Poisson Hurdle Model Research Articles

Poisson hurdle model for monitoring the inflation of zeros

AbstractSeveral control charts have been developed in the literature to monitor zero inflation using classic and simple linear regression models with covariates. Simple linear regression models may not be appropriate, especially when the response variable is skewed or count. When the response distribution follows the exponential family; however, the generalized linear model (GLM) gives a more flexible approach. The goal of this study is to use the Poisson hurdle model to provide GLM‐based Shewhart‐type control charts. To calculate monitoring statistics, the Pearson residuals (PRs) are obtained using the Poisson hurdle model. A detailed Monte Carlo simulation analysis is used to analyze the attributes of the suggested charts. Besides this, a real‐life data set is used to show the practical application of the charts.

Adoption and impacts of messaging applications and participation in agricultural information-sharing groups: an empirical analysis with Brazilian farmers

PurposeThis study aimed to identify the determinants of farmers' participation in agricultural information-sharing digital groups and their impacts on farm performance.Design/methodology/approachPrimary data of the 2015/2016 crop year collected from 175 cattle farmers were analyzed using descriptive statistics and econometric models. Farmers who had smartphones and participated in social groups/applications, especially those created to exchange agricultural information, were considered adopters of the technology.FindingsA Poisson hurdle model showed that farmers' decision to participate in agricultural information-sharing digital groups is determined by schooling, age (negative effect) and use of tools for planning production. The intensity of participation is affected by risk propensity, interaction with specialist advisors, use of tools for planning production and participation in cooperatives. The authors also found empirical evidence that farmers' participation in agricultural information-sharing digital groups positively affects farm income per hectare.Research limitations/implicationsThe results of this study are important for accelerating the diffusion of low-cost digital technologies, which are powerful tools for improving farmers' sharing and access to valuable information in real time and in locations far from urban areas.Originality/valueTo the best of the authors’ knowledge, this is the first empirical analysis of the adoption and impacts of agricultural information-sharing digital groups/applications by Brazilian cattle farmers. The diffusion of simple digital technologies is important for reducing heterogeneity and increasing the efficiency of cattle production.

Poisson hurdle model-based method for clustering microbiome features.

High-throughput sequencing technologies have greatly facilitated microbiome research and have generated a large volume of microbiome data with the potential to answer key questions regarding microbiome assembly, structure and function. Cluster analysis aims to group features that behave similarly across treatments, and such grouping helps to highlight the functional relationships among features and may provide biological insights into microbiome networks. However, clustering microbiome data are challenging due to the sparsity and high dimensionality. We propose a model-based clustering method based on Poisson hurdle models for sparse microbiome count data. We describe an expectation-maximization algorithm and a modified version using simulated annealing to conduct the cluster analysis. Moreover, we provide algorithms for initialization and choosing the number of clusters. Simulation results demonstrate that our proposed methods provide better clustering results than alternative methods under a variety of settings. We also apply the proposed method to a sorghum rhizosphere microbiome dataset that results in interesting biological findings. R package is freely available for download at https://cran.r-project.org/package=PHclust. Supplementary data are available at Bioinformatics online.

Simulation Study of Bayesian Hurdle Poisson Regression on the Number of Deaths from Chronic Filariasis in Indonesia

One regression model to explain the relationship between predictor and response variable in the form of count is Poisson regression. In the case of certain Poisson with the presence of many zero values, causing overdispersion can be overcome with the Poisson Hurdle model. There is a good method for estimating the parameters on small sample sizes for all distributions, namely the Bayesian method. The response variable of the original data does not follow Poisson distribution, so parameter will be estimated by Bayesian method. The performance of the Bayesian Hurdle Poisson regression can be seen from simulation data on various sample sizes and overdispersion levels generated based on the parameters of original data showing that the Bayesian Hurdle Poisson regression model proposed in this study is suitable for large sample sizes or with varying levels of overdispersion due <img src=image/13426825_01.gif> or <img src=image/13426825_02.gif> because normal distribution is used as prior. Even though the response variable of the simulation data is generated with a Poisson distribution, it still does not follow a Poisson distribution because it's in accordance with the original data. The parameter estimated based on the simulation data is similar to the parameter estimated on the original data (both the estimator of the MLE Hurdle Poisson regression parameter and the parameter estimator of the Bayesian Hurdle Poisson regression). This indicates that the simulation scenario is appropriate.

