Zero-inflated Negative Binomial Distribution Research Articles

Differences in end-of-life care patterns between types of hospice used for cancer patients: a retrospective cohort study.

In response to the rapid aging population and increasing number of cancer patients, discussions on dignified end-of-life (EoL) decisions are active around the world. Therefore, this study aimed to identify the differences in EoL care patterns between types of hospice used for cancer patients. In this population-based cohort study, the Korean National Health Insurance Service cohort data containing all registered cancer patients who died between 2017 and 2021 were used. A total of 408,964 individuals were eligible for analysis. The variable of interest, the type of hospice used in the 6months before death, was classified as follows: (1) Non-hospice users; (2) Hospital-based hospice single users; (3) Home-based hospice single users; (4) Combined hospice users. The outcomes were set as patterns of care, including intense care and supportive care. To identify differences in care patterns between hospice types, a generalized linear model with zero-inflated negative binomial distribution was applied. Hospice enrollment was associated with less intense care and more supportive care near death. Notably, those who used combined hospice care had the lowest probability and frequency of receiving intense care (aOR: 0.18, 95% CI: 0.17-0.19, aRR: 0.47, 95% CI: 0.44-0.49), while home-based hospice single users had the highest probability and frequency of receiving supportive care (Prescription for narcotic analgesics, aOR: 2.95, 95% CI: 2.69-3.23, aRR: 1.45, 95% CI: 1.41-1.49; Mental health care, aOR: 3.40, 95% CI: 3.13-3.69, aRR: 1.35, 95% CI: 1.31-1.39). Our findings suggest that although intense care for life-sustaining decreases with hospice enrollment, QoL at the EoL actually improves with appropriate supportive care. This study is meaningful in that it not only offers valuable insight into hospice care for terminally ill patients, but also provides policy implications for the introduction of patient-centered community-based hospice services.

ScTPC: a novel semisupervised deep clustering model for scRNA-seq data.

Continuous advancements in single-cell RNA sequencing (scRNA-seq) technology have enabled researchers to further explore the study of cell heterogeneity, trajectory inference, identification of rare cell types, and neurology. Accurate scRNA-seq data clustering is crucial in single-cell sequencing data analysis. However, the high dimensionality, sparsity, and presence of "false" zero values in the data can pose challenges to clustering. Furthermore, current unsupervised clustering algorithms have not effectively leveraged prior biological knowledge, making cell clustering even more challenging. This study investigates a semisupervised clustering model called scTPC, which integrates the triplet constraint, pairwise constraint, and cross-entropy constraint based on deep learning. Specifically, the model begins by pretraining a denoising autoencoder based on a zero-inflated negative binomial distribution. Deep clustering is then performed in the learned latent feature space using triplet constraints and pairwise constraints generated from partial labeled cells. Finally, to address imbalanced cell-type datasets, a weighted cross-entropy loss is introduced to optimize the model. A series of experimental results on 10 real scRNA-seq datasets and five simulated datasets demonstrate that scTPC achieves accurate clustering with a well-designed framework. scTPC is a Python-based algorithm, and the code is available from https://github.com/LF-Yang/Code or https://zenodo.org/records/10951780.

The Applications of Generalized Poisson Regression Models to Insurance Claim Data

Predictive modeling has been widely used for insurance rate making. In this paper, we focus on insurance claim count data and address their common issues with more flexible modeling techniques. In particular, we study the zero-inflated and hurdle-generalized Poisson and negative binomial distributions in a functional form for modeling insurance claim count data. It is shown that these models are useful in addressing the problem of excess zeros and over-dispersion of the claim count variable. In addition, we show that including the exposure as a covariate in both the zero and the count part of the model is an effective approach to incorporating exposure information in zero-inflated and hurdle models. We illustrate the effectiveness and versatility of the introduced models using three real datasets. The results suggest their promising applications in insurance risk classification and beyond.

TsImpute: an accurate two-step imputation method for single-cell RNA-seq data.

