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This paper aims to discuss the Bayesian estimation approach for the zero-inflated cure class of models, which extends the standard cure model by accommodating zero-inflated data in the survival analysis context. A comprehensive simulation study is carried out to assess the performance of the estimation procedure. A new estimation methodology is illustrated using a real dataset related to women diagnosed with invasive cervical cancer in Brazil., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2021 Informa UK Limited, trading as Taylor & Francis Group.)

Background: 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., Methods: 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., Results: 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., Conclusions: 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., Competing Interests: Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at http://dx.doi.org/10.21037/atm-20-6363). SR reports grants from Gesundheitscampus Brandenburg - Konsequenzen der altersassoziierten Zell - und Organfunktionen, grants from Initiative of the Brandenburgian Ministry of Science, Research and Culture (MWFK) during the conduct of the study; JC reports scholarship from Deutscher Akademischer Austauschdienst/German Academic Exchange Service (DAAD) during the conduct of part of the study. The other authors have no conflicts of interest to declare., (2021 Annals of Translational Medicine. All rights reserved.)

A latent factor model for count data is popularly applied in deconvoluting mixed signals in biological data as exemplified by sequencing data for transcriptome or microbiome studies. Due to the availability of pure samples such as single-cell transcriptome data, the accuracy of the estimates could be much improved. However, the advantage quickly disappears in the presence of excessive zeros. To correctly account for this phenomenon in both mixed and pure samples, we propose a zero-inflated non-negative matrix factorization and derive an effective multiplicative parameter updating rule. In simulation studies, our method yielded the smallest bias. We applied our approach to brain gene expression as well as fecal microbiome datasets, illustrating the superior performance of the approach. Our method is implemented as a publicly available R-package, iNMF., (© 2021 Walter de Gruyter GmbH, Berlin/Boston.)

In obstetrics and gynecology, knowledge about how women's features are associated with childbirth is important. This leads to establishing guidelines and can help managers to describe the dynamics of pregnant women's hospital stays. Then, time is a variable of great importance and can be described by survival models. An issue that should be considered in the modeling is the inclusion of women for whom the duration of labor cannot be observed due to fetal death, generating a proportion of times equal to zero. Additionally, another proportion of women's time may be censored due to some intervention. The aim of this paper was to present the Log-Normal zero-inflated cure regression model and to evaluate likelihood-based parameter estimation by a simulation study. In general, the inference procedures showed a better performance for larger samples and low proportions of zero inflation and cure. To exemplify how this model can be an important tool for investigating the course of the childbirth process, we considered the Better Outcomes in Labor Difficulty project dataset and showed that parity and educational level are associated with the main outcomes. We acknowledge the World Health Organization for granting us permission to use the dataset., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2021 Informa UK Limited, trading as Taylor & Francis Group.)

Psychiatric syndromes in dementia are often derived from the Neuropsychiatric Inventory (NPI) using principal component analysis (PCA). The validity of this statistical approach can be questioned, since the excessive proportion of zeros and skewness of NPI items may distort the estimated relations between the items. We propose a novel version of PCA, ZIBP-PCA, where a zero-inflated bivariate Poisson (ZIBP) distribution models the pairwise covariance between the NPI items. We compared the performance of the method to classical PCA under zero-inflation using simulations, and in two dementia-cohorts (N = 830, N = 1349). Simulations showed that component loadings from PCA were biased due to zero-inflation, while the loadings of ZIBP-PCA remained unaffected. ZIBP-PCA obtained a simpler component structure of "psychosis," "mood" and "agitation" in both dementia-cohorts, compared to PCA. The principal components from ZIBP-PCA had component loadings as follows: First, the component interpreted as "psychosis" was loaded by the items delusions and hallucinations. Second, the "mood" component was loaded by depression and anxiety. Finally, the "agitation" component was loaded by irritability and aggression. In conclusion, PCA is not equipped to handle zero-inflation. Using the NPI, PCA fails to identify components with a valid interpretation, while ZIBP-PCA estimates simple and interpretable components to characterize the psychopathology of dementia.

