Journal articles: 'Zero-Inflated counts'

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Preisser, John S., D. Leann Long, and John W. Stamm. "Matching the Statistical Model to the Research Question for Dental Caries Indices with Many Zero Counts." Caries Research 51, no. 3 (2017): 198–208. http://dx.doi.org/10.1159/000452675.

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Marginalized zero-inflated count regression models have recently been introduced for the statistical analysis of dental caries indices and other zero-inflated count data as alternatives to traditional zero-inflated and hurdle models. Unlike the standard approaches, the marginalized models directly estimate overall exposure or treatment effects by relating covariates to the marginal mean count. This article discusses model interpretation and model class choice according to the research question being addressed in caries research. Two data sets, one consisting of fictional dmft counts in 2 groups and the other on DMFS among schoolchildren from a randomized clinical trial comparing 3 toothpaste formulations to prevent incident dental caries, are analyzed with negative binomial hurdle, zero-inflated negative binomial, and marginalized zero-inflated negative binomial models. In the first example, estimates of treatment effects vary according to the type of incidence rate ratio (IRR) estimated by the model. Estimates of IRRs in the analysis of the randomized clinical trial were similar despite their distinctive interpretations. The choice of statistical model class should match the study's purpose, while accounting for the broad decline in children's caries experience, such that dmft and DMFS indices more frequently generate zero counts. Marginalized (marginal mean) models for zero-inflated count data should be considered for direct assessment of exposure effects on the marginal mean dental caries count in the presence of high frequencies of zero counts.

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Alam, Morshed, Naim Al Mahi, and Munni Begum. "Zero-Inflated Models for RNA-Seq Count Data." Journal of Biomedical Analytics 1, no. 2 (2018): 55–70. http://dx.doi.org/10.30577/jba.2018.v1n2.23.

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One of the main objectives of many biological studies is to explore differential gene expression profiles between samples. Genes are referred to as differentially expressed (DE) if the read counts change across treatments or conditions systematically. Poisson and negative binomial (NB) regressions are widely used methods for non-over-dispersed (NOD) and over-dispersed (OD) count data respectively. However, in the presence of excessive number of zeros, these methods need adjustments. In this paper, we consider a zero-inflated Poisson mixed effects model (ZIPMM) and zero-inflated negative binomial mixed effects model (ZINBMM) to address excessive zero counts in the NOD and OD RNA-seq data respectively in the presence of random effects. We apply these methods to both simulated and real RNA-seq datasets. The ZIPMM and ZINBMM perform better on both simulated and real datasets.

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Han, Bo, and Jian Xu. "Analysis of Crash Counts Using a Multilevel Zero-Inflated Negative Binomial Model." Advanced Materials Research 912-914 (April 2014): 1164–68. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.1164.

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Due to that roadway crashes are generally discrete and rare, researchers frequently have several observational units (e.g., census tract, segment) with excess zeros reported crashes during the period. In this study, a multilevel zero-inflated negative binomial (MZINB) model was developed for analysis, allowing for overdispersion and excess zeros, as well as the factors of roadway design and traffic characteristic. Several goodness-of-fit measures are used for examining and comparing, using Markov chain Monte Carlo (MCMC) methods. The estimation results show that MZINB model is better than multilevel zero-inflated Poisson (MZIP) model and zero-inflated negative binomial (ZINB) and zero-inflated Poisson (ZIP) models.

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MÖller, Tobias A., Christian H. Weiß, and Hee-Young Kim. "Modelling counts with state-dependent zero inflation." Statistical Modelling 20, no. 2 (2018): 127–47. http://dx.doi.org/10.1177/1471082x18800514.

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We introduce a state-dependent zero-inflation mechanism for count distributions with unbounded or bounded support. Instead of uniformly downweighting the parent distribution, this flexible approach allows us to generate most of the zeros from either low or high counts. We derive the stochastic properties of the inflated distributions and discuss special instances designed for zero inflation caused by, for example, excessive demand or underreporting. Furthermore, we apply the state-dependent zero-inflation mechanism to generalize existing models for count time series with bounded support.

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Purhadi, Yuliani Setia Dewi, and Luthfatul Amaliana. "Zero Inflated Poisson and Geographically Weighted Zero- Inflated Poisson Regression Model: Application to Elephantiasis (Filariasis) Counts Data." Journal of Mathematics and Statistics 11, no. 2 (2015): 52–60. http://dx.doi.org/10.3844/jmssp.2015.52.60.

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Ghosh, Souparno, Alan E. Gelfand, Kai Zhu, and James S. Clark. "The k-ZIG: Flexible Modeling for Zero-Inflated Counts." Biometrics 68, no. 3 (2012): 878–85. http://dx.doi.org/10.1111/j.1541-0420.2011.01729.x.

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Cantoni, Eva, and Marie Auda. "Stochastic variable selection strategies for zero-inflated models." Statistical Modelling 18, no. 1 (2017): 3–23. http://dx.doi.org/10.1177/1471082x17711068.

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When count data exhibit excess zero, that is more zero counts than a simpler parametric distribution can model, the zero-inflated Poisson (ZIP) or zero-inflated negative binomial (ZINB) models are often used. Variable selection for these models is even more challenging than for other regression situations because the availability of p covariates implies 4 p possible models. We adapt to zero-inflated models an approach for variable selection that avoids the screening of all possible models. This approach is based on a stochastic search through the space of all possible models, which generates a chain of interesting models. As an additional novelty, we propose three ways of extracting information from this rich chain and we compare them in two simulation studies, where we also contrast our approach with regularization (penalized) techniques available in the literature. The analysis of a typical dataset that has motivated our research is also presented, before concluding with some recommendations.

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Jang, Jong-Hwan, Junggu Choi, Hyun Woong Roh, et al. "Deep Learning Approach for Imputation of Missing Values in Actigraphy Data: Algorithm Development Study." JMIR mHealth and uHealth 8, no. 7 (2020): e16113. http://dx.doi.org/10.2196/16113.