Single-cell RNA sequencing (scRNA-seq) technology has enabled discovering gene expression patterns at single cell resolution. However, due to technical limitations, there are usually excessive zeros, called "dropouts," in scRNA-seq data, which may mislead the downstream analysis. Therefore, it is crucial to impute these dropouts to recover the biological information. We propose a two-step imputation method called tsImpute to impute scRNA-seq data. At the first step, tsImpute adopts zero-inflated negative binomial distribution to discriminate dropouts from true zeros and performs initial imputation by calculating the expected expression level. At the second step, it conducts clustering with this modified expression matrix, based on which the final distance weighted imputation is performed. Numerical results based on both simulated and real data show that tsImpute achieves favorable performance in terms of gene expression recovery, cell clustering, and differential expression analysis. The R package of tsImpute is available at https://github.com/ZhengWeihuaYNU/tsImpute.

Zero-Inflated Autoregressive Conditional Duration Model for Discrete Trade Durations with Excessive Zeros

Abstract In finance, durations between successive transactions are usually modeled by the autoregressive conditional duration model based on a continuous distribution omitting zero values. Zero or close-to-zero durations can be caused by either split transactions or independent transactions. We propose a discrete model allowing for excessive zero values based on the zero-inflated negative binomial distribution with score dynamics. This model allows to distinguish between the processes generating split and standard transactions. We use the existing theory on score models to establish the invertibility of the score filter and verify that sufficient conditions hold for the consistency and asymptotic normality of the maximum likelihood of the model parameters. In an empirical study, we find that split transactions cause between 92 % and 98 % of zero and close-to-zero values. Furthermore, the loss of decimal places in the proposed approach is less severe than the incorrect treatment of zero values in continuous models.

A bivariate zero-inflated negative binomial model and its applications to biomedical settings.

The zero-inflated negative binomial distribution has been widely used for count data analyses in various biomedical settings due to its capacity of modeling excess zeros and overdispersion. When there are correlated count variables, a bivariate model is essential for understanding their full distributional features. Examples include measuring correlation of two genes in sparse single-cell RNA sequencing data and modeling dental caries count indices on two different tooth surface types. For these purposes, we develop a richly parametrized bivariate zero-inflated negative binomial model that has a simple latent variable framework and eight free parameters with intuitive interpretations. In the scRNA-seq data example, the correlation is estimated after adjusting for the effects of dropout events represented by excess zeros. In the dental caries data, we analyze how the treatment with Xylitol lozenges affects the marginal mean and other patterns of response manifested in the two dental caries traits. An R package "bzinb" is available on Comprehensive R Archive Network.

A marginal modelling approach for predicting wildfire extremes across the contiguous United States

This paper details a methodology proposed for the EVA 2021 conference data challenge. The aim of this challenge was to predict the number and size of wildfires over the contiguous US between 1993 and 2015, with more importance placed on extreme events. In the data set provided, over 14% of both wildfire count and burnt area observations are missing; the objective of the data challenge was to estimate a range of marginal probabilities from the distribution functions of these missing observations. To enable this prediction, we make the assumption that the marginal distribution of a missing observation can be informed using non-missing data from neighbouring locations. In our method, we select spatial neighbourhoods for each missing observation and fit marginal models to non-missing observations in these regions. For the wildfire counts, we assume the compiled data sets follow a zero-inflated negative binomial distribution, while for burnt area values, we model the bulk and tail of each compiled data set using non-parametric and parametric techniques, respectively. Cross validation is used to select tuning parameters, and the resulting predictions are shown to significantly outperform the benchmark method proposed in the challenge outline. We conclude with a discussion of our modelling framework, and evaluate ways in which it could be extended.

ScGCL: an imputation method for scRNA-seq data based on graph contrastive learning.