Background: The estimation of microbial networks can provide important insight into the ecological relationships among the organisms that comprise the microbiome. However, there are a number of critical statistical challenges in the inference of such networks from high-throughput data. Since the abundances in each sample are constrained to have a fixed sum and there is incomplete overlap in microbial populations across subjects, the data are both compositional and zero-inflated., Results: We propose the COmpositional Zero-Inflated Network Estimation (COZINE) method for inference of microbial networks which addresses these critical aspects of the data while maintaining computational scalability. COZINE relies on the multivariate Hurdle model to infer a sparse set of conditional dependencies which reflect not only relationships among the continuous values, but also among binary indicators of presence or absence and between the binary and continuous representations of the data. Our simulation results show that the proposed method is better able to capture various types of microbial relationships than existing approaches. We demonstrate the utility of the method with an application to understanding the oral microbiome network in a cohort of leukemic patients., Conclusions: Our proposed method addresses important challenges in microbiome network estimation, and can be effectively applied to discover various types of dependence relationships in microbial communities. The procedure we have developed, which we refer to as COZINE, is available online at https://github.com/MinJinHa/COZINE .

Count time series data with excess zeros are observed in several applied disciplines. When these zero-inflated counts are sequentially recorded, they might result in serial dependence. Ignoring the zero-inflation and the serial dependence might produce inaccurate results. In this paper, Markov zero-inflated count time series models based on a joint distribution on consecutive observations are proposed. The joint distribution function of the consecutive observations is constructed through copula functions. First- and second-order Markov chains are considered with the univariate margins of zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), or zero-inflated Conway-Maxwell-Poisson (ZICMP) distributions. Under the Markov models, bivariate copula functions such as the bivariate Gaussian, Frank, and Gumbel are chosen to construct a bivariate distribution of two consecutive observations. Moreover, the trivariate Gaussian and max-infinitely divisible copula functions are considered to build the joint distribution of three consecutive observations. Likelihood-based inference is performed and asymptotic properties are studied. To evaluate the estimation method and the asymptotic results, simulated examples are studied. The proposed class of models are applied to sandstorm counts example. The results suggest that the proposed models have some advantages over some of the models in the literature for modeling zero-inflated count time series data., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2020 Informa UK Limited, trading as Taylor & Francis Group.)

Reproduction by individuals is typically recorded as count data (e.g., number of fledglings from a nest or inflorescences on a plant) and commonly modeled using Poisson or negative binomial distributions, which assume that variance is greater than or equal to the mean. However, distributions of reproductive effort are often underdispersed (i.e., variance < mean). When used in hypothesis tests, models that ignore underdispersion will be overly conservative and may fail to detect significant patterns. Here we show that generalized Poisson (GP) and Conway‐Maxwell‐Poisson (CMP) distributions are better choices for modeling reproductive effort because they can handle both overdispersion and underdispersion; we provide examples of how ecologists can use GP and CMP distributions in generalized linear models (GLMs) and generalized linear mixed models (GLMMs) to quantify patterns in reproduction. Using a new R package, glmmTMB, we construct GLMMs to investigate how rainfall and population density influence the number of fledglings in the warbler Oreothlypis celata and how flowering rate of Heliconia acuminata differs between fragmented and continuous forest. We also demonstrate how to deal with zero‐inflation, which occurs when there are more zeros than expected in the distribution, e.g., due to complete reproductive failure by some individuals. [ABSTRACT FROM AUTHOR]

For count responses, there are situations in biomedical and sociological applications in which extra zeroes occur. Modeling correlated (e.g. repeated measures and clustered) zero-inflated count data includes special challenges because the correlation between measurements for a subject or a cluster needs to be taken into account. Moreover, zero-inflated count data are often faced with over/under dispersion problem. In this paper, we propose a random effect model for repeated measurements or clustered data with over/under dispersed response called random effect zero-inflated exponentiated-exponential geometric regression model. The proposed method was illustrated through real examples. The performance of the model and asymptotical properties of the estimations were investigated using simulation studies., Competing Interests: No potential conflict of interest was reported by the authors., (© 2019 Informa UK Limited, trading as Taylor & Francis Group.)

Metagenomics enables the study of gene abundances in complex mixtures of microorganisms and has become a standard methodology for the analysis of the human microbiome. However, gene abundance data is inherently noisy and contains high levels of biological and technical variability as well as an excess of zeros due to non-detected genes. This makes the statistical analysis challenging. In this study, we present a new hierarchical Bayesian model for inference of metagenomic gene abundance data. The model uses a zero-inflated overdispersed Poisson distribution which is able to simultaneously capture the high gene-specific variability as well as zero observations in the data. By analysis of three comprehensive datasets, we show that zero-inflation is common in metagenomic data from the human gut and, if not correctly modelled, it can lead to substantial reductions in statistical power. We also show, by using resampled metagenomic data, that our model has, compared to other methods, a higher and more stable performance for detecting differentially abundant genes. We conclude that proper modelling of the gene-specific variability, including the excess of zeros, is necessary to accurately describe gene abundances in metagenomic data. The proposed model will thus pave the way for new biological insights into the structure of microbial communities.