Associations between women's empowerment, care seeking, and quality of malaria care for children: A cross-sectional analysis of demographic and health surveys in 16 sub-Saharan African countries.

BackgroundFever and malaria are highly prevalent among children under five across sub-Saharan Africa, but utilization and quality of care for febrile illness remain insufficient. Many studies examine socioeconomic and demographic determinants of care seeking; however, few assess how women’s empowerment influences care seeking and quality. We examine associations of women’s empowerment with: a) care utilization for children with fever and malaria and b) the quality of that care in 16 sub-Saharan African countries.MethodsThis cross-sectional study used data from Demographic and Health Surveys conducted between 2010 and 2018. We constructed indices for economic, educational, sociocultural, and health-related empowerment and calculated the proportion of children with fever and malaria who sought care and received a range of recommended clinical actions. We used multivariable Poisson hurdle models to assess associations between empowerment, utilization, and number of components of quality care, controlling for socioeconomic and demographic factors.ResultsOur sample consisted of 25 871 febrile children, 4731 of whom had malaria diagnosed by rapid diagnostic test. Empowerment among mothers of children with fever was 0.50 (interquartile range, 0.38-0.63). In both the fever and malaria groups, over 30% of children were not taken for care. Among care seekers, febrile children received on average 0.47 (SD = 0.37) of components of quality care, and children with malaria received 0.38 (SD = 0.34). Multidimensional women’s empowerment was significantly associated with care seeking and quality among febrile children, and with quality among children with malaria. Associations persisted after adjustment for socioeconomic and demographic characteristics.ConclusionsResults demonstrate substantial gaps in women’s empowerment and poor utilization and quality of care for fever and malaria among children. Increased women’s empowerment is associated with seeking care and, separately, obtaining high-quality care. To improve health outcomes, consideration of how empowering women can promote care seeking and extract quality from the health system is warranted.

Generalized Poisson Hurdle Model for Count Data and Its Application in Ear Disease.

For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.

Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models

Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how the zeros were generated and potentially help mitigate the effects of overdispersion relative to the assumed count distribution. Which model to use depends on how the zeros are generated: zero-inflated models add an additional probability mass on zero, while hurdle models are two-part models comprised of a degenerate distribution for the zeros and a zero-truncated distribution. Developing confidence intervals for such models is challenging since no closed-form function is available to calculate the mean. In this study, generalized fiducial inference is used to construct confidence intervals for the means of zero-inflated Poisson and Poisson hurdle models. The proposed methods are assessed by an intensive simulation study. An illustrative example demonstrates the inference methods.

Modelling the cone yields of Korean pine

Korean pine is the most important plantation tree species in northeast China. Besides timber, it produces edible seeds. Economic comparisons between alternative management schedules of Korean pine plantations require information on tree growth but also on seed yields since Korean pine seeds generate significant economic returns. This study developed models for the cone yields of Korean pine. Data were collected from 24 permanent sample plots during 2004–2018. Model types suitable for modelling count data with a high proportion of zero counts, namely zero-inflated and hurdle models, were tested as alternatives to those types of Poisson and negative binomial models that did not include a sub-model for the excess of zeros. Correlations between observations collected from the same plot and tree were taken into account by fitting mixed-effects models. There was much annual variation in seed production, which was modelled by using indicator variables for different years. The other predictors of the cone models were tree diameter at the breast height, stand basal area, competitive position of the tree in the stand (basal area in larger trees) and site index. It was concluded that the best model types for predicting cone yields in simulation and optimization studies were negative binomial hurdle model and Poisson hurdle model. The same models were evaluated to be the most recommendable also in cases where probabilistic predictions are needed, for instance in stochastic optimization.