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Background Data collected by an actigraphy device worn on the wrist or waist can provide objective measurements for studies related to physical activity; however, some data may contain intervals where values are missing. In previous studies, statistical methods have been applied to impute missing values on the basis of statistical assumptions. Deep learning algorithms, however, can learn features from the data without any such assumptions and may outperform previous approaches in imputation tasks. Objective The aim of this study was to impute missing values in data using a deep learning approach. Methods To develop an imputation model for missing values in accelerometer-based actigraphy data, a denoising convolutional autoencoder was adopted. We trained and tested our deep learning–based imputation model with the National Health and Nutrition Examination Survey data set and validated it with the external Korea National Health and Nutrition Examination Survey and the Korean Chronic Cerebrovascular Disease Oriented Biobank data sets which consist of daily records measuring activity counts. The partial root mean square error and partial mean absolute error of the imputed intervals (partial RMSE and partial MAE, respectively) were calculated using our deep learning–based imputation model (zero-inflated denoising convolutional autoencoder) as well as using other approaches (mean imputation, zero-inflated Poisson regression, and Bayesian regression). Results The zero-inflated denoising convolutional autoencoder exhibited a partial RMSE of 839.3 counts and partial MAE of 431.1 counts, whereas mean imputation achieved a partial RMSE of 1053.2 counts and partial MAE of 545.4 counts, the zero-inflated Poisson regression model achieved a partial RMSE of 1255.6 counts and partial MAE of 508.6 counts, and Bayesian regression achieved a partial RMSE of 924.5 counts and partial MAE of 605.8 counts. Conclusions Our deep learning–based imputation model performed better than the other methods when imputing missing values in actigraphy data.

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Maiti, Raju, Atanu Biswas, and Samarjit Das. "Time Series of Zero-Inflated Counts and their Coherent Forecasting." Journal of Forecasting 34, no. 8 (2015): 694–707. http://dx.doi.org/10.1002/for.2368.

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DENWOOD, M. J., M. J. STEAR, L. MATTHEWS, S. W. J. REID, N. TOFT, and G. T. INNOCENT. "The distribution of the pathogenic nematodeNematodirus battusin lambs is zero-inflated." Parasitology 135, no. 10 (2008): 1225–35. http://dx.doi.org/10.1017/s0031182008004708.

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SUMMARYUnderstanding the frequency distribution of parasites and parasite stages among hosts is essential for efficient experimental design and statistical analysis, and is also required for the development of sustainable methods of controlling infection.Nematodirus battusis one of the most important organisms that infect sheep but the distribution of parasites among hosts is unknown. An initial analysis indicated a high frequency of animals withoutN. battusand with zero egg counts, suggesting the possibility of a zero-inflated distribution. We developed a Bayesian analysis using Markov chain Monte Carlo methods to estimate the parameters of the zero-inflated negative binomial distribution. The analysis of 3000 simulated data sets indicated that this method out-performed the maximum likelihood procedure. Application of this technique to faecal egg counts from lambs in a commercial upland flock indicated thatN. battuscounts were indeed zero-inflated. Estimating the extent of zero-inflation is important for effective statistical analysis and for the accurate identification of genetically resistant animals.

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Brodziak, Jon, and William A. Walsh. "Model selection and multimodel inference for standardizing catch rates of bycatch species: a case study of oceanic whitetip shark in the Hawaii-based longline fishery." Canadian Journal of Fisheries and Aquatic Sciences 70, no. 12 (2013): 1723–40. http://dx.doi.org/10.1139/cjfas-2013-0111.

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One key issue for standardizing catch per unit effort (CPUE) of bycatch species is how to model observations of zero catch per fishing operation. Typically, the fraction of zero catches is high, and catch counts may be overdispersed. In this study, we develop a model selection and multimodel inference approach to standardize CPUE in a case study of oceanic whitetip shark (Carcharhinus longimanus) bycatch in the Hawaii-based pelagic longline fishery. Alternative hypotheses for shark catch per longline set were characterized by the variance to mean ratio of the count distribution. Zero-inflated and non-inflated Poisson, negative binomial, and delta-gamma models were fit to fishery observer data using stepwise variable selection. Alternative hypotheses were compared using multimodel inference. Results from the best-fitting zero-inflated negative binomial model showed that standardized CPUE of oceanic whitetip sharks decreased by about 90% during 1995–2010 because of increased zero catch sets and decreased CPUE on sets with positive catch. Our model selection approach provides an objective way to address the question of how to treat zero catches when analyzing bycatch CPUE.

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Pittman, Brian, Eugenia Buta, Suchitra Krishnan-Sarin, Stephanie S. O’Malley, Thomas Liss, and Ralitza Gueorguieva. "Models for Analyzing Zero-Inflated and Overdispersed Count Data: An Application to Cigarette and Marijuana Use." Nicotine & Tobacco Research 22, no. 8 (2018): 1390–98. http://dx.doi.org/10.1093/ntr/nty072.

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Abstract Introduction This article describes different methods for analyzing counts and illustrates their use on cigarette and marijuana smoking data. Methods The Poisson, zero-inflated Poisson (ZIP), hurdle Poisson (HUP), negative binomial (NB), zero-inflated negative binomial (ZINB), and hurdle negative binomial (HUNB) regression models are considered. The different approaches are evaluated in terms of the ability to take into account zero-inflation (extra zeroes) and overdispersion (variance larger than expected) in count outcomes, with emphasis placed on model fit, interpretation, and choosing an appropriate model given the nature of the data. The illustrative data example focuses on cigarette and marijuana smoking reports from a study on smoking habits among youth e-cigarette users with gender, age, and e-cigarette use included as predictors. Results Of the 69 subjects available for analysis, 36% and 64% reported smoking no cigarettes and no marijuana, respectively, suggesting both outcomes might be zero-inflated. Both outcomes were also overdispersed with large positive skew. The ZINB and HUNB models fit the cigarette counts best. According to goodness-of-fit statistics, the NB, HUNB, and ZINB models fit the marijuana data well, but the ZINB provided better interpretation. Conclusion In the absence of zero-inflation, the NB model fits smoking data well, which is typically overdispersed. In the presence of zero-inflation, the ZINB or HUNB model is recommended to account for additional heterogeneity. In addition to model fit and interpretability, choosing between a zero-inflated or hurdle model should ultimately depend on the assumptions regarding the zeros, study design, and the research question being asked. Implications Count outcomes are frequent in tobacco research and often have many zeros and exhibit large variance and skew. Analyzing such data based on methods requiring a normally distributed outcome are inappropriate and will likely produce spurious results. This study compares and contrasts appropriate methods for analyzing count data, specifically those with an over-abundance of zeros, and illustrates their use on cigarette and marijuana smoking data. Recommendations are provided.

