australia. These trends are similar to those found in the Northern Hemisphere.

A hierarchical Poisson mixture regression model to analyse maternity length of hospital stay

Inpatient length of stay (LOS) is often considered as a proxy of hospital resource consumption. Using statewide obstetrical delivery data, a two-component Poisson mixture model provides a reasonable fit to the heterogeneous LOS distribution. Adopting the generalized linear mixed model (GLMM) approach, random effects are introduced to the two-component Poisson mixture regression model to account for the inherent correlation of patients clustered within hospitals. An EM algorithm is developed for the joint estimation of regression coefficients and variance component parameters. Related diagnostic measures for assessing model adequacy are derived. When applying the method to analyse maternity LOS, appropriate risk factors for the short-stay and long-stay subgroups can be identified from the respective Poisson components. In addition, predicted random hospital effects enable the comparison of relative efficiencies among hospitals after adjustment for patient case-mix and health provision characteristics.

A zero-inflated Poisson mixed model to analyze diagnosis related groups with majority of same-day hospital stays

With increasing trend of same-day procedures and operations performed for hospital admissions, it is important to analyze those Diagnosis Related Groups (DRGs) consisting of mainly same-day separations. A zero-inflated Poisson (ZIP) mixed model is presented to identify health- and patient-related characteristics associated with length of stay (LOS) and to model variations in LOS within such DRGs. Random effects are introduced to account for inter-hospital variations and the dependence of clustered LOS observations via the generalized linear mixed models (GLMM) approach. Parameter estimation is achieved by maximizing an appropriate log-likelihood function using the EM algorithm to obtain approximate residual maximum likelihood (REML) estimates. An S-Plus macro is developed to provide a unified ZIP modeling approach. The determination of pertinent factors would benefit hospital administrators and clinicians to manage LOS and expenditures efficiently.

A review of some extensions to generalized linear models

Although generalized linear models are reasonably well known, they are not as widely used in medical statistics as might be appropriate, with the exception of logistic, log-linear, and some survival models. At the same time, the generalized linear modelling methodology is decidedly outdated in that more powerful methods, involving wider classes of distributions, non-linear regression, censoring and dependence among responses, are required. Limitations of the generalized linear modelling approach include the need for the iterated weighted least squares (IWLS) procedure for estimation and deviances for inferences; these restrict the class of models that can be used and do not allow direct comparisons among models from different distributions. Powerful non-linear optimization routines are now available and comparisons can more fruitfully be made using the complete likelihood function. The link function is an artefact, necessary for IWLS to function with linear models, but that disappears once the class is extended to truly non-linear models. Restricting comparisons of responses under different treatments to differences in means can be extremely misleading if the shape of the distribution is changing. This may involve changes in dispersion, or of other shape-related parameters such as the skewness in a stable distribution, with the treatments or covariates. Any exact likelihood function, defined as the probability of the observed data, takes into account the fact that all observable data are interval censored, thus directly encompassing the various types of censoring possible with duration-type data. In most situations this can now be as easily used as the traditional approximate likelihood based on densities. Finally, methods are required for incorporating dependencies among responses in models including conditioning on previous history and on random effects. One important procedure for constructing such likelihoods is based on Kalman filtering.

On the EM algorithm for overdispersed count data

In this paper, we consider the use of the EM algorithm for the fitting of distributions by maximum likelihood to overdispersed count data. In the course of this, we also provide a review of various approaches that have been proposed for the analysis of such data. As the Poisson and binomial regression models, which are often adopted in the first instance for these analyses, are particular examples of a generalized linear model (GLM), the focus of the account is on the modifications and extensions to GLMs for the handling of overdispersed count data.