Spatial model for risk prediction and sub-national prioritization to aid poliovirus eradication in Pakistan

BackgroundPakistan is one of only three countries where poliovirus circulation remains endemic. For the Pakistan Polio Eradication Program, identifying high risk districts is essential to target interventions and allocate limited resources.MethodsUsing a hierarchical Bayesian framework we developed a spatial Poisson hurdle model to jointly model the probability of one or more paralytic polio cases, and the number of cases that would be detected in the event of an outbreak. Rates of underimmunization, routine immunization, and population immunity, as well as seasonality and a history of cases were used to project future risk of cases.ResultsThe expected number of cases in each district in a 6-month period was predicted using indicators from the previous 6-months and the estimated coefficients from the model. The model achieves an average of 90% predictive accuracy as measured by area under the receiver operating characteristic (ROC) curve, for the past 3 years of cases.ConclusionsThe risk of poliovirus has decreased dramatically in many of the key reservoir areas in Pakistan. The results of this model have been used to prioritize sub-national areas in Pakistan to receive additional immunization activities, additional monitoring, or other special interventions.

The Effect of Sample Size on the Efficiency of Count Data Models: Application to Marriage Data

Abstract: Sample size requirements are common in many multivariate analysis techniques as one of the measures taken to ensure the robustness of such techniques, such requirements have not been of interest in the area of count data models. As such, this study investigated the effect of sample size on the efficiency of six commonly used count data models namely: Poisson regression model (PRM), Negative binomial regression model (NBRM), Zero-inflated Poisson (ZIP), Zero-inflated negative binomial (ZINB), Poisson Hurdle model (PHM) and Negative binomial hurdle model (NBHM). The data used in this study were sourced from Data First and were collected by Statistics South Africa through the Marriage and Divorce database. PRM, NBRM, ZIP, ZINB, PHM and NBHM were applied to ten randomly selected samples ranging from 4392 to 43916 and differing by 10% in size. The six models were compared using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Vuong’s test for over-dispersion, McFadden RSQ, Mean Square Error (MSE) and Mean Absolute Deviation (MAD).The results revealed that generally, the Negative Binomial-based models outperformed Poisson-based models. However, the results did not reveal the effect of sample size variations on the efficiency of the models since there was no consistency in the change in AIC, BIC, Vuong’s test for over-dispersion, McFadden RSQ, MSE and MAD as the sample size increased.

The Effect of Sample Size on the Efficiency of Count Data Models: Application to Marriage Data

Abstract: Sample size requirements are common in many multivariate analysis techniques as one of the measures taken to ensure the robustness of such techniques, such requirements have not been of interest in the area of count data models. As such, this study investigated the effect of sample size on the efficiency of six commonly used count data models namely: Poisson regression model (PRM), Negative binomial regression model (NBRM), Zero-inflated Poisson (ZIP), Zero-inflated negative binomial (ZINB), Poisson Hurdle model (PHM) and Negative binomial hurdle model (NBHM). The data used in this study were sourced from Data First and were collected by Statistics South Africa through the Marriage and Divorce database. PRM, NBRM, ZIP, ZINB, PHM and NBHM were applied to ten randomly selected samples ranging from 4392 to 43916 and differing by 10% in size. The six models were compared using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Vuong’s test for over-dispersion, McFadden RSQ, Mean Square Error (MSE) and Mean Absolute Deviation (MAD).The results revealed that generally, the Negative Binomial-based models outperformed Poisson-based models. However, the results did not reveal the effect of sample size variations on the efficiency of the models since there was no consistency in the change in AIC, BIC, Vuong’s test for over-dispersion, McFadden RSQ, MSE and MAD as the sample size increased.

