Zero-inflated Data Research Articles

Zero-Inflated Beta Distribution Regression Modeling

A frequent challenge encountered with ecological data is how to interpret, analyze, or model data having a high proportion of zeros. Much attention has been given to zero-inflated count data, whereas models for non-negative continuous data with an abundance of 0s are much fewer. We consider zero-inflated data on the unit interval and provide modeling to capture two types of 0s in the context of a Beta regression model. We model 0s due to missing by chance through left-censoring of a latent regression and 0s due to unsuitability using an independent Bernoulli specification. We extend the model by introducing spatial random effects. We specify models hierarchically, employing latent variables, and fit them within a Bayesian framework. Our motivating dataset consists of percent cover abundance of two plant families at a collection of sites in the Cape Floristic Region of South Africa. We find that environmental features enable learning about both types of 0s as well as positive percent cover. We also show that the spatial random effects model improves predictive performance. The proposed modeling enables ecologists to extract a better understanding of an organism’s absence due to unsuitability vs. missingness by chance, as well as abundance behavior when present.Supplementary materials accompanying this paper appear online.

Evaluating capability of a bivariate zero-inflated poisson process

A zero-inflated Poisson (ZIP) distribution is commonly used for modelling zero-inflated process data with single type of defect, and for developing appropriate tools for instituting statistical process control of manufacturing processes. However, in reality, such manufacturing scenarios are very common where more than one type of defect can occur. For example, occurrences of defects like solder short circuits (shorts) and absence of solder (skips) are very common on printed circuit boards. In literature, different forms of bivariate zero-inflated Poisson (BZIP) distributions are proposed, which can be used for modelling the manufacturing scenarios where two types of defects can occur. Control charts are designed for monitoring for such processes using BZIP models. Although evaluation of capability is an integral part of statistical process control of a manufacturing process, researchers have given very little effort on this aspect of zero-inflated processes. Only a few articles attempted to evaluate the capability of a univariate zero-inflated process and no work is reported on evbaluating capability of a bivariate zero-inflated process. In this paper, a methodology for measuring capability of a bivariate zero-inflated process is presented. The proposed methodology is illustrated using two case studies.

Zero-Inflated Patent Data Analysis Using Generating Synthetic Samples

Due to the expansion of the internet, we encounter various types of big data such as web documents or sensing data. Compared to traditional small data such as experimental samples, big data provide more chances to find hidden and novel patterns with big data analysis using statistics and machine learning algorithms. However, as the use of big data increases, problems also occur. One of them is a zero-inflated problem in structured data preprocessed from big data. Most count values are zeros because a specific word is found in only some documents. In particular, since most of the patent data are in the form of a text document, they are more affected by the zero-inflated problem. To solve this problem, we propose a generation of synthetic samples using statistical inference and tree structure. Using patent document and simulation data, we verify the performance and validity of our proposed method. In this paper, we focus on patent keyword analysis as text big data analysis, and we encounter the zero-inflated problem just like other text data.

Finding the Right Distribution for Highly Skewed Zero-inflated Clinical Data


 Discrete, highly skewed distributions with excess numbers of zeros often result in biased estimates and misleading inferences if the zeros are not properly addressed. A clinical example of children with electrophysiologic disorders in which many of the children are treated without surgery is provided. The purpose of the current study was to identify the optimal modeling strategy for highly skewed, zeroinflated data often observed in the clinical setting by: (a) simulating skewed, zero-inflated count data; (b) fitting simulated data with Poisson, Negative Binomial, Zero-Inflated Poisson (ZIP) and Zero-inflated Negative Binomial (ZINB) models; and, (c) applying the aforementioned models to actual, highlyskewed, clinical data of children with an EP disorder. The ZIP model was observed to be the optimal model based on traditional fit statistics as well as estimates of bias, mean-squared error, and coverage. 