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Zhu, Huirong, Stacia M. DeSantis, and Sheng Luo. "Joint modeling of longitudinal zero-inflated count and time-to-event data: A Bayesian perspective." Statistical Methods in Medical Research 27, no. 4 (2016): 1258–70. http://dx.doi.org/10.1177/0962280216659312.

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Longitudinal zero-inflated count data are encountered frequently in substance-use research when assessing the effects of covariates and risk factors on outcomes. Often, both the time to a terminal event such as death or dropout and repeated measure count responses are collected for each subject. In this setting, the longitudinal counts are censored by the terminal event, and the time to the terminal event may depend on the longitudinal outcomes. In the study described herein, we expand the class of joint models for longitudinal and survival data to accommodate zero-inflated counts and time-to-event data by using a Cox proportional hazards model with piecewise constant baseline hazard. We use a Bayesian framework via Markov chain Monte Carlo simulations implemented in the BUGS programming language. Via an extensive simulation study, we apply the joint model and obtain estimates that are more accurate than those of the corresponding independence model. We apply the proposed method to an alpha-tocopherol, beta-carotene lung cancer prevention study.

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Habeeb Hashim, Luay, and Ahmad Naeem Flaih. "Modeling the Rainfall Count data Using Some Zero Type models with application." Journal of Al-Qadisiyah for computer science and mathematics 11, no. 2 (2019): 14–27. http://dx.doi.org/10.29304/jqcm.2019.11.2.554.

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Count data, including zero counts arise in a wide variety of application, hence models for counts have become widely popular in many fields. In the statistics field, one may define the count data as that type of observation which takes only the non-negative integers value. Sometimes researchers may Counts more zeros than the expected. Excess zero can be defined as Zero-Inflation. Data with abundant zeros are especially popular in health, marketing, finance, econometric, ecology, statistics quality control, geographical, and environmental fields when counting the occurrence of certain behavioral and natural events, such as frequency of alcohol use, take drugs, number of cigarettes smoked, the occurrence of earthquakes, rainfall, and etc. Some models have been used to analyzing count data such as the zero-inflated Poisson (ZIP) model and the negative binomial model. In this paper, the models, Poisson, Negative Binomial, ZIP, and ZINB were been used to analyze rainfall data.

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Baetschmann, Gregori, and Rainer Winkelmann. "Modeling zero-inflated count data when exposure varies: With an application to tumor counts." Biometrical Journal 55, no. 5 (2013): 679–86. http://dx.doi.org/10.1002/bimj.201200021.

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Liu, Xueyan, Bryan Winter, Li Tang, Bo Zhang, Zhiwei Zhang, and Hui Zhang. "Simulating comparisons of different computing algorithms fitting zero-inflated Poisson models for zero abundant counts." Journal of Statistical Computation and Simulation 87, no. 13 (2017): 2609–21. http://dx.doi.org/10.1080/00949655.2017.1327590.

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LEE, J. H., G. HAN, W. J. FULP, and A. R. GIULIANO. "Analysis of overdispersed count data: application to the Human Papillomavirus Infection in Men (HIM) Study." Epidemiology and Infection 140, no. 6 (2011): 1087–94. http://dx.doi.org/10.1017/s095026881100166x.

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SUMMARYThe Poisson model can be applied to the count of events occurring within a specific time period. The main feature of the Poisson model is the assumption that the mean and variance of the count data are equal. However, this equal mean-variance relationship rarely occurs in observational data. In most cases, the observed variance is larger than the assumed variance, which is called overdispersion. Further, when the observed data involve excessive zero counts, the problem of overdispersion results in underestimating the variance of the estimated parameter, and thus produces a misleading conclusion. We illustrated the use of four models for overdispersed count data that may be attributed to excessive zeros. These are Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial models. The example data in this article deal with the number of incidents involving human papillomavirus infection. The four models resulted in differing statistical inferences. The Poisson model, which is widely used in epidemiology research, underestimated the standard errors and overstated the significance of some covariates.

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Tang, Zheng-Zheng, and Guanhua Chen. "Zero-inflated generalized Dirichlet multinomial regression model for microbiome compositional data analysis." Biostatistics 20, no. 4 (2018): 698–713. http://dx.doi.org/10.1093/biostatistics/kxy025.

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Summary There is heightened interest in using high-throughput sequencing technologies to quantify abundances of microbial taxa and linking the abundance to human diseases and traits. Proper modeling of multivariate taxon counts is essential to the power of detecting this association. Existing models are limited in handling excessive zero observations in taxon counts and in flexibly accommodating complex correlation structures and dispersion patterns among taxa. In this article, we develop a new probability distribution, zero-inflated generalized Dirichlet multinomial (ZIGDM), that overcomes these limitations in modeling multivariate taxon counts. Based on this distribution, we propose a ZIGDM regression model to link microbial abundances to covariates (e.g. disease status) and develop a fast expectation–maximization algorithm to efficiently estimate parameters in the model. The derived tests enable us to reveal rich patterns of variation in microbial compositions including differential mean and dispersion. The advantages of the proposed methods are demonstrated through simulation studies and an analysis of a gut microbiome dataset.

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Rumahorbo, Kusni Rohani, Budi Susetyo, and Kusman Sadik. "PEMODELAN DATA TERSENSOR KANAN MENGGUNAKAN ZERO INFLATED NEGATIVE BINOMIAL DAN HURDLE NEGATIVE BINOMIAL." Indonesian Journal of Statistics and Its Applications 3, no. 2 (2019): 184–201. http://dx.doi.org/10.29244/ijsa.v3i2.247.

