Modeling accident frequencies as zero-altered probability processes: An empirical inquiry

Effectiveness of sampling plans by attributes based on mixture distributions characterising microbial clustering in food

Methodologic Challenges in the Analysis of Count Data in Radiology Health Services Research

In recent years, there has been considerable interest in regression models based on zero-inflated distributions. These models are commonly encountered in many disciplines, such as medicine, public health, and environmental sciences, among others. The zero-inflated Poisson (ZIP) model has been typically considered for these types of problems. However, the ZIP model can fail if the non-zero counts are overdispersed in relation to the Poisson distribution, hence the zero-inflated negative binomial (ZINB) model may be more appropriate. In this paper, we present a Bayesian approach for fitting the ZINB regression model. This model considers that an observed zero may come from a point mass distribution at zero or from the negative binomial model. The likelihood function is utilized to compute not only some Bayesian model selection measures, but also to develop Bayesian case-deletion influence diagnostics based on q-divergence measures. The approach can be easily implemented using standard Bayesian software, such as WinBUGS. The performance of the proposed method is evaluated with a simulation study. Further, a real data set is analyzed, where we show that ZINB regression models seems to fit the data better than the Poisson counterpart.

Statistical modelling for falls count data

Zero-inflated count data are characterized by an excessive frequency of zeros that cannot be adequately analyzed by a single distribution, such as Poisson or negative binomial. This problem is pervasive in many practical applications, including document–keyword matrix derived from text corpora, where most keyword frequencies are zero. Conventional statistical approaches, such as the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models, explicitly separate a structural zero component from a count component, but they typically assume independent observations and can be unstable when covariates are high-dimensional and sparse. To address these limitations, this paper proposes a graph-based zero-inflated learning framework that combines simple graph convolution (SGC) with zero-inflated count regression heads such as ZIP and ZINB. We first construct an observation graph by connecting similar samples, and then apply SGC to propagate and smooth features over the graph, producing convolutional representations that incorporate neighborhood information while remaining computationally lightweight. The resulting representations are used as covariates in ZIP and ZINB heads, which preserve probabilistic interpretability through maximum likelihood learning. Our experiments on simulated zero-inflated datasets with controlled zero ratios demonstrate that the proposed ZIP+SGC and ZINB+SGC consistently reduce prediction errors compared with their non-graph baselines, as measured by mean absolute error and root mean squared error. Overall, the proposed approach provides an efficient and interpretable way to integrate graph neural computation with zero-inflated modeling for sparse count prediction problems.

Smoking is a habit that is not good for health. Smoking habits are generally practiced by adults but it is possible for teenagers to do so.The Report of Southeast Asia Tobacco Control Alliance (SEATCA) entitled The Tobacco Control Atlas, ASEAN Region shows that Indonesia is the country with the highest number of smokers in ASEAN, namely 65.19 million people. This figure is equivalent to 34 percent of the total population of Indonesia in 2016. Based on these data, the authors are interested in modeling the daily cigarette consumption data for adults in Indonesia obtained from the 2015 Indonesia Family Life Survey. The variables used include the variable amount of cigarette consumption, education, level of welfare and income per month. The author wants to compare the best model that can be used to model the daily cigarette consumption of adults in Indonesia. The models being compared are Zero Inflated Poisson Regression (ZIP), Zero Inflated Negative Binomial Regression (ZINB) and Binomial Negative Hurdle Regression (HNB). The comparison results of the three models obtained that the best model is the Zero Inflated Negative Binomial (ZINB) Regression model because it has the smallest Akaike's Information Criterion (AIC) value.

Testing overdispersion in the zero-inflated Poisson model

Forest tree ingrowth is a highly variable and largely stochastic process. Consequently, predicting occurrence, frequency, and composition of ingrowth is a challenging task but of great importance in long-term forest growth and yield model projections. However, ingrowth data often require different statistical techniques other than traditional Gaussian regression, because these data are often bounded, skewed, and non-normal and commonly contain a large fraction of zeros. This study presents a set of regression models based on discrete Poisson and negative binomial probability distributions for ingrowth data collected from permanent sample plots in the Acadian Forest Region of North America. Models considered here include regular Poisson, zero-inflated Poisson (ZIP), zero-altered Poisson (ZAP; hurdle Poisson), regular negative binomial (NB), zero-inflated negative binomial (ZINB), and zero-altered negative binomial (ZANB; hurdle NB). Plot-level random effects were incorporated into each of these models. The ZINB model with random effects was found to provide the best fit statistics for modeling annualized occurrence and frequency of ingrowth. The key explanatory variables were stand basal area per hectare, percentage of hardwood basal area, number of trees per hectare, a measure of site quality, and the minimum measured diameter at breast height of each plot. A similar model was developed to predict species composition. All models showed logical behavior despite the high variability observed in the original data.

To determine the most appropriate regression models to use when assessing risk factors for severe hypoglycaemia and to investigate the impact of model misspecification and its clinical implications. A total of 1229 children with Type 1 diabetes (mean age 11.7 years sd 4.1), of which 605 (49.2%) were males, were studied. Prospective assessment of severe hypoglycaemia (an event leading to loss of consciousness or seizure) was made over the 9-year period, 1992-2001. Patients were seen every 3 months and episodes of hypoglycaemia along with clinical data were recorded. Over 70% of children never experienced a severe hypoglycaemic event. Data were analysed using the Poisson regression, negative binomial, zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models. The over-dispersion and likelihood ratio statistics were calculated and the analytical methods compared. The Poisson regression model did not fit the data well. The negative binomial and the zero inflated Poisson and negative binomial models fitted the data better than Poisson. The commonly used Poisson regression models to analyse hypoglycaemia epidemiology may lead to biased parameter estimates and incorrect determination of risk factors for hypoglycaemia. We recommend the use of the negative binomial or zero inflated models to examine any risk factors associated with severe hypoglycaemia. Careful consideration must be given to the interpretation of hypoglycaemia surveys and their analysis.