Poisson and negative binomial regression models for zero-inflated data: an experimental study

Count data regression has been widely used in various disciplines, particularly health area. Classical models like Poisson and negative binomial regression may not provide reasonable performance in the presence of excessive zeros and overdispersion problems. Zero-inflated and Hurdle variants of these models can be a remedy for dealing with these problems. As well as zero-inflated and Hurdle models, alternatives based on some biased estimators like ridge and Liu may improve the performance against to multicollinearity problem except excessive zeros and overdispersion. In this study, ten different regression models including classical Poisson and negative binomial regression with their variants based on zero-inflated, Hurdle, ridge and Liu approaches have been compared by using a health data. Some criteria including Akaike information criterion, log-likelihood value, mean squared error and mean absolute error have been used to investigate the performance of models. The results show that the zero-inflated negative binomial regression model provides the best fit for the data. The final model estimations have been obtained via this model and interpreted in detail. Finally, the experimental results suggested that models except the classical models should be considered as powerful alternatives for modelling count and give better insights to the researchers in applying statistics on working similar data structures.

MarZIC: A Marginal Mediation Model for Zero-Inflated Compositional Mediators with Applications to Microbiome Data.

Background: The human microbiome can contribute to pathogeneses of many complex diseases by mediating disease-leading causal pathways. However, standard mediation analysis methods are not adequate to analyze the microbiome as a mediator due to the excessive number of zero-valued sequencing reads in the data and that the relative abundances have to sum to one. The two main challenges raised by the zero-inflated data structure are: (a) disentangling the mediation effect induced by the point mass at zero; and (b) identifying the observed zero-valued data points that are not zero (i.e., false zeros). Methods: We develop a novel marginal mediation analysis method under the potential-outcomes framework to address the issues. We also show that the marginal model can account for the compositional structure of microbiome data. Results: The mediation effect can be decomposed into two components that are inherent to the two-part nature of zero-inflated distributions. With probabilistic models to account for observing zeros, we also address the challenge with false zeros. A comprehensive simulation study and the application in a real microbiome study showcase our approach in comparison with existing approaches. Conclusions: When analyzing the zero-inflated microbiome composition as the mediators, MarZIC approach has better performance than standard causal mediation analysis approaches and existing competing approach.

ALTERNATIVES TO THE CLASSICAL FREQUENTIST CONFIDENCE INTERVAL FOR DESCRIBING ZERO-INFLATED LEAF DISEASE SEVERITY

This paper presents the bootstrap percentile interval and the Bayesian credible interval as alternatives to the classical frequentist confidence interval for analysis of zero-inflated data. The indicated methods were applied to soybean downy mildew severity data obtained by stratified sampling in two municipalities in the state of São Paulo: Estiva Gerbi and Piracicaba. The amplitudes of the frequentist and bootstrap percentile confidence intervals were similar. For the Bayesian approach, the credible intervals of the posterior predictive distribution were considered using the zero-inflated beta distribution as likelihood. The credible intervals showed a wider range and included values in the upper bounds of the intervals greater than those observed in the data. We conclude that Bayesian inference is more complex, but allows incorporation of prior information regarding regional and seasonal aspects, contributing to better disease management in the field. When this information is not known, nonparametric bootstrap resampling is a simple alternative to construct intervals for zero-inflated data without assuming the distribution function.

Differential expression of single-cell RNA-seq data usingTweedie models.

The performance of computational methods and software to identify differentially expressed features in single-cell RNA-sequencing (scRNA-seq) has been shown to be influenced by several factors, including the choice of the normalization method used and the choice of the experimental platform (or library preparation protocol) to profile gene expression in individual cells. Currently, it is up to the practitioner to choose the most appropriate differential expression (DE) method out of over 100 DE tools available to date, each relying on their own assumptions to model scRNA-seq expression features. To model the technological variability in cross-platform scRNA-seq data, here we propose to use Tweedie generalized linear models that can flexibly capture a large dynamic range of observed scRNA-seq expression profiles across experimental platforms induced by platform- and gene-specific statistical properties such as heavy tails, sparsity, and gene expression distributions. We also propose a zero-inflated Tweedie model that allows zero probability mass to exceed a traditional Tweedie distribution to model zero-inflated scRNA-seq data with excessive zero counts. Using both synthetic and published plate- and droplet-based scRNA-seq datasets, we perform a systematic benchmark evaluation of more than 10 representative DE methods and demonstrate that our method (Tweedieverse) outperforms the state-of-the-art DE approaches across experimental platforms in terms of statistical power and false discovery rate control. Our open-source software (R/Bioconductor package) is available at https://github.com/himelmallick/Tweedieverse.