Spatiotemporal hurdle models for zero-inflated count data: Exploring trends in emergency department visits

Motivated by a study exploring spatiotemporal trends in emergency department use, we develop a class of two-part hurdle models for the analysis of zero-inflated areal count data. The models consist of two components-one for the probability of any emergency department use and one for the number of emergency department visits given use. Through a hierarchical structure, the models incorporate both patient- and region-level predictors, as well as spatially and temporally correlated random effects for each model component. The random effects are assigned multivariate conditionally autoregressive priors, which induce dependence between the components and provide spatial and temporal smoothing across adjacent spatial units and time periods, resulting in improved inferences. To accommodate potential overdispersion, we consider a range of parametric specifications for the positive counts, including truncated negative binomial and generalized Poisson distributions. We adopt a Bayesian inferential approach, and posterior computation is handled conveniently within standard Bayesian software. Our results indicate that the negative binomial and generalized Poisson hurdle models vastly outperform the Poisson hurdle model, demonstrating that overdispersed hurdle models provide a useful approach to analyzing zero-inflated spatiotemporal data.

Brief motivational interventions for college student drinking may not be as powerful as we think: an individual participant-level data meta-analysis.

For over 2 decades, brief motivational interventions (BMIs) have been implemented on college campuses to reduce heavy drinking and related negative consequences. Such interventions include in-person motivational interviews (MIs), often incorporating personalized feedback (PF), and stand-alone PF interventions delivered via mail, computer, or the Web. Both narrative and meta-analytic reviews using aggregate data from published studies suggest at least short-term efficacy of BMIs, although overall effect sizes have been small. This study was an individual participant-level data (IPD) meta-analysis of 17 randomized clinical trials evaluating BMIs. Unlike typical meta-analysis based on summary data, IPD meta-analysis allows for an analysis that correctly accommodates the sampling, sample characteristics, and distributions of the pooled data. In particular, highly skewed distributions with many zeroes are typical for drinking outcomes, but have not been adequately accounted for in existing studies. Data are from Project INTEGRATE, one of the largest IPD meta-analysis projects to date in alcohol intervention research, representing 6,713 individuals each with 2 to 5 repeated measures up to 12months postbaseline. We used Bayesian multilevel over dispersed Poisson hurdle models to estimate intervention effects on drinks per week and peak drinking, and Gaussian models for alcohol problems. Estimates of overall intervention effects were very small and not statistically significant for any of the outcomes. We further conducted post hoc comparisons of 3 intervention types (individual MI with PF, PF only, and group MI) versus control. There was a small, statistically significant reduction in alcohol problems among participants who received an individual MI with PF. Short-term and long-term results were similar. This study questions the efficacy and magnitude of effects of BMIs for college drinking prevention and intervention and suggests a need for the development of more effective intervention strategies.

Elevated Serum 25(OH)-Vitamin D Levels Are Negatively Correlated with Molar-Incisor Hypomineralization

To date, the precise etiology of molar-incisor hypomineralization (MIH) is uncertain. Vitamin D plays a key role in hard tissue formation. Therefore, this study aimed to analyze the relationship between serum 25-hydroxy-vitamin D (25(OH)D) status and dental health data obtained from 1,048 children in a 10-year follow-up of the Munich GINIplus and LISAplus birth cohorts. The dental examination included the diagnosis of MIH and recording of (non-)cavitated caries lesions in primary and permanent teeth. Serum 25(OH)D concentrations were taken from blood samples of the 10-year investigation and measured with a fully automated, modular system. Different logistic regression and Poisson hurdle models were calculated. MIH was diagnosed in 13.6% of the study population. Approximately 16.4% of the children demonstrated caries-related defects (D3-4MFS > 0). The mean season-adjusted concentration of 25(OH)D was 75.8 nmol/l (standard deviation 22.0 nmol/l). After adjusting for sex, age, body mass index, parental education, equivalent income, and television/personal computer (TV/PC) viewing hours, a 10 nmol/l increase in serum 25(OH)D concentrations was significantly associated with a lower odds ratio of having MIH (OR = 0.89; P = 0.006). Furthermore, higher 25(OH)D values were associated with a lower number of caries-affected permanent teeth. It is concluded that elevated serum 25(OH)D concentrations were associated with better dental health parameters.