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Health is a very important thing for humanity. One way to look at a person's health condition is through the number of unhealthy days which can also shows the productivity of the community in a region. Modeling the number of unhealthy days which are examples of count data can be done using Poisson regression. Problems that are often faced in data counts are overdispersion and excess zero. Poisson regression cannot be applied to data that experiences both of these. Zero Inflated Negative Binomial and Hurdle Negative Binomial modeling was performed on data with 2 conditions, uncensored and censored. The explanatory variables used are gender, age, marital status, education level, home ownership status and rural-urban status. According to the results of the AIC and RMSE calculation, Zero Inflated Negative Binomial on censored data showed the best performance for estimating the number of unhealthy days.

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Zhang, Xinyan, and Nengjun Yi. "Fast zero-inflated negative binomial mixed modeling approach for analyzing longitudinal metagenomics data." Bioinformatics 36, no. 8 (2020): 2345–51. http://dx.doi.org/10.1093/bioinformatics/btz973.

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Abstract Motivation Longitudinal metagenomics data, including both 16S rRNA and whole-metagenome shotgun sequencing data, enhanced our abilities to understand the dynamic associations between the human microbiome and various diseases. However, analytic tools have not been fully developed to simultaneously address the main challenges of longitudinal metagenomics data, i.e. high-dimensionality, dependence among samples and zero-inflation of observed counts. Results We propose a fast zero-inflated negative binomial mixed modeling (FZINBMM) approach to analyze high-dimensional longitudinal metagenomic count data. The FZINBMM approach is based on zero-inflated negative binomial mixed models (ZINBMMs) for modeling longitudinal metagenomic count data and a fast EM-IWLS algorithm for fitting ZINBMMs. FZINBMM takes advantage of a commonly used procedure for fitting linear mixed models, which allows us to include various types of fixed and random effects and within-subject correlation structures and quickly analyze many taxa. We found that FZINBMM remarkably outperformed in computational efficiency and was statistically comparable with two R packages, GLMMadaptive and glmmTMB, that use numerical integration to fit ZINBMMs. Extensive simulations and real data applications showed that FZINBMM outperformed other previous methods, including linear mixed models, negative binomial mixed models and zero-inflated Gaussian mixed models. Availability and implementation FZINBMM has been implemented in the R package NBZIMM, available in the public GitHub repository http://github.com//nyiuab//NBZIMM. Supplementary information Supplementary data are available at Bioinformatics online.

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Rakitzis, Athanasios C., Philippe Castagliola, and Petros E. Maravelakis. "Cumulative sum control charts for monitoring geometrically inflated Poisson processes: An application to infectious disease counts data." Statistical Methods in Medical Research 27, no. 2 (2016): 622–41. http://dx.doi.org/10.1177/0962280216641985.

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In this work, we study upper-sided cumulative sum control charts that are suitable for monitoring geometrically inflated Poisson processes. We assume that a process is properly described by a two-parameter extension of the zero-inflated Poisson distribution, which can be used for modeling count data with an excessive number of zero and non-zero values. Two different upper-sided cumulative sum-type schemes are considered, both suitable for the detection of increasing shifts in the average of the process. Aspects of their statistical design are discussed and their performance is compared under various out-of-control situations. Changes in both parameters of the process are considered. Finally, the monitoring of the monthly cases of poliomyelitis in the USA is given as an illustrative example.

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Wang, Craig, Paul R. Torgerson, Johan Höglund, and Reinhard Furrer. "Zero-inflated hierarchical models for faecal egg counts to assess anthelmintic efficacy." Veterinary Parasitology 235 (February 2017): 20–28. http://dx.doi.org/10.1016/j.vetpar.2016.12.007.

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Neelon, Brian, and Dongjun Chung. "The LZIP: A Bayesian latent factor model for correlated zero-inflated counts." Biometrics 73, no. 1 (2016): 185–96. http://dx.doi.org/10.1111/biom.12558.

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Mirkamali, Sayed Jamal, and Mojtaba Ganjali. "A general location model with zero-inflated counts and skew normal outcomes." Journal of Applied Statistics 44, no. 15 (2016): 2716–28. http://dx.doi.org/10.1080/02664763.2016.1261813.

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Li, Cong, Shuai Cui, and Dehui Wang. "Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient." Entropy 23, no. 3 (2021): 372. http://dx.doi.org/10.3390/e23030372.

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In this research, we consider monitoring mean and correlation changes from zero-inflated autocorrelated count data based on the integer-valued time series model with random survival rate. A cumulative sum control chart is constructed due to its efficiency, the corresponding calculation methods of average run length and the standard deviation of the run length are given. Practical guidelines concerning the chart design are investigated. Extensive computations based on designs of experiments are conducted to illustrate the validity of the proposed method. Comparisons with the conventional control charting procedure are also provided. The analysis of the monthly number of drug crimes in the city of Pittsburgh is displayed to illustrate our current method of process monitoring.

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Abiodun, Gbenga J., Olusola S. Makinde, Abiodun M. Adeola, et al. "A Dynamical and Zero-Inflated Negative Binomial Regression Modelling of Malaria Incidence in Limpopo Province, South Africa." International Journal of Environmental Research and Public Health 16, no. 11 (2019): 2000. http://dx.doi.org/10.3390/ijerph16112000.