Profiling the Atopic Dermatitis Epidermal Transcriptome by Tape Stripping and BRB-seq.

Tape stripping is a non-invasive skin sampling technique, which has recently gained use for the study of the transcriptome of atopic dermatitis (AD), a common inflammatory skin disorder characterized by a defective epidermal barrier and perturbated immune response. Here, we performed BRB-seq—a low cost, multiplex-based, transcriptomic profiling technique—on tape-stripped skin from 30 AD patients and 30 healthy controls to evaluate the methods’ ability to assess the epidermal AD transcriptome. An AD signature consisting of 91 differentially expressed genes, specific for skin barrier and inflammatory response, was identified. The gene expression in the outermost layers, stratum corneum and stratum granulosum, of the skin showed highest correlation between tape-stripped skin and matched full-thickness punch biopsies. However, we observed that low and highly variable transcript counts, probably due to low RNA yield and RNA degradation in the tape-stripped skin samples, were a limiting factor for epidermal transcriptome profiling as compared to punch biopsies. We conclude that deep BRB-seq of tape-stripped skin is needed to counteract large between-sample RNA yield variation and highly zero-inflated data in order to apply this protocol for population-wide screening of the epidermal transcriptome in inflammatory skin diseases.

A Review on Differential Abundance Analysis Methods for Mass Spectrometry-Based Metabolomic Data.

This review presents an overview of the statistical methods on differential abundance (DA) analysis for mass spectrometry (MS)-based metabolomic data. MS has been widely used for metabolomic abundance profiling in biological samples. The high-throughput data produced by MS often contain a large fraction of zero values caused by the absence of certain metabolites and the technical detection limits of MS. Various statistical methods have been developed to characterize the zero-inflated metabolomic data and perform DA analysis, ranging from simple tests to more complex models including parametric, semi-parametric, and non-parametric approaches. In this article, we discuss and compare DA analysis methods regarding their assumptions and statistical modeling techniques.

Deep structural clustering for single-cell RNA-seq data jointly through autoencoder and graph neural network.

Single-cell RNA sequencing (scRNA-seq) permits researchers to study the complex mechanisms of cell heterogeneity and diversity. Unsupervised clustering is of central importance for the analysis of the scRNA-seq data, as it can be used to identify putative cell types. However, due to noise impacts, high dimensionality and pervasive dropout events, clustering analysis of scRNA-seq data remains a computational challenge. Here, we propose a new deep structural clustering method for scRNA-seq data, named scDSC, which integrate the structural information into deep clustering of single cells. The proposed scDSC consists of a Zero-Inflated Negative Binomial (ZINB) model-based autoencoder, a graph neural network (GNN) module and a mutual-supervised module. To learn the data representation from the sparse and zero-inflated scRNA-seq data, we add a ZINB model to the basic autoencoder. The GNN module is introduced to capture the structural information among cells. By joining the ZINB-based autoencoder with the GNN module, the model transfers the data representation learned by autoencoder to the corresponding GNN layer. Furthermore, we adopt a mutual supervised strategy to unify these two different deep neural architectures and to guide the clustering task. Extensive experimental results on six real scRNA-seq datasets demonstrate that scDSC outperforms state-of-the-art methods in terms of clustering accuracy and scalability. Our method scDSC is implemented in Python using the Pytorch machine-learning library, and it is freely available at https://github.com/DHUDBlab/scDSC.

Multiple comparisons of precipitation variations in different areas using simultaneous confidence intervals for all possible ratios of variances of several zero-inflated lognormal models.

Flash flooding and landslides regularly cause injury, death, and homelessness in Thailand. An advancedwarning system is necessary for predicting natural disasters, and analyzing the variability of daily precipitation might be usable in this regard. Moreover, analyzing the differences in precipitation data among multiple weather stations could be used to predict variations in meteorological conditions throughout the country. Since precipitation data in Thailand follow a zero-inflated lognormal (ZILN) distribution, multiple comparisons of precipitation variation in different areas can be addressed by using simultaneous confidence intervals (SCIs) for all possible pairwise ratios of variances of several ZILN models. Herein, we formulate SCIs using Bayesian, generalized pivotal quantity (GPQ), and parametric bootstrap (PB) approaches. The results of a simulation study provide insight into the performances of the SCIs. Those based on PB and the Bayesian approach via probability matching with the beta prior performed well in situations with a large amount of zero-inflated data with a large variance. Besides, the Bayesian based on the reference-beta prior and GPQ SCIs can be considered as alternative approaches for small-to-large and medium-to-large sample sizes from large population, respectively. These approaches were applied to estimate the precipitation variability among weather stations in lower southern Thailand to illustrate their efficacies.