Purpose: The goal was to compare the micronucleus (MN) and dicentric plus ring chromosomes (D + R) assays for dose assessment in cases of partial body irradiations (PBI). Materials and methods: We constructed calibration curves for each assay at doses ranging from 0 to 5 Gy of X-rays at dose rate of 0.275 Gy/min. To simulate partial-body exposures, blood samples from two donors were irradiated with 0.5, 1, 2 and 4 Gy and the ratios of irradiated to unirradiated blood were 25, 50, and 100%. Different tests were used to confirm if all samples were overdispersed or zero-inflated and for partial-body dose assessment we used the Qdr, Dolphin and Bayesian model. Results: In our samples for D + R calibration curve, practically all doses agreed with Poisson assumption, but MN exhibited overdispersed and zero-inflated cellular distributions. The exact Poisson tests and zero-inflated tests demonstrate that virtually all samples of D + R from PBI simulation fit the Poisson distribution and were not zero-inflated, but the MN samples were also overdispersed and zero-inflated. In the partial-body estimation, when Qdr and Dolphin methods were used the D + R results were better than MN, but the doses estimation defined by the Bayesian methodology were more accurate than the classical methods. Conclusions: Dicentric chromosomes continue to prove to be the best biological marker for dose assessment. However exposure scenarios of partial-body estimation, overdispersion and zero-inflation may not occur, it being a critical point not only for dose assessment, but also to confirm partial-body exposure. MN could be used as alternative assay for partial-body dose estimation, but in case of an accident without any information, the MN assay could not define whether the accident was a whole-body irradiation (WBI) or a PBI.

Understanding how organisms distribute themselves in response to interacting species, ecosystems, climate, human development and time is fundamental to ecological study and practice. A measure to quantify the relationship among organisms and their environments is intensity of use: the rate of use of a specific resource in a defined unit of time. Estimating the intensity of use differs from estimating probabilities of occupancy or selection, which can remain constant even when the intensity of use varies. We describe a method to evaluate the intensity of use across conditions that vary in both space and time. We demonstrate its application on a large mammal community where linear developments and human activity are conjectured to influence the interactions between white-tailed deer (Odocoileus virginianus) and wolves (Canis lupus) with possible consequences on threatened woodland caribou (Rangifer tarandus caribou). We collect and quantify intensity of use data for multiple, interacting species with the goal of assessing management efficacy, including a habitat restoration strategy for linear developments. We test whether blocking linear developments by spreading logs across a 200-m interval can be applied as an immediate mitigation to reduce the intensities of use by humans, predator and prey species in a boreal caribou range. We deployed camera traps on linear developments with and without restoration treatments in a landscape exposed to both timber and oil development. We collected a three-year dataset and employed spatial recurrent event models to analyse intensity of use by an interacting human and large mammal community across a range of environmental and climatic conditions. Spatial recurrent event models revealed that intensity of use by humans influenced the intensity of use by all five large mammal species evaluated, and the intensities of use by wolves and deer were inextricably linked in space and time. Conditions that resist travel on linear developments had a strong negative effect on the intensity of human and large mammal use. Mitigation strategies that resist, or redirect, animal travel on linear developments can reduce the effects of resource development on interacting human and predator-prey interactions. Our approach is easily applied to other continuous time point-based survey methodologies and shows that measuring the intensity of use within animal communities can help scientists monitor, mitigate and understand ecological states and processes., (© 2019 The Authors. Journal of Animal Ecology © 2019 British Ecological Society.)

We describe a new pathway for multivariate analysis of data consisting of counts of species abundances that includes two key components: copulas, to provide a flexible joint model of individual species, and dissimilarity-based methods, to integrate information across species and provide a holistic view of the community. Individual species are characterized using suitable (marginal) statistical distributions, with the mean, the degree of over-dispersion, and/or zero-inflation being allowed to vary among a priori groups of sampling units. Associations among species are then modeled using copulas, which allow any pair of disparate types of variables to be coupled through their cumulative distribution function, while maintaining entirely the separate individual marginal distributions appropriate for each species. A Gaussian copula smoothly captures changes in an index of association that excludes joint absences in the space of the original species variables. A permutation-based filter with exact family-wise error can optionally be used a priori to reduce the dimensionality of the copula estimation problem. We describe in detail a Monte Carlo expectation maximization algorithm for efficient estimation of the copula correlation matrix with discrete marginal distributions (counts). The resulting fully parameterized copula models can be used to simulate realistic ecological community data under fully specified null or alternative hypotheses. Distributions of community centroids derived from simulated data can then be visualized in ordinations of ecologically meaningful dissimilarity spaces. Multinomial mixtures of data drawn from copula models also yield smooth power curves in dissimilarity-based settings. Our proposed analysis pathway provides new opportunities to combine model-based approaches with dissimilarity-based methods to enhance understanding of ecological systems. We demonstrate implementation of the pathway through an ecological example, where associations among fish species were found to increase after the establishment of a marine reserve.