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Recent studies have considered the connections between malaria incidence and climate variables using mathematical and statistical models. Some of the statistical models focused on time series approach based on Box–Jenkins methodology or on dynamic model. The latter approach allows for covariates different from its original lagged values, while the Box–Jenkins does not. In real situations, malaria incidence counts may turn up with many zero terms in the time series. Fitting time series model based on the Box–Jenkins approach and ARIMA may be spurious. In this study, a zero-inflated negative binomial regression model was formulated for fitting malaria incidence in Mopani and Vhembe―two of the epidemic district municipalities in Limpopo, South Africa. In particular, a zero-inflated negative binomial regression model was formulated for daily malaria counts as a function of some climate variables, with the aim of identifying the model that best predicts reported malaria cases. Results from this study show that daily rainfall amount and the average temperature at various lags have a significant influence on malaria incidence in the study areas. The significance of zero inflation on the malaria count was examined using the Vuong test and the result shows that zero-inflated negative binomial regression model fits the data better. A dynamical climate-based model was further used to investigate the population dynamics of mosquitoes over the two regions. Findings highlight the significant roles of Anopheles arabiensis on malaria transmission over the regions and suggest that vector control activities should be intense to eradicate malaria in Mopani and Vhembe districts. Although An. arabiensis has been identified as the major vector over these regions, our findings further suggest the presence of additional vectors transmitting malaria in the study regions. The findings from this study offer insight into climate-malaria incidence linkages over Limpopo province of South Africa.

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Xu, Tao, Guangjin Zhu, and Shaomei Han. "Study of depression influencing factors with zero-inflated regression models in a large-scale population survey." BMJ Open 7, no. 11 (2017): e016471. http://dx.doi.org/10.1136/bmjopen-2017-016471.

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ObjectivesThe number of depression symptoms can be considered as count data in order to get complete and accurate analyses findings in studies of depression. This study aims to compare the goodness of fit of four count outcomes models by a large survey sample to identify the optimum model for a risk factor study of the number of depression symptoms.Methods15 820 subjects, aged 10 to 80 years old, who were not suffering from serious chronic diseases and had not run a high fever in the past 15 days, agreed to take part in this survey; 15 462 subjects completed all the survey scales. The number of depression symptoms was the sum of the ‘positive’ responses of seven depression questions. Four count outcomes models and a logistic model were constructed to identify the optimum model of the number of depression symptoms.ResultsThe mean number of depression symptoms was 1.37±1.55. The over-dispersion test statisticOwas 308.011. The alpha dispersion parameter was 0.475 (95% CI 0.443 to 0.508), which was significantly larger than 0. The Vuong test statisticZwas 6.782 and the P value was <0.001, which showed that there were too many zero counts to be accounted for with traditional negative binomial distribution. The zero-inflated negative binomial (ZINB) model had the largest log likelihood and smallest AIC and BIC, suggesting best goodness of fit. In addition, predictive probabilities for many counts in the ZINB model fitted the observed counts best.ConclusionsAll fitting test statistics and the predictive probability curve produced the same findings that the ZINB model was the best model for fitting the number of depression symptoms, assessing both the presence or absence of depression and its severity.

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Bermúdez, Lluís, Dimitris Karlis, and Isabel Morillo. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models." Risks 8, no. 1 (2020): 10. http://dx.doi.org/10.3390/risks8010010.

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When modelling insurance claim count data, the actuary often observes overdispersion and an excess of zeros that may be caused by unobserved heterogeneity. A common approach to accounting for overdispersion is to consider models with some overdispersed distribution as opposed to Poisson models. Zero-inflated, hurdle and compound frequency models are typically applied to insurance data to account for such a feature of the data. However, a natural way to deal with unobserved heterogeneity is to consider mixtures of a simpler models. In this paper, we consider k-finite mixtures of some typical regression models. This approach has interesting features: first, it allows for overdispersion and the zero-inflated model represents a special case, and second, it allows for an elegant interpretation based on the typical clustering application of finite mixture models. k-finite mixture models are applied to a car insurance claim dataset in order to analyse whether the problem of unobserved heterogeneity requires a richer structure for risk classification. Our results show that the data consist of two subpopulations for which the regression structure is different.

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Zhang, Xinyan, Boyi Guo, and Nengjun Yi. "Zero-Inflated gaussian mixed models for analyzing longitudinal microbiome data." PLOS ONE 15, no. 11 (2020): e0242073. http://dx.doi.org/10.1371/journal.pone.0242073.

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Motivation The human microbiome is variable and dynamic in nature. Longitudinal studies could explain the mechanisms in maintaining the microbiome in health or causing dysbiosis in disease. However, it remains challenging to properly analyze the longitudinal microbiome data from either 16S rRNA or metagenome shotgun sequencing studies, output as proportions or counts. Most microbiome data are sparse, requiring statistical models to handle zero-inflation. Moreover, longitudinal design induces correlation among the samples and thus further complicates the analysis and interpretation of the microbiome data. Results In this article, we propose zero-inflated Gaussian mixed models (ZIGMMs) to analyze longitudinal microbiome data. ZIGMMs is a robust and flexible method which can be applicable for longitudinal microbiome proportion data or count data generated with either 16S rRNA or shotgun sequencing technologies. It can include various types of fixed effects and random effects and account for various within-subject correlation structures, and can effectively handle zero-inflation. We developed an efficient Expectation-Maximization (EM) algorithm to fit the ZIGMMs by taking advantage of the standard procedure for fitting linear mixed models. We demonstrate the computational efficiency of our EM algorithm by comparing with two other zero-inflated methods. We show that ZIGMMs outperform the previously used linear mixed models (LMMs), negative binomial mixed models (NBMMs) and zero-inflated Beta regression mixed model (ZIBR) in detecting associated effects in longitudinal microbiome data through extensive simulations. We also apply our method to two public longitudinal microbiome datasets and compare with LMMs and NBMMs in detecting dynamic effects of associated taxa.

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TRUONG, BUU-CHAU, KIM-HUNG PHO, CONG-CHANH DINH, and MICHAEL McALEER. "ZERO-INFLATED POISSON REGRESSION MODELS: APPLICATIONS IN THE SCIENCES AND SOCIAL SCIENCES." Annals of Financial Economics 16, no. 02 (2021): 2150006. http://dx.doi.org/10.1142/s2010495221500068.