Consumer Health Information and the Demand for Physician Visits

The present study empirically investigates the effect of consumer health information on the demand for physician visits. Using a direct information measure based on questions from the Swiss Health Survey, we estimate a Poisson hurdle model for office visits. We find that information has a negative effect on health care utilization, contradicting previous findings in the literature. We consider differences in the used information measures to be the most likely explanation for the different findings. However, our results suggest that increasing consumer health information has the potential to reduce health care expenditures.

Predictive spatial risk model of poliovirus to aid prioritization and hasten eradication in Nigeria.

BackgroundOne of the challenges facing the Global Polio Eradication Initiative is efficiently directing limited resources, such as specially trained personnel, community outreach activities, and satellite vaccinator tracking, to the most at-risk areas to maximize the impact of interventions. A validated predictive model of wild poliovirus circulation would greatly inform prioritization efforts by accurately forecasting areas at greatest risk, thus enabling the greatest effect of program interventions.MethodsUsing Nigerian acute flaccid paralysis surveillance data from 2004-2013, we developed a spatial hierarchical Poisson hurdle model fitted within a Bayesian framework to study historical polio caseload patterns and forecast future circulation of type 1 and 3 wild poliovirus within districts in Nigeria. A Bayesian temporal smoothing model was applied to address data sparsity underlying estimates of covariates at the district level.ResultsWe find that calculated vaccine-derived population immunity is significantly negatively associated with the probability and number of wild poliovirus case(s) within a district. Recent case information is significantly positively associated with probability of a case, but not the number of cases. We used lagged indicators and coefficients from the fitted models to forecast reported cases in the subsequent six-month periods. Over the past three years, the average predictive ability is 86 ± 2% and 85 ± 4% for wild poliovirus type 1 and 3, respectively. Interestingly, the predictive accuracy of historical transmission patterns alone is equivalent (86 ± 2% and 84 ± 4% for type 1 and 3, respectively). We calculate uncertainty in risk ranking to inform assessments of changes in rank between time periods.ConclusionsThe model developed in this study successfully predicts districts at risk for future wild poliovirus cases in Nigeria. The highest predicted district risk was 12.8 WPV1 cases in 2006, while the lowest district risk was 0.001 WPV1 cases in 2013. Model results have been used to direct the allocation of many different interventions, including political and religious advocacy visits. This modeling approach could be applied to other vaccine preventable diseases for use in other control and elimination programs.

Predictive spatial risk model of polio virus to aid prioritization and hasten eradication in endemic countries

Background: Polio eradication was declared a “programmatic emergency for global public health” by the world health assembly in 2012. Efficient prioritization of high risk areas would greatly improve the impact of the substantial resources of the Global Polio Eradication Initiative. Currently, one method for polio risk assessment has been described in the litterature, however this method has not been historically validated and fails to address uncertainty. Methods & Materials: Data, including vaccination history, collected from individuals through Acute Flaccid Paralysis (AFP) surveillence in Nigeria and Pakistan, used to calculate district level immunity and relevant covariates. We constructed heirachical temporal bayesian models to reduce measurement error in data and spatially smoothed Poisson hurdle models to assess predictors of wild polio virus (WPV) tranmission. Best fitting models used to forecast future district infection, predictive accuracy assessed with reciever operating characteristic (ROC) analysis. Results: Measurement error models greatly reduce changes in indicators from one time period to another. Calculated population immunity is a strongly associated with the presence of WPV and number of WPV cases within a district in Nigeria. In Pakistan, routine immunization dose history (not available through Nigerian AFP data) and zero-dose fraction are strongly associated with both aspects of WPV tranmission. A district risk list ordered according to model outputs demonstrates high forecast accuracy historically, with mean area under the ROC curve greater than 0.80 over the past three years. Model uncertainty propogated through to rank uncertainty, and the probability of a district belonging in the highest risk N district list can be calcuated. Conclusion: The measurement error smoothing model is a useful tool for estimation of important variables at small adminsitrative areas. With the Poisson hurdle model, we can study differential relatitionships between predictors and two aspects of WPV tranmsission. Historically forecast accuracy confirms the usefulness of this modeling approach in a disease control and elimination application. The quantification of uncertainty is essential to inform objectives descisions regarding changes in prioritization status of a district from one time period to another. These models can be naturally extended to other vaccine-preventable diseases, such as measles. In Nigeria, these models have been incorporated into national program planning.