Single-cell RNA-sequencing (scRNA-seq) is widely used to reveal cellular heterogeneity, complex disease mechanisms and cell differentiation processes. Due to high sparsity and complex gene expression patterns, scRNA-seq data present a large number of dropout events, affecting downstream tasks such as cell clustering and pseudo-time analysis. Restoring the expression levels of genes is essential for reducing technical noise and facilitating downstream analysis. However, existing scRNA-seq data imputation methods ignore the topological structure information of scRNA-seq data and cannot comprehensively utilize the relationships between cells. Here, we propose a single-cell Graph Contrastive Learning method for scRNA-seq data imputation, named scGCL, which integrates graph contrastive learning and Zero-inflated Negative Binomial (ZINB) distribution to estimate dropout values. scGCL summarizes global and local semantic information through contrastive learning and selects positive samples to enhance the representation of target nodes. To capture the global probability distribution, scGCL introduces an autoencoder based on the ZINB distribution, which reconstructs the scRNA-seq data based on the prior distribution. Through extensive experiments, we verify that scGCL outperforms existing state-of-the-art imputation methods in clustering performance and gene imputation on 14 scRNA-seq datasets. Further, we find that scGCL can enhance the expression patterns of specific genes in Alzheimer's disease datasets. The code and data of scGCL are available on Github: https://github.com/zehaoxiong123/scGCL. Supplementary data are available at Bioinformatics online.

Modeling of Parking Violations Using Zero-Inflated Negative Binomial Regression: A Case Study for Berlin

Parking violations cause numerous problems, thus affecting daily mobility. Nevertheless, there are no extensive statistics on illegal parking in Germany, implying that the causes of this misconduct are still unexplored. The objective of this paper is to present a count data modeling approach for parking violations based on video footage taken from the windshields of driving vehicles, incorporating spatial data from OpenStreetMap (OSM). The main benefit of this data source is the transferability of the data collection procedure just by installing a recording device in vehicles of municipal services like waste collection. Moreover, the data from OSM are freely available for all cities. To account for excess zero counts in the street segments, a zero-inflated negative binomial distribution model was used to explain the number of violations per 100 m. “Excess” zeros were modeled using the logit part of the model, whereas the remaining counts of parking violations were fitted by the negative binomial model. Much effort was made to present the results of the count data models in an interpretable way. The most intuitive way seemed to be predictions of parking violations per 100 m (incidence rate) for different settings. Incidence rates were predicted for variations in explanatory variables, holding all other variables constant. We found parking violations per 100 m to be highest in main shopping streets. In addition, free parking spaces negatively- and the number of points of interest (such as buildings, craft stores, and shops) positively affected illegal parking.

Dose-Dependent Transmissibility of Chromosome Aberrations in Human Lymphocytes at First Mitosis. II. Biological Effectiveness of Heavy Charged Particles Versus Gamma Rays.

Chromosome aberrations (CAs) are large scale structural rearrangements to the genome that have been used as a proxy endpoint of mutagenic and carcinogenic potential. And yet, many types of CAs are incapable of causing either of these effects simply because they are lethal. Using 24-color multi-fluor combinatorial painting (mFISH), we examined CAs in normal human lymphocytes exposed to graded doses of 1 GeV/nucleon accelerated 56Fe ions and 662 keV 137Cs gamma rays. As expected, the high-linear energy transfer (LET) heavy ions were considerably more potent per unit dose at producing total yields of CAs compared to low-LET gamma rays. As also anticipated, the frequency distribution of aberrations per cell exposed to 56Fe ions was significantly overdispersed compared to the Poisson distribution, containing excess numbers of cells devoid of aberrations. We used the zero-inflated negative binomial (ZINB) distribution to model these data. Based on objective cytogenetic criteria that are subject to caveats we discuss, each cell was individually evaluated in terms of likely survival (i.e., its ability to transmit to daughter cell progeny). For 56Fe ion irradiations, the frequency of surviving cells harboring complex aberrations represented a significant portion of aberration-bearing cells, while for gamma irradiation no survivable cells containing complex aberrations were observed. When the dose responses for the two radiation types were compared, and the analysis was limited to surviving cells that contained aberrations, we were surprised to find the high-LET 56Fe ions only marginally more potent than the low-LET gamma rays for doses less than 1 Gy. In fact, based on dose-response modeling, they were predicted to be less effective than gamma rays at somewhat higher doses. The major implication of these findings is that measures of relative biological effectiveness that fail to account for coincident lethality will tend to overstate the impact of transmissible chromosomal damage from high-LET particle exposure.