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This paper makes a theoretical contribution by presenting a detailed derivation of a zero-inflated Poisson (ZIP) model, and then deriving the parameters of the ZIP model using a fishing data set. This model has several practical applications, and is largely performed to model count data that have an excess number of zero counts. In the scope of the paper, we introduce the complete formulae, the likelihood and log-likelihood functions and the estimating equation of the ZIP model. We then investigate the theory of large sample properties of this model under some regularity conditions. A simulation study and a fishing data set are studied for the ZIP model. The results in the actual application in this work are meaningful, useful and crucial in reality. The results also provide reliable evidence for obtaining the largest number of fish while fishing. This is the contribution of this research in terms of applications. Finally, the important applications of this model in practice, some conclusions, and future work is also presented for consideration.

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Lee, Kyu Ha, Brent A. Coull, Anna-Barbara Moscicki, Bruce J. Paster, and Jacqueline R. Starr. "Bayesian variable selection for multivariate zero-inflated models: Application to microbiome count data." Biostatistics 21, no. 3 (2018): 499–517. http://dx.doi.org/10.1093/biostatistics/kxy067.

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Summary Microorganisms play critical roles in human health and disease. They live in diverse communities in which they interact synergistically or antagonistically. Thus for estimating microbial associations with clinical covariates, such as treatment effects, joint (multivariate) statistical models are preferred. Multivariate models allow one to estimate and exploit complex interdependencies among multiple taxa, yielding more powerful tests of exposure or treatment effects than application of taxon-specific univariate analyses. Analysis of microbial count data also requires special attention because data commonly exhibit zero inflation, i.e., more zeros than expected from a standard count distribution. To meet these needs, we developed a Bayesian variable selection model for multivariate count data with excess zeros that incorporates information on the covariance structure of the outcomes (counts for multiple taxa), while estimating associations with the mean levels of these outcomes. Though there has been much work on zero-inflated models for longitudinal data, little attention has been given to high-dimensional multivariate zero-inflated data modeled via a general correlation structure. Through simulation, we compared performance of the proposed method to that of existing univariate approaches, for both the binary (“excess zero”) and count parts of the model. When outcomes were correlated the proposed variable selection method maintained type I error while boosting the ability to identify true associations in the binary component of the model. For the count part of the model, in some scenarios the univariate method had higher power than the multivariate approach. This higher power was at a cost of a highly inflated false discovery rate not observed with the proposed multivariate method. We applied the approach to oral microbiome data from the Pediatric HIV/AIDS Cohort Oral Health Study and identified five (of 44) species associated with HIV infection.

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Morgan, Charity J., Mark F. Lenzenweger, Donald B. Rubin, and Deborah L. Levy. "A hierarchical finite mixture model that accommodates zero-inflated counts, non-independence, and heterogeneity." Statistics in Medicine 33, no. 13 (2014): 2238–50. http://dx.doi.org/10.1002/sim.6091.

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DeSantis, Stacia M., and Dipankar Bandyopadhyay. "Hidden Markov models for zero-inflated Poisson counts with an application to substance use." Statistics in Medicine 30, no. 14 (2011): 1678–94. http://dx.doi.org/10.1002/sim.4207.

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Xu, Xiaofei, Ying Chen, Cathy W. S. Chen, and Xiancheng Lin. "Adaptive log-linear zero-inflated generalized Poisson autoregressive model with applications to crime counts." Annals of Applied Statistics 14, no. 3 (2020): 1493–515. http://dx.doi.org/10.1214/20-aoas1360.

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FANG, R., B. D. WAGNER, J. K. HARRIS, and S. A. FILLON. "Zero-inflated negative binomial mixed model: an application to two microbial organisms important in oesophagitis." Epidemiology and Infection 144, no. 11 (2016): 2447–55. http://dx.doi.org/10.1017/s0950268816000662.

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SUMMARYAltered microbial communities are thought to play an important role in eosinophilic oesophagitis, an allergic inflammatory condition of the oesophagus. Identification of the majority of organisms present in human-associated microbial communities is feasible with the advent of high throughput sequencing technology. However, these data consist of non-negative, highly skewed sequence counts with a large proportion of zeros. In addition, hierarchical study designs are often performed with repeated measurements or multiple samples collected from the same subject, thus requiring approaches to account for within-subject variation, yet only a small number of microbiota studies have applied hierarchical regression models. In this paper, we describe and illustrate the use of a hierarchical regression-based approach to evaluate multiple factors for a small number of organisms individually. More specifically, the zero-inflated negative binomial mixed model with random effects in both the count and zero-inflated parts is applied to evaluate associations with disease state while adjusting for potential confounders for two organisms of interest from a study of human microbiota sequence data in oesophagitis.

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Neelon, Brian, Howard H. Chang, Qiang Ling, and Nicole S. Hastings. "Spatiotemporal hurdle models for zero-inflated count data: Exploring trends in emergency department visits." Statistical Methods in Medical Research 25, no. 6 (2016): 2558–76. http://dx.doi.org/10.1177/0962280214527079.

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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.

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Wang, Peiming. "Markov zero-inflated Poisson regression models for a time series of counts with excess zeros." Journal of Applied Statistics 28, no. 5 (2001): 623–32. http://dx.doi.org/10.1080/02664760120047951.

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Lee, Sangyeol, Dongwon Kim, and Seongwoo Seok. "Modeling and inference for counts time series based on zero-inflated exponential family INGARCH models." Journal of Statistical Computation and Simulation 91, no. 11 (2021): 2227–48. http://dx.doi.org/10.1080/00949655.2021.1890732.

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Lee, Yong-Gil, Jeong-Dong Lee, Yong-Il Song, and Se-Jun Lee. "An in-depth empirical analysis of patent citation counts using zero-inflated count data model: The case of KIST." Scientometrics 70, no. 1 (2007): 27–39. http://dx.doi.org/10.1007/s11192-007-0102-z.

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He, B., M. Xie, T. N. Goh, and P. Ranjan. "On the Estimation Error in Zero-Inflated Poisson Model for Process Control." International Journal of Reliability, Quality and Safety Engineering 10, no. 02 (2003): 159–69. http://dx.doi.org/10.1142/s0218539303001068.