More than 60% of accidents in Iran occur within 30 kilometers of cities entrance roads. Therefore the number of accidents per kilometer in these regions, in contrast to the other parts of roads is very considerable. The city of Tehran, as the capital of Iran, is the cross point of major arterials of passenger and freight transportation. Thus the evaluation of road safety, entering and exiting the city in the 30 kilometers buffer, can be considered to improve countrywide road safety. To investigate the effects of roadway characteristics and traffic conditions, including number of traffic violations, on accident frequency within 30 km of Tehran entrance roads, Poisson and Negative Binomial regression model were calibrated in this study. Although the goodness of fit index in Poisson model is much greater than the Negative Binomial model, the accident data dispersion in this study implies that Negative Binomial model is more appropriate to show the influences of effective variables. According to results of modeling, the variables including average daily volume, share of heavy vehicles, average daily speed violations and number of direct accesses and interchanges have effective influence on accident frequencies. Controlling access to roads and using effective actions to reduce the speed and number of speed violation can be accounted as effective policies to reduce accident frequencies within 30 km of Tehran entrance roads.

Modeling Vehicle-pedestrian Crashes With Excess Zero Along Malaysia Federal Roads

Zero-inflated models are frequently used to deal with data having many zeros. A commonly used model for over-dispersed data containing zeros is known as the zero-inflated Poisson model. However, to account for the heterogeneity of counts that leads to excess variance besides inflation of zeros in the data using a more flexible model than the zero-inflated Poisson model, a zero-inflated negative binomial (ZINB) is suggested. In the present study, Shewhart and exponentially weighted moving average (EWMA) control charts are suggested to monitor the ZINB data. The charts are compared using the average run length and standard deviation of run length by using extensive Monte Carlo simulations. Besides a comprehensive simulation study assuming different settings of parameters of ZINB, a real data set is used to show the practicality of the proposed charts. The results indicate that the EWMA chart is better than the Shewhart chart.

Modelling of vertical integration in commercial poultry production of Ghana: A count data model analysis

In Nigeria, literature on the integration of traffic of pavement condition and traffic characteristics in predicting road traffic accident frequency on 2-lane highways are scanty, hence this article to fill the gap. A comparison of road traffic accident frequency prediction models on IIesha-Akure-Owo road based on the data observed between 2012 and 2014 is presented. Negative Binomial (NB), Ordered Logistic (OL) and Zero Inflated Negative Binomial (ZINB) models were used to model the frequency of road traffic accident occurrence using road traffic accident data from the Federal Road Safety Commission (FRSC) and pavement conditions parameters from pavement evaluation unit of the Federal Ministry of Works, Kaduna. The explanatory variables were: annual average daily traffic (aadt), shoulder factor (sf), rut depth (rd), pavement condition index (pci), and international roughness index (iri). The explanatory variables that were statistically significant for the three models are aadt, sf and iri with the estimated coefficients having the expected signs. The number of road traffic accident on the road increases with the traffic volume and the international roughness index while it decreases with shoulder factor. The systematic variation explained by the models amounts to 87.7, 78.1 and 74.4% for NB, ZINB and OL respectively. The research findings suggest the accident prediction models that should be integrated into pavement rehabilitation.
 
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Single-cell RNA sequencing (scRNA-seq) has emerged as a transformative technology for elucidating cellular heterogeneity at unprecedented resolution. However, technical limitations such as limited sequencing depth and mRNA capture efficiency often result in zero counts, commonly referred to as "dropout zeros" in scRNA-seq data. These zeros pose significant challenges to downstream analysis, as they can distort the interpretation of cellular transcriptomes. While numerous computational methods have been developed to address this challenge, existing approaches frequently suffer from either insufficient imputation of zeros (under-imputation) or excessive modification of zeros (over-imputation). Here, we propose a precisely balanced imputation (PbImpute) method designed to achieve optimal equilibrium between dropout recovery and biological zero preservation in scRNA-seq data. PbImpute employs a multistage approach: (1) Initial discrimination between technical dropouts and biological zeros through parameter optimization of a new zero-inflated negative binomial (ZINB) distribution model, followed by initial imputation; (2) Application of a uniquely designed static repair algorithm to enhance data fidelity; (3) Secondary dropout identification based on gene expression frequency and partition-specific coefficient of variation; (4) Graph-embedding neural network-based imputation; and (5) Implementation of a uniquely designed dynamic repair mechanism to mitigate over-imputation effects. PbImpute distinguishes itself by uniquely integrating ZINB modeling with static and dynamic repair. This advantageous combined approach achieves a balance between over- and under-imputation, while simultaneously preserving true biological zeros and reducing signal distortion. Comprehensive evaluation using both simulated and real scRNA-seq data sets demonstrated that PbImpute achieves superior performance (F1 Score = 0.88 at 83% dropout rate, ARI = 0.78 on PBMC) in discriminating between technical dropouts and biological zeros compared to state-of-the-art methods. The method significantly improves gene-gene and cell-cell correlation structures, enhances differential expression analysis sensitivity, optimizes clustering resolution and dimensional reduction visualization, and facilitates more accurate trajectory inference. Ablation studies confirmed the essential contribution of both the imputation and repair modules to the method's performance. The code is available at https://github.com/WyBioTeam/PbImpute. By enhancing the accuracy of scRNA-seq data imputation, PbImpute can improve the identification of cell subpopulations and the detection of differentially expressed genes, thereby facilitating more precise analyses of cellular heterogeneity and advancing disease research.