Space–time zero-inflated count models of Harbor seals

Environmental data are spatial, temporal, and often come with many zeros. In this paper, we included space–time random effects in zero-inflated Poisson (ZIP) and ‘hurdle’ models to investigate haulout patterns of harbor seals on glacial ice. The data consisted of counts, for 18 dates on a lattice grid of samples, of harbor seals hauled out on glacial ice in Disenchantment Bay, near Yakutat, Alaska. A hurdle model is similar to a ZIP model except it does not mix zeros from the binary and count processes. Both models can be used for zero-inflated data, and we compared space–time ZIP and hurdle models in a Bayesian hierarchical model. Space–time ZIP and hurdle models were constructed by using spatial conditional autoregressive (CAR) models and temporal first-order autoregressive (AR(1)) models as random effects in ZIP and hurdle regression models. We created maps of smoothed predictions for harbor seal counts based on ice density, other covariates, and spatio-temporal random effects. For both models predictions around the edges appeared to be positively biased. The linex loss function is an asymmetric loss function that penalizes overprediction more than underprediction, and we used it to correct for prediction bias to get the best map for space–time ZIP and hurdle models.

Modelling zero-inflated count data when exposure varies: with an application to tumor counts)

This paper is concerned with the analysis of zero-inflated count data when time of exposure varies. It proposes a modified zero-inflated count data model where the probability of an extra zero is derived from an underlying duration model with Weibull hazard rate. The new model is compared to the standard Poisson model with logit zero inflation in an application to the effect of treatment with thiotepa on the number of new bladder tumors.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 Elsevier B V All rights reserved

What Belongs Where? Variable Selection for Zero-Inflated Count Models with an Application to the Demand for Health Care

This paper develops stochastic search variable selection (SSVS) for zero-inflated count models which are commonly used in health economics. This allows for either model averaging or model selection in situations with many potential regressors. The proposed techniques are applied to a data set from Germany considering the demand for health care. A package for the free statistical software environment R is provided.

Relations between zero-inflated variables in trials with horticultural crops

Certain characteristics of some vegetable crops allow multiple harvests during the production cycle; however, to our knowledge, no study has described the behavior of fruit production with progression of the production cycle in vegetable crops with multiple harvests that present data overdispersion. We aimed to characterize the data overdispersion of zero-inflated variables and identify the behavior of these variables during the production cycle of several vegetable crops with multiple harvests. Data from 11 uniformity trials were used without applying treatments; these comprise the database from the Experimental Plants Group at the Federal University of Santa Maria, Brazil. The trials were conducted using four horticultural species grown during different cultivation seasons, cultivation environments, and experimental structures. Although at each harvest, a larger number of basic units with harvest fruit was observed than units without harvest fruit, the basic unit percentage without fruit was high, generating an overdispersion within each individual harvest. The variability within each harvest was high and increased with the evolution of the production cycle of Capsicum annuum, Solanum lycopersicum var. cerasiforme, Phaseolus vulgaris, and Cucurbita pepo species. However, the correlation coefficient between the mean weight and number of harvest fruits tended to remain constant during the crop production cycle. These behaviors show that harvest management should be done individually, at each harvest, such that data overdispersion is reduced.

Multivariate models for correlated count data

In this study, we deal with the problem of overdispersion beyond extra zeros for a collection of counts that can be correlated. Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial distributions have been considered. First, we propose a multivariate count model in which all counts follow the same distribution and are correlated. Then we extend this model in a sense that correlated counts may follow different distributions. To accommodate correlation among counts, we have considered correlated random effects for each individual in the mean structure, thus inducing dependency among common observations to an individual. The method is applied to real data to investigate variation in food resources use in a species of marsupial in a locality of the Brazilian Cerrado biome. © 2013 Copyright Taylor and Francis Group, LLC.

The zero-inflated Conway-Maxwell-Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Score Test for Zero-Inflation in Correlated Count Data

To account for the preponderance of zero counts and simultaneous correlation of observations, a class of zero-inflated Poisson mixed regression models is applicable for accommodating the within-cluster dependence. In this paper, a score test for zero-inflation is developed for assessing correlated count data with excess zeros. The sampling distribution and the 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 further illustrated using a data set on recurrent urinary tract infections. Copyright (c) 2005 John Wiley & Sons, Ltd.