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The control chart based on a Poisson distribution has often been used to monitor the number of defects in sampling units. However, many false alarms could be observed due to extra zero counts, especially for high-quality processes. Therefore, some alternatives have been developed to alleviate this problem, one of which is the control chart based on the zero-inflated Poisson distribution. This distribution takes into account the extra zeros present in the data, and yield more accurate results than the Poisson distribution. However, implementing a control chart is often based on the assumption that the parameters are either known or an accurate estimate is available. For a high quality process, an accurate estimate may require a very large sample size, which is seldom available. In this paper the effect of estimation error is investigated. An analytical approximation is derived to compute shift detection probability and run length distribution. The study shows that the false alarm rates are higher than the desirable level for smaller values of the sample size. This is further supported by smaller average run length. In general, the quantitative results from this paper can be utilized to select a minimum size of the initial sample for estimating the control limits so that certain average run length requirements are met.

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Xu, Jian, and Ke Si You. "The Effects of Land Use, Design and Environment on Traffic Fatalities." Advanced Materials Research 838-841 (November 2013): 2081–87. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.2081.

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Developing statistics methods to distinguish significant factors associated with roadways is one of the most feasible accesses to understand the nature of traffic accidents. In this study, zero-inflated negative binomial (ZINB) model was developed to allow for overdispersion and excess zeros, as well as the factors of land use, design and environment to examine the effects. The statistical tests show that ZINB model is preferred to zero-inflated Poisson and negative binomial models due to its ability to describe crash counts associated with severe injuries and fatalities more effectively. The results show that fatalities are positively associated with segment length, surface width, land use variables and rainfall. For example, an increase of one inch rainfall will result in an increase of 0.02% in fatalities. Interestingly, distances to hospitals yield positive impact, which suggests that longer distances lead to higher fatalities, presumably due to time lost in transporting crash victims to hospitals.

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Rahayu, Lili Puspita, Kusman Sadik, and Indahwati Indahwati. "Overdispersion study of poisson and zero-inflated poisson regression for some characteristics of the data on lamda, n, p." International Journal of Advances in Intelligent Informatics 2, no. 3 (2016): 140. http://dx.doi.org/10.26555/ijain.v2i3.73.

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Poisson distribution is one of discrete distribution that is often used in modeling of rare events. The data obtained in form of counts with non-negative integers. One of analysis that is used in modeling count data is Poisson regression. Deviation of assumption that often occurs in the Poisson regression is overdispersion. Cause of overdispersion is an excess zero probability on the response variable. Solving model that be used to overcome of overdispersion is zero-inflated Poisson (ZIP) regression. The research aimed to develop a study of overdispersion for Poisson and ZIP regression on some characteristics of the data. Overdispersion on some characteristics of the data that were studied in this research are simulated by combining the parameter of Poisson distribution (λ), zero probability (p), and sample size (n) on the response variable then comparing the Poisson and ZIP regression models. Overdispersion study on data simulation showed that the larger λ, n, and p, the better is the model of ZIP than Poisson regression. The results of this simulation are also strengthened by the exploration of Pearson residual in Poisson and ZIP regression.

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SANDBERG, MARIANNE, MERETE HOFSHAGEN, ØYVIN ØSTENSVIK, EYSTEIN SKJERVE, and GILES INNOCENT. "Survival of Campylobacter on Frozen Broiler Carcasses as a Function of Time." Journal of Food Protection 68, no. 8 (2005): 1600–1605. http://dx.doi.org/10.4315/0362-028x-68.8.1600.

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In the Norwegian Action Plan against Campylobacter in broilers, carcasses from flocks identified as positive before slaughter are either heat treated or frozen for 5 weeks to reduce the number of Campylobacter. The objective of this study was to estimate the effect of freezing time and predict the number of Campylobacter on naturally infected or contaminated broiler carcasses following freezing for 2, 4, 6, 8, 10, 13, 21, 35, and 120 days by nonparametric and parametric linear statistical models. From each of the five flocks, 27 carcasses were sampled. Each carcass was cut in two pieces along the chest bone. Half was put into the freezer (−20°C), whereas the other was deskinned and quantitative culturing was conducted from a 10-g sample of the skin. Fifteen frozen halves were selected at random at each time point following freezing from 2 to 120 days, and skin samples from these were cultured quantitatively and qualitatively. In regard to the log reduction of Campylobacter, almost similar results were obtained using three statistical methods; median regression on the change in Campylobacter counts, zero-inflated negative binomial regression, and a Bayesian Markov chain Monte Carlo (decay) model on original counts. Overall, a 2-log reduction of Campylobacter was obtained after 3 weeks of freezing. Only a marginal extra effect was observed when extending the freezing to 5 weeks. Although freezing appears to be an efficient way to reduce the level of Campylobacter on broiler carcasses, in 80% of the carcasses Campylobacter could still be detected using quantitative culturing following 120 days of freezing. Based on the high number of zeros, these data should be modeled by a zero-inflated model. The best statistical fit in regard to goodness-of-fit measures was the zero-inflated negative binomial log link model, closely followed by the Poisson model. Thus, in our continued search for a better way to describe the data, we used the Poisson distribution in the mixed Bayesian decay models.

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Hasan, M. Tariqul, Gary Sneddon, and Renjun Ma. "Regression analysis of zero-inflated time-series counts: application to air pollution related emergency room visit data." Journal of Applied Statistics 39, no. 3 (2012): 467–76. http://dx.doi.org/10.1080/02664763.2011.595778.

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Burger, Divan A., and Emmanuel Lesaffre. "Nonlinear mixed‐effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero‐inflated discrete Weibull distribution." Statistics in Medicine 40, no. 23 (2021): 5078–95. http://dx.doi.org/10.1002/sim.9112.

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Wang, Yi (Victor), Paolo Gardoni, Colleen Murphy, and Stéphane Guerrier. "Predicting Fatality Rates Due to Earthquakes Accounting for Community Vulnerability." Earthquake Spectra 35, no. 2 (2019): 513–36. http://dx.doi.org/10.1193/022618eqs046m.