IccCounts: An R Package to Estimate the Intraclass Correlation Coefficient for Assessing Agreement with Count Data

The intraclass correlation coefficient (ICC) is a widely used index to assess agreement with continuous data. The common approach for estimating the ICC involves estimating the variance components of a linear mixed model under assumptions such as linearity and normality of effects. However, if the outcomes are counts these assumptions are not met and the ICC estimates are biased and inefficient. In this situation, it is necessary to use alternative approaches that are better suited for count data. Here, the iccCounts R package is introduced for estimating the ICC under the Poisson, Negative Binomial, Zero-Inflated Poisson and Zero-Inflated Negative Binomial distributions. The utility of the iccCounts package is illustrated by three examples that involve the assessment of repeatability and concordance with count data.

Environmental factors driving fine-scale ixodid tick abundance patterns

Tick abundance is an essential demographic parameter to infer tick-borne pathogen transmission risks. Spatiotemporal patterns of tick abundance are heterogeneous, so its determinants at small spatial scales need to be understood to reduce their negative effects on hosts. Current knowledge of these determinants is scarce, especially in Mediterranean environments, limiting the possibilities for designing efficient tick control strategies. With the goal of unravelling tick abundance determinants and informing new tick management strategies, we estimated tick burdens on 1965 wild ungulates in Doñana National Park, Spain, annually between 2010 and 2020. Under the hypothesis of a predominant host influence on tick abundance, we modelled the burdens of Rhipicephalus annulatus, Hyalomma lusitanicum, and Ixodes ricinus with relevant predictors grouped into four factors: i) environment; ii) host population; iii) host individual; and iv) land-use. Generalized linear mixed models with a zero-inflated negative binomial distribution were built. Additionally, we analysed the differential contribution to abundance of each factor by deviance partitioning. We finally estimated the similarity in the environmental space of tick species by analysing their niche overlap with the environmental principal component analysis method. Our work hypothesis was confirmed for R. annulatus and H. lusitanicum, but we found that tick abundance at a fine spatial scale is jointly driven by multiple drivers, including all four factors considered in this study. This result points out that understanding the demography of ticks is a complex multifactorial issue, even at small spatial scales. We found no niche differences between the three tick species at the study spatial scale, thus showing similar host and environmental dependencies. Overall results identify that host aggregation areas displaying environmentally favourable traits for ticks are relevant tick and vector-borne pathogen transmission hotspots. Our findings will facilitate the design of new strategies to reduce the negative effects of tick parasitism.

Investigating the effect of pesticides on Daphnia population dynamics by inferring structure and parameters of a stochastic model

Identifying sublethal pesticide effects on aquatic organisms is a challenge for environmental risk assessment. Long-term population experiments can help assessing chronic toxicity. However, population experiments are subject to stochasticity (demographic, environmental, and genetic). Therefore, identifying sublethal chronic effects from “noisy” data can be difficult. Model-based analysis can support this process.We use stochastic, age-structured population models applied to data from long-term population experiments with Daphnia galeata in 1L aquaria with and without chronic pesticide treatments (diazinon and diuron) at sublethal concentrations. Posterior analysis following Bayesian inference of model parameters and states helped choosing an adequate description of life-history characteristics under the specific experimental conditions (a zero-inflated negative binomial distribution for reproduction and mortality without density dependence). For the insecticide treatments, the inferred marginal posterior parameter distributions indicated the need for a mortality rate that increases with time, indicating cumulative chronic toxic effects of diazinon on Daphnia populations. With this study, we demonstrate how stochastic models can be used to infer mechanisms from population data to help identifying sublethal pesticide effects.

Spatial transcriptomics prediction from histology jointly through Transformer and graph neural networks.

The rapid development of spatial transcriptomics allows the measurement of RNA abundance at a high spatial resolution, making it possible to simultaneously profile gene expression, spatial locations of cells or spots, and the corresponding hematoxylin and eosin-stained histology images. It turns promising to predict gene expression from histology images that are relatively easy and cheap to obtain. For this purpose, several methods are devised, but they have not fully captured the internal relations of the 2D vision features or spatial dependency between spots. Here, we developed Hist2ST, a deep learning-based model to predict RNA-seq expression from histology images. Around each sequenced spot, the corresponding histology image is cropped into an image patch and fed into a convolutional module to extract 2D vision features. Meanwhile, the spatial relations with the whole image and neighbored patches are captured through Transformer and graph neural network modules, respectively. These learned features are then used to predict the gene expression by following the zero-inflated negative binomial distribution. To alleviate the impact by the small spatial transcriptomics data, a self-distillation mechanism is employed for efficient learning of the model. By comprehensive tests on cancer and normal datasets, Hist2ST was shown to outperform existing methods in terms of both gene expression prediction and spatial region identification. Further pathway analyses indicated that our model could reserve biological information. Thus, Hist2ST enables generating spatial transcriptomics data from histology images for elucidating molecular signatures of tissues.