Count data with excess zeros encountered in many applications often exhibit extra variation. Therefore, zero-inflated Poisson (ZIP) model may fail to fit such data. In this paper, a zero-inflated double Poisson model (ZIDP), which is generalization of the ZIP model, is studied and the score tests for the significance of dispersion and zero-inflation in ZIDP model are developed. Meanwhile, this work also develops homogeneous tests for dispersion and/or zero-inflation parameter, and corresponding score test statistics are obtained. One numerical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Unlike zero-inflated Poisson regression, marginalized zero-inflated Poisson (MZIP) models for counts with excess zeros provide estimates with direct interpretations for the overall effects of covariates on the marginal mean. In the presence of missing covariates, MZIP and many other count data models are ordinarily fitted using complete case analysis methods due to lack of appropriate statistical methods and software. This article presents an estimation method for MZIP models with missing covariates. The method, which is applicable to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data on the caries preventive effects of a school-based fluoride mouthrinse program., (© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Normalization is the first critical step in microbiome sequencing data analysis used to account for variable library sizes. Current RNA-Seq based normalization methods that have been adapted for microbiome data fail to consider the unique characteristics of microbiome data, which contain a vast number of zeros due to the physical absence or under-sampling of the microbes. Normalization methods that specifically address the zero-inflation remain largely undeveloped. Here we propose geometric mean of pairwise ratios-a simple but effective normalization method-for zero-inflated sequencing data such as microbiome data. Simulation studies and real datasets analyses demonstrate that the proposed method is more robust than competing methods, leading to more powerful detection of differentially abundant taxa and higher reproducibility of the relative abundances of taxa., Competing Interests: Jun Chen is an Academic Editor for PeerJ.

Binomial N-mixture models have proven very useful in ecology, conservation, and monitoring: they allow estimation and modeling of abundance separately from detection probability using simple counts. Recently, doubts about parameter identifiability have been voiced. I conducted a large-scale screening test with 137 bird data sets from 2,037 sites. I found virtually no identifiability problems for Poisson and zero-inflated Poisson (ZIP) binomial N-mixture models, but negative-binomial (NB) models had problems in 25% of all data sets. The corresponding multinomial N-mixture models had no problems. Parameter estimates under Poisson and ZIP binomial and multinomial N-mixture models were extremely similar. Identifiability problems became a little more frequent with smaller sample sizes (267 and 50 sites), but were unaffected by whether the models did or did not include covariates. Hence, binomial N-mixture model parameters with Poisson and ZIP mixtures typically appeared identifiable. In contrast, NB mixtures were often unidentifiable, which is worrying since these were often selected by Akaike's information criterion. Identifiability of binomial N-mixture models should always be checked. If problems are found, simpler models, integrated models that combine different observation models or the use of external information via informative priors or penalized likelihoods, may help., (© 2017 by the Ecological Society of America.)

Purpose To show a novel application of a weighted zero-inflated negative binomial model in modeling count data with excess zeros and heterogeneity to quantify the regional variation in HIV-AIDS prevalence in sub-Saharan African countries. Methods Data come from latest round of the Demographic and Health Survey (DHS) conducted in three countries (Ethiopia-2011, Kenya-2009 and Rwanda-2010) using a two-stage cluster sampling design. The outcome is an aggregate count of HIV cases in each census enumeration area of each country. The outcome data are characterized by excess zeros and heterogeneity due to clustering. We compare scale weighted zero-inflated negative binomial models with and without random effects to account for zero-inflation, complex survey design and clustering. Finally, we provide marginalized rate ratio estimates from the best zero-inflated negative binomial model. Results The best fitting zero-inflated negative binomial model is scale weighted and with a common random intercept for the three countries. Rate ratio estimates from the final model show that HIV prevalence is associated with age and gender distribution, HIV acceptance, HIV knowledge, and its regional variation is associated with divorce rate, burden of sexually transmitted diseases and rural residence. Conclusions Scale weighted zero-inflated negative binomial with proper modeling of random effects is shown to be the best model for count data from a complex survey design characterized by excess zeros and extra heterogeneity. In our data example, the final rate ratio estimates show significant regional variation in the factors associated with HIV prevalence indicating that HIV intervention strategies should be tailored to the unique factors found in each country.