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The existing prediction models for earthquake fatalities usually require a detailed building inventory that might not be readily available. In addition, existing models tend to overlook the socioeconomic characteristics of communities of interest as well as zero-fatality data points. This paper presents a methodology that develops a probabilistic zero-inflated beta regression model to predict earthquake fatality rates given the geographic distributions of earthquake intensities with data reflecting community vulnerability. As an illustration, the prediction model is calibrated using fatality data from 61 earthquakes affecting Taiwan from 1999 to 2016, as well as information on the socioeconomic and environmental characteristics of the affected communities. Using a local seismic hazard map, the calibrated prediction model is used in a seismic risk analysis for Taiwan that predicts the expected fatality rates and counts caused by earthquakes in future years.

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Hailu Amare, Hiwot, and Bernt Lindtjørn. "Helminth infections among rural schoolchildren in Southern Ethiopia: A cross-sectional multilevel and zero-inflated regression model." PLOS Neglected Tropical Diseases 14, no. 12 (2020): e0008002. http://dx.doi.org/10.1371/journal.pntd.0008002.

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Although the prevalence of helminths infection among schoolchildren is known, there has been little progress in the application of count model for modelling the risk factors of helminths egg. Only a few studies applied multilevel analysis to explore the variation in helminths prevalence across schools and classes. This study aimed to assess the prevalence, intensity of helminths infection, and identify risk factors at the individual-, household-, and school-level among schoolchildren in Southern Ethiopia. Using multistage random sampling, we recruited 864 students in the Wonago District. We applied multilevel-logistic and zero-inflated negative binomial regression models (ZINB). Risk factors were concentrated at the individual level; school-level and class-level variables explained less than 5% of the variance. The overall helminths prevalence was 56% (479/850); Trichuris trichiura prevalence was 42.4% (360/850); and Ascaris lumbricoides prevalence was 18.7% (159/850). The rate of any helminths increased among thin children (AOR: 1.73 [95% CI: (1.04, 2.90]), anemic (AOR: 1.45 [95% CI: 1.04, 2.03]), mothers who had no formal education (AOR: 2.08 [95% CI: 1.25, 3.47]), and those in households using open containers for water storage (AOR: 2.06 [95% CI: 1.07, 3.99]). In the ZINB model, A. lumbricoides infection intensity increased with increasing age (AOR: 1.08 [95% CI: 1.01, 1.16]) and unclean fingernails (AOR: 1.47 [95% CI: 1.07, 2.03]). Handwashing with soap (AOR: 0.68 [95% CI: 0.48, 0.95]), de-worming treatment [AOR: 0.57 (95% CI: 0.33, 0.98)], and using water from protected sources [AOR: 0.46 (95% CI: 0.28, 0.77)] were found to be protective against helminths infection. After controlling for clustering effects at the school and class levels and accounting for excess zeros in fecal egg counts, we found an association between helminths infection and the following variables: age, thinness, anemia, unclean fingernails, handwashing, de-worming treatment, mother’s education, household water source, and water storage protection. Improving hygiene behavior, providing safe water at school and home, and strengthening de-worming programs is required to improve the health of schoolchildren in rural Gedeo.

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Antonio, Katrien, Edward W. Frees, and Emiliano A. Valdez. "A Multilevel Analysis of Intercompany Claim Counts." ASTIN Bulletin 40, no. 1 (2010): 151–77. http://dx.doi.org/10.2143/ast.40.1.2049223.

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AbstractIt is common for professional associations and regulators to combine the claims experience of several insurers into a database known as an “intercompany” experience data set. In this paper, we analyze data on claim counts provided by the General Insurance Association of Singapore, an organization consisting of most of the general insurers in Singapore. Our data comes from the financial records of automobile insurance policies followed over a period of nine years. Because the source contains a pooled experience of several insurers, we are able to study company effects on claim behavior, an area that has not been systematically addressed in either the insurance or the actuarial literatures.We analyze this intercompany experience using multilevel models. The multilevel nature of the data is due to: a vehicle is observed over a period of years and is insured by an insurance company under a “fleet” policy. Fleet policies are umbrella-type policies issued to customers whose insurance covers more than a single vehicle. We investigate vehicle, fleet and company effects using various count distribution models (Poisson, negative binomial, zero-inflated and hurdle Poisson). The performance of these various models is compared; we demonstrate how our model can be used to update a priori premiums to a posteriori premiums, a common practice of experience-rated premium calculations. Through this formal model structure, we provide insights into effects that company-specific practice has on claims experience, even after controlling for vehicle and fleet effects.

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Kim, Minjeong, and Jiye Ju. "Exploring Influencing Factor on Difference between Adoption and Frequency of Inter-Local Collaboration in Korea: Applying Zero-inflated Counts Data." Korean Association of Governance Studies 30, no. 1 (2020): 23–49. http://dx.doi.org/10.26847/mspa.2020.30.1.23.

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Langsetmo, Lisa, Abigail Johnson, Ryan Demmer, Kristine Ensrud, Eric Orwoll, and James Shikany. "The Associations Between Physical Activity and Gut Microbiota Among Older Community-Dwelling Men." Innovation in Aging 4, Supplement_1 (2020): 839. http://dx.doi.org/10.1093/geroni/igaa057.3075.

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Abstract We determined the relationship between objectively measured physical activity (PA) and the gut microbiome among community-dwelling older men from the Osteoporotic Fractures in Men (MrOS) cohort participants at Visit 4 (2014-16). Eligible men (n=373, mean age 84 y) included participants with 5-day activity assessment and stool samples analyzed for 16S marker genes. Armband data together with sex, height, and weight were used to estimate total steps and energy expenditure. We used linear regression analysis, principal coordinate analysis, zero-inflated Gaussian models to assess association between PA and α-diversity, β-diversity, and specific taxa, respectively, with adjustments for age, race, BMI, clinical center, library size, and number of chronic conditions. There was a slight association between PA and β-diversity but no association with α-diversity. After multivariate adjustment, those who had higher step counts vs lower step counts had higher relative abundance of Cetobacterium and lower relative abundance of Coprobacillus, Adlercreutzia, Erysipelotrichaceae CC-115.

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Journal articles on the topic 'Zero-Inflated counts'

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