SMGR: a joint statistical method for integrative analysis of single-cell multi-omics data.

Unravelling the regulatory programs from single-cell multi-omics data has long been one of the major challenges in genomics, especially in the current emerging single-cell field. Currently there is a huge gap between fast-growing single-cell multi-omics data and effective methods for the integrative analysis of these inherent sparse and heterogeneous data. In this study, we have developed a novel method, Single-cell Multi-omics Gene co-Regulatory algorithm (SMGR), to detect coherent functional regulatory signals and target genes from the joint single-cell RNA-sequencing (scRNA-seq) and single-cell assay for transposase-accessible chromatin using sequencing (scATAC-seq) data obtained from different samples. Given that scRNA-seq and scATAC-seq data can be captured by zero-inflated Negative Binomial distribution, we utilize a generalized linear regression model to identify the latent representation of consistently expressed genes and peaks, thus enables the identification of co-regulatory programs and the elucidation of regulating mechanisms. Results from both simulation and experimental data demonstrate that SMGR outperforms the existing methods with considerably improved accuracy. To illustrate the biological insights of SMGR, we apply SMGR to mixed-phenotype acute leukemia (MPAL) and identify the MPAL-specific regulatory program with significant peak-gene links, which greatly enhance our understanding of the regulatory mechanisms and potential targets of this complex tumor.

Identification of cell-type-specific spatially variable genes accounting for excess zeros.

MotivationSpatial transcriptomic techniques can profile gene expressions while retaining the spatial information, thus offering unprecedented opportunities to explore the relationship between gene expression and spatial locations. The spatial relationship may vary across cell types, but there is a lack of statistical methods to identify cell-type-specific spatially variable (SV) genes by simultaneously modeling excess zeros and cell-type proportions.ResultsWe develop a statistical approach CTSV to detect cell-type-specific SV genes. CTSV directly models spatial raw count data and considers zero-inflation as well as overdispersion using a zero-inflated negative binomial distribution. It then incorporates cell-type proportions and spatial effect functions in the zero-inflated negative binomial regression framework. The R package pscl is employed to fit the model. For robustness, a Cauchy combination rule is applied to integrate P-values from multiple choices of spatial effect functions. Simulation studies show that CTSV not only outperforms competing methods at the aggregated level but also achieves more power at the cell-type level. By analyzing pancreatic ductal adenocarcinoma spatial transcriptomic data, SV genes identified by CTSV reveal biological insights at the cell-type level.Availability and implementationThe R package of CTSV is available at https://bioconductor.org/packages/devel/bioc/html/CTSV.html.Supplementary information Supplementary data are available at Bioinformatics online.

Measuring capabilities of zero-inflated processes

The high-quality processes usually have more count of zeros than are expected under chance variation of its underlying Poisson or other count distribution. Therefore, these processes are usually referred to as zero-inflated processes. The zeroinflated processes are commonly modelled by zero-inflated Poisson (ZIP) or zero-inflated negative binomial (ZINB) distribution. In a manufacturing set up, the evaluation of process capability index of a zero-inflated process can be useful in many ways, e.g. i) predicting how well the process will hold the specifications, ii) selecting between competing vendors, and iii) assisting product developers/designers in modifying the process, etc. However, researchers have given very little attentions on this aspect of zero-inflated processes. Only one such attempt is reported in literature. But, it does not always represent the true capabilities of zero-inflated processes, and sometimes it may give very misleading impression about the capability of the concerned process. In this article, the concept of Borges and Ho (2001) is applied to zero-inflated processes and a new approach for computation of process capability index of zero-inflated processes is developed. The proposed method reveals the true capabilities of zero-inflated processes consistently. Application of the proposed approach and its effectiveness are illustrated using two datasets published by past researchers.