The marginalized two-part (MTP) model for semicontinuous data proposed by Smith et al. provides direct inference for the effect of covariates on the marginal mean of positively continuous data with zeros. This brief note addresses mischaracterizations of the MTP model by Gebregziabher et al. Additionally, the MTP model is extended to incorporate the three-parameter generalized gamma distribution, which takes many well-known distributions as special cases, including the Weibull, gamma, inverse gamma, and log-normal distributions.

Pain intensity is often measured in clinical and research settings using the 0 to 10 numeric rating scale (NRS). NRS scores are recorded as discrete values, and in some samples they may display a high proportion of zeroes and a right-skewed distribution. Despite this, statistical methods for normally distributed data are frequently used in the analysis of NRS data. We present results from an observational cross-sectional study examining the association of NRS scores with patient characteristics using data collected from a large cohort of 18,935 veterans in Department of Veterans Affairs care diagnosed with a potentially painful musculoskeletal disorder. The mean (variance) NRS pain was 3.0 (7.5), and 34% of patients reported no pain (NRS = 0). We compared the following statistical models for analyzing NRS scores: linear regression, generalized linear models (Poisson and negative binomial), zero-inflated and hurdle models for data with an excess of zeroes, and a cumulative logit model for ordinal data. We examined model fit, interpretability of results, and whether conclusions about the predictor effects changed across models. In this study, models that accommodate zero inflation provided a better fit than the other models. These models should be considered for the analysis of NRS data with a large proportion of zeroes., Perspective: We examined and analyzed pain data from a large cohort of veterans with musculoskeletal disorders. We found that many reported no current pain on the NRS on the diagnosis date. We present several alternative statistical methods for the analysis of pain intensity data with a large proportion of zeroes., (Published by Elsevier Inc.)

There is growing interest in analysing high-dimensional count data, which often exhibit quasi-sparsity corresponding to an overabundance of zeros and small nonzero counts. Existing methods for analysing multivariate count data via Poisson or negative binomial log-linear hierarchical models with zero-inflation cannot flexibly adapt to quasi-sparse settings. We develop a new class of continuous local-global shrinkage priors tailored to quasi-sparse counts. Theoretical properties are assessed, including flexible posterior concentration and stronger control of false discoveries in multiple testing. Simulation studies demonstrate excellent small-sample properties relative to competing methods. We use the method to detect rare mutational hotspots in exome sequencing data and to identify North American cities most impacted by terrorism.

Sometimes there is interest in a dichotomized outcome indicating whether a count variable is positive or zero. Under this scenario, the application of ordinary logistic regression may result in efficiency loss, which is quantifiable under an assumed model for the counts. In such situations, a shared-parameter hurdle model is investigated for more efficient estimation of regression parameters relating to overall effects of covariates on the dichotomous outcome, while handling count data with many zeroes. One model part provides a logistic regression containing marginal log odds ratio effects of primary interest, while an ancillary model part describes the mean count of a Poisson or negative binomial process in terms of nuisance regression parameters. Asymptotic efficiency of the logistic model parameter estimators of the two-part models is evaluated with respect to ordinary logistic regression. Simulations are used to assess the properties of the models with respect to power and Type I error, the latter investigated under both misspecified and correctly specified models. The methods are applied to data from a randomized clinical trial of three toothpaste formulations to prevent incident dental caries in a large population of Scottish schoolchildren., (© The Author(s) 2014.)

Public health research often concerns relationships between exposures and correlated count outcomes. When counts exhibit more zeros than expected under Poisson sampling, the zero-inflated Poisson (ZIP) model with random effects may be used. However, the latent class formulation of the ZIP model can make marginal inference on the sampled population challenging. This article presents a marginalized ZIP model with random effects to directly model the mean of the mixture distribution consisting of 'susceptible' individuals and excess zeroes, providing straightforward inference for overall exposure effects. Simulations evaluate finite sample properties, and the new methods are applied to a motivational interviewing-based safer sex intervention trial, designed to reduce the number of unprotected sexual acts.