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

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

SCDRHA: A scRNA-Seq Data Dimensionality Reduction Algorithm Based on Hierarchical Autoencoder.

Dimensionality reduction of high-dimensional data is crucial for single-cell RNA sequencing (scRNA-seq) visualization and clustering. One prominent challenge in scRNA-seq studies comes from the dropout events, which lead to zero-inflated data. To address this issue, in this paper, we propose a scRNA-seq data dimensionality reduction algorithm based on a hierarchical autoencoder, termed SCDRHA. The proposed SCDRHA consists of two core modules, where the first module is a deep count autoencoder (DCA) that is used to denoise data, and the second module is a graph autoencoder that projects the data into a low-dimensional space. Experimental results demonstrate that SCDRHA has better performance than existing state-of-the-art algorithms on dimension reduction and noise reduction in five real scRNA-seq datasets. Besides, SCDRHA can also dramatically improve the performance of data visualization and cell clustering.

DIF Detection With Zero-Inflation Under the Factor Mixture Modeling Framework.

Response data containing an excessive number of zeros are referred to as zero-inflated data. When differential item functioning (DIF) detection is of interest, zero-inflation can attenuate DIF effects in the total sample and lead to underdetection of DIF items. The current study presents a DIF detection procedure for response data with excess zeros due to the existence of unobserved heterogeneous subgroups. The suggested procedure utilizes the factor mixture modeling (FMM) with MIMIC (multiple-indicator multiple-cause) to address the compromised DIF detection power via the estimation of latent classes. A Monte Carlo simulation was conducted to evaluate the suggested procedure in comparison to the well-known likelihood ratio (LR) DIF test. Our simulation study results indicated the superiority of FMM over the LR DIF test in terms of detection power and illustrated the importance of accounting for latent heterogeneity in zero-inflated data. The empirical data analysis results further supported the use of FMM by flagging additional DIF items over and above the LR test.

Multifinality, equifinality, and fanning: Developmental concepts and statistical implications

Multifinality, equifinality, and fanning are important developmental concepts that emphasize understanding interindividual variability in trajectories over time. However, each concept implies that there are points in a developmental window where interindividual variability is more limited. We illustrate the multifinality concept under manipulations of variance in starting points, using both normal and zero-inflated simulated data. Results indicate that standardized estimates and effect sizes are inflated when predicting components of growth models with limited interindividual variance, which could lead to overinterpretation of the practical importance of findings. Conceptual implications are considered and recommendations are provided for evaluating developmental changes in common situations that researchers may encounter.

Zero-Inflated Models for Count Data: An Application to Number of Antenatal Care Service Visits

The risk of maternal death in developing countries is projected to be one in 61, while for developed countries it is estimated to be one in 2800. Antenatal care is a protective obstetric health care system aimed at improving the outcome of the pregnant fetus by routine pregnancy monitoring. One of the most important functions of antenatal care is to offer health information and services that can significantly improve the health of women and their infants. 6450 pregnant women from Ethiopian Demographic and Health Survey of 2016 were used to analyze the determinants of the barriers in number of antenatal care service visits among pregnant women in Ethiopia. The data were found to have excess zeros (35%); thus several count data models such as Poisson, Negative Binomial, Zero Inflated Poisson, Zero Inflated Negative Binomial and Hurdle regression models were modeled and fitted. From the exploratory analysis the results showed that among those eligible pregnant women, it was seen that 2240 (34.7%) of them did not visit antenatal care service during their periods of pregnancy months. The visualization of data using scatter plot depicts that all of the variables selected for modeling have an influence on the event of not visiting antenatal care cervices while each of these variables had opposite slope in non-zero number of such events in their respective categories. To select the model which best fits the data, models were compared based on their Akaike information criterion value by using the simulation study. The simulation experiment revealed that models for zero-inflated data such as; Zero Inflated Poisson, Zero Inflated Negative Binomial and Hurdle were models that fitted the data better than the classical models Poisson and Negative Binomial. Each of these zero-inflated models was compared using Voung test and Hurdle model was better fitted the data which was characterized by excess zeros and high variability in the non-zero outcome than any other zero-inflated models. In this study, maternal education, partner education level, age of mothers, religion of mothers and wealth index are major predictors of antenatal care service utilization. Through simulation experiment, it was found that Zero Inflated Poisson, Zero Inflated Negative Binomial and Hurdle models were better fitted zero-inflated data than Poisson and Negative Binomial. Voung test suggests that Hurdle model was better fitted zero-inflated (ZI) data than any other zero inflated models and therefore, it was selected as the best parsimonious model.