Investigating how autonomy-supportive teaching moderates the relation between student honesty and premeditated cheating.

Cheating at the post-secondary level is a skewed phenomenon. While personality and environmental factors are associated with cheating, few studies account for the zero inflation when predicting cheating behaviour. In this study, we explore a person-situation interaction hypothesis where teacher autonomy support (AS) could modify the relation between students' honesty trait and premeditated cheating. Participants were 710 college students and 31 teachers. Teacher and student reports of teacher AS were collected and students also completed self-reports of honesty and premeditated cheating. Given that cheating had a zero-inflated negative binomial distribution, we can investigate two separate outcomes: likelihood of cheating and magnitude of cheating. Predictably, student honesty trait predicted lower likelihood and magnitude of cheating. AS, whether student- or teacher-reported, moderated the relation between honesty and likelihood of cheating. In low perceived AS teaching environments, student honesty was associated with cheating likelihood. However, there was no such relation in high perceived AS teaching environments. Students' honesty generally predicts lower cheating. However, the educational environment provided by the teacher influences the strength of this association. The less autonomy-supportive students perceive the educational environment, the more their personality is important in predicting the likelihood of cheating.

Nonlinear mixed‐effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero‐inflated discrete Weibull distribution

This article proposes a Bayesian regression model for nonlinear zero-inflated longitudinal count data that models the median count as an alternative to the mean count. The nonlinear model generalizes a recently introduced linear mixed-effects model based on the zero-inflated discrete Weibull (ZIDW) distribution. The ZIDW distribution is more robust to severe skewness in the data than conventional zero-inflated count distributions such as the zero-inflated negative binomial (ZINB) distribution. Moreover, the ZIDW distribution is attractive because of its convenience to model the median counts given its closed-form quantile function. The median is a more robust measure of central tendency than the mean when the data, for instance, zero-inflated counts, are right-skewed. In an application of the model we consider a biphasic mixed-effects model consisting of an intercept term and two slope terms. Conventionally, the ZIDW model separately specifies the predictors for the zero-inflation probability and the counting process's median count. In our application, the two latent class interpretations are not clinically plausible. Therefore, we propose a marginal ZIDW model that directly models the biphasic median counts marginally. We also consider the marginal ZINB model to make inferences about the nonlinear mean counts over time. Our simulation study shows that the models have good properties in terms of accuracy and confidence interval coverage.

CountfitteR: efficient selection of count distributions to assess DNA damage.

DNA double-strand breaks can be counted as discrete foci by imaging techniques. In personalized medicine and pharmacology, the analysis of counting data is relevant for numerous applications, e.g., for cancer and aging research and the evaluation of drug efficacy. By default, it is assumed to follow the Poisson distribution. This assumption, however, may lead to biased results and faulty conclusions in datasets with excess zero values (zero-inflation), a variance larger than the mean (overdispersion), or both. In such cases, the assumption of a Poisson distribution would skew the estimation of mean and variance, and other models like the negative binomial (NB), zero-inflated Poisson or zero-inflated NB distributions should be employed. The model chosen has an influence on the parameter estimation (mean value and confidence interval). Yet the choice of the suitable distribution model is not trivial. To support, simplify and objectify this process, we have developed the countfitteR software as an R package. We used a Bayesian approach for distribution model selection and the shiny web application framework for interactive data analysis. We show the application of our software based on examples of DNA double-strand break count data from phenotypic imaging by multiplex fluorescence microscopy. In analyzing numerous datasets of molecular pharmacological markers (phosphorylated histone H2AX and p53 binding protein), countfitteR demonstrated an equal or superior statistical performance compared to the usually employed two-step procedure, with an overall power of up to 98%. In addition, it still gave information in cases with no result at all from the two-step procedure. In our data sample we found that the NB distribution was the most frequent, with the Poisson distribution taking second place. countfitteR can perform an automated distribution model selection and thus support the data analysis and lead to objective statistically verifiable estimated values. Originally designed for the analysis of foci in biomedical image data, countfitteR can be used in a variety of areas where non-Poisson distributed counting data is prevalent.