An extension of an over-dispersion test for count data

While over-dispersion in capture–recapture studies is well known to lead to poor estimation of population size, current diagnostic tools to detect the presence of heterogeneity have not been specifically developed for capture–recapture studies. To address this, a simple and efficient method of testing for over-dispersion in zero-truncated count data is developed and evaluated. The proposed method generalizes an over-dispersion test previously suggested for un-truncated count data and may also be used for testing residual over-dispersion in zero-inflation data. Simulations suggest that the asymptotic distribution of the test statistic is standard normal and that this approximation is also reasonable for small sample sizes. The method is also shown to be more efficient than an existing test for over-dispersion adapted for the capture–recapture setting. Studies with zero-truncated and zero-inflated count data are used to illustrate the test procedures.

Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.

Predictors of temporary and permanent work disability in patients with inflammatory bowel disease: results of the swiss inflammatory bowel disease cohort study.

BACKGROUND: Inflammatory bowel disease can decrease the quality of life and induce work disability. We sought to (1) identify and quantify the predictors of disease-specific work disability in patients with inflammatory bowel disease and (2) assess the suitability of using cross-sectional data to predict future outcomes, using the Swiss Inflammatory Bowel Disease Cohort Study data. METHODS: A total of 1187 patients were enrolled and followed up for an average of 13 months. Predictors included patient and disease characteristics and drug utilization. Potential predictors were identified through an expert panel and published literature. We estimated adjusted effect estimates with 95% confidence intervals using logistic and zero-inflated Poisson regression. RESULTS: Overall, 699 (58.9%) experienced Crohn's disease and 488 (41.1%) had ulcerative colitis. Most important predictors for temporary work disability in patients with Crohn's disease included gender, disease duration, disease activity, C-reactive protein level, smoking, depressive symptoms, fistulas, extraintestinal manifestations, and the use of immunosuppressants/steroids. Temporary work disability in patients with ulcerative colitis was associated with age, disease duration, disease activity, and the use of steroids/antibiotics. In all patients, disease activity emerged as the only predictor of permanent work disability. Comparing data at enrollment versus follow-up yielded substantial differences regarding disability and predictors, with follow-up data showing greater predictor effects. CONCLUSIONS: We identified predictors of work disability in patients with Crohn's disease and ulcerative colitis. Our findings can help in forecasting these disease courses and guide the choice of appropriate measures to prevent adverse outcomes. Comparing cross-sectional and longitudinal data showed that the conduction of cohort studies is inevitable for the examination of disability.

Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Predictors for hospitalization and outpatient visits in patients with inflammatory bowel disease: results from the Swiss Inflammatory Bowel Disease Cohort Study.

OBJECTIVES: Patients with inflammatory bowel disease (IBD) have a high resource consumption, with considerable costs for the healthcare system. In a system with sparse resources, treatment is influenced not only by clinical judgement but also by resource consumption. We aimed to determine the resource consumption of IBD patients and to identify its significant predictors. MATERIALS AND METHODS: Data from the prospective Swiss Inflammatory Bowel Disease Cohort Study were analysed for the resource consumption endpoints hospitalization and outpatient consultations at enrolment [1187 patients; 41.1% ulcerative colitis (UC), 58.9% Crohn's disease (CD)] and at 1-year follow-up (794 patients). Predictors of interest were chosen through an expert panel and a review of the relevant literature. Logistic regressions were used for binary endpoints, and negative binomial regressions and zero-inflated Poisson regressions were used for count data. RESULTS: For CD, fistula, use of biologics and disease activity were significant predictors for hospitalization days (all P-values <0.001); age, sex, steroid therapy and biologics were significant predictors for the number of outpatient visits (P=0.0368, 0.023, 0.0002, 0.0003, respectively). For UC, biologics, C-reactive protein, smoke quitters, age and sex were significantly predictive for hospitalization days (P=0.0167, 0.0003, 0.0003, 0.0076 and 0.0175 respectively); disease activity and immunosuppressive therapy predicted the number of outpatient visits (P=0.0009 and 0.0017, respectively). The results of multivariate regressions are shown in detail. CONCLUSION: Several highly significant clinical predictors for resource consumption in IBD were identified that might be considered in medical decision-making. In terms of resource consumption and its predictors, CD and UC show a different behaviour.