Modeling longitudinal drinking data in clinical trials: An application to the COMBINE study

BackgroundThere is a lack of consensus in the literature as to how to define drinking outcomes in clinical trials. Typically, separate statistical models are fit to assess treatment effects on several summary drinking measures. These summary measures do not capture the complexity of drinking behavior. We used the COMBINE study to illustrate a statistical approach for examining treatment effects on high-resolution drinking data. MethodsThis is a secondary data analysis of COMBINE participants randomly assigned to naltrexone, acamprosate, with medical management and/or combined behavioral intervention (CBI). Using a Poisson hurdle model, abstinence and number of drinks were simultaneously modeled as a function of treatment and covariates. An emphasis was placed on the evaluation of “risky drinking” (3 drinks/day for women and 4 for men). ResultsDuring treatment, naltrexone increased the odds of abstinence vs placebo naltrexone (OR=1.35 [1.06, 1.65]) but receiving CBI in addition to naltrexone (vs not) obscured this effect; thus, the naltrexone effect was largest in the group not receiving CBI (OR=1.87 [1.29, 2.46]). Naltrexone vs placebo naltrexone also reduced the risk of drinking in those who resumed risky drinking (RR=0.58 [0.24, 0.93]) and increased the odds of maintaining low risk drinking (OT=1.99 [1.07, 2.90]). Both effects were strongest in the absence of CBI when only “medical management” was provided. ConclusionsThe hurdle model is an appropriate statistical tool for assessing the effect of treatment on the two part drinking process, abstinence and number of drinks. When applied to COMBINE, results bolster the use of naltrexone in promoting abstinence and reduction in risky drinking.

A Spatial Poisson Hurdle Model for Exploring Geographic Variation in Emergency Department Visits.

We develop a spatial Poisson hurdle model to explore geographic variation in emergency department (ED) visits while accounting for zero inflation. The model consists of two components: a Bernoulli component that models the probability of any ED use (i.e., at least one ED visit per year), and a truncated Poisson component that models the number of ED visits given use. Together, these components address both the abundance of zeros and the right-skewed nature of the nonzero counts. The model has a hierarchical structure that incorporates patient- and area-level covariates, as well as spatially correlated random effects for each areal unit. Because regions with high rates of ED use are likely to have high expected counts among users, we model the spatial random effects via a bivariate conditionally autoregressive (CAR) prior, which introduces dependence between the components and provides spatial smoothing and sharing of information across neighboring regions. Using a simulation study, we show that modeling the between-component correlation reduces bias in parameter estimates. We adopt a Bayesian estimation approach, and the model can be fit using standard Bayesian software. We apply the model to a study of patient and neighborhood factors influencing emergency department use in Durham County, North Carolina.

The k‐ZIG: Flexible Modeling for Zero‐Inflated Counts

Many applications involve count data from a process that yields an excess number of zeros. Zero-inflated count models, in particular, zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models, along with Poisson hurdle models, are commonly used to address this problem. However, these models struggle to explain extreme incidence of zeros (say more than 80%), especially to find important covariates. In fact, the ZIP may struggle even when the proportion is not extreme. To redress this problem we propose the class of k-ZIG models. These models allow more flexible modeling of both the zero-inflation and the nonzero counts, allowing interplay between these two components. We develop the properties of this new class of models, including reparameterization to a natural link function. The models are straightforwardly fitted within a Bayesian framework. The methodology is illustrated with simulated data examples as well as a forest seedling dataset obtained from the USDA Forest Service's Forest Inventory and Analysis program.