Application of a Bayesian Statistical Framework for Planetary Protection as a Means of Verifying Low-Biomass, Zero-Inflated Test Data from Spacecraft

Planetary Protection is applicable for missions to biologically sensitive targets of interest in the solar system. For robotic missions landing on the Martian surface, Earth-based biological contamination must be reduced, controlled, and monitored to adhere to forward planetary protection requirements. To address the overall biological load limit and microbial density requirements per spacecraft each component is tracked based on its manufacturing pedigree and/or directly assessed using a direct sampling technique with either a swab or wipe. The tracking and reporting of requirements compliance has varied from mission to mission and reporting of numbers has consistently leaned towards the conservative worst-case scenario. With an increase in the number of missions and mission complexities, the need to establish a technically sound, statistical, and biological solution that provides a single point solution which addresses the distribution of spacecraft contamination becomes critical. Select components of the InSight mission, launched in 2018, have been used as a test case to evaluate the efficacy of applying Bayesian statistics to planetary protection data sets. Eight representative components covering the various bounding cases of high and low surface area, biological count, and sampling devices were analyzed as well as an assembly level case to evaluate the rollup of directly sampled and manufacturing pedigree components. A Bayesian approach was developed leveraging different priors from the zero-inflated data sets and compared to the heritage and existing NASA bioburden assessment approaches. In addition, several non-informative priors were evaluated for use in performing bioburden calculations. The results have demonstrated a viable framework to enable a Bayesian statistical approach to be further developed and utilized for planetary protection requirements assessment.

An R package AZIAD for analysing zero-inflated and zero-altered data

We introduce a newly developed R package AZIAD for analysing zero-inflated or zero-altered data. Compared with existing R packages, AZIAD covers a much larger class of zero-inflated and hurdle models, including both discrete and continuous cases. It provides more accurate parameter estimates, along with the corresponding Fisher information matrix and confidence intervals. It achieves significantly larger power for model identification and selection. To facilitate the potential users, in this paper we provide detailed formulae and theoretical justifications for AZIAD, as well as new theoretical results on zero-inflated and zero-altered models. We use simulation studies to show the advantages of AZIAD functions over existing R packages and provide real data examples and executable R code to illustrate how to use our package for sparse data analysis and model selection.

A Study of ZIP and ZINB Regression Modeling for Count Data with Excess Zeros

Count data with excess number of zeros can cause overdispersion problems. Overdispersion is the presence of greater variability in a data set than would be expected. Overdispersion due to zero-inflated data can be handled either by Zero-inflated Poisson (ZIP) regression or Zero-inflated Negative Binomial (ZINB) regression. In this paper, the performances of different models have been compared based on their MSE, RMSE, bias, and AIC using simulation. The simulated data were generated using ZIP and ZINB distributions. The data were generated using a combination of observation size (n), mean (µ), and the proportion of zeros observation (ω) were imposed to facilitate comparison. To ensure the present of overdispersion, the score test has been applied to the generated data. As expected, the results showed that ZIP and ZINB regression performed better when compared to the Poisson regression. Moreover, in general the simulation results showed that ZINB regression showed better performance than ZIP and Poisson regressions. In this paper, ZINB regression was applied to analyze maternal mortality rate in East Java. The results showed that maternal mortality was significantly affected by the percentage of pregnant woman visiting the clinics for the first time as well as by the percentage of pregnant woman visiting clinics for the fourth time.