Excess Zeros Research Articles

A zero-inflated mixture spatially varying coefficient modeling of cholera incidences

Spatial disease modeling remains an important public health tool. For cholera, the presence of zero counts is common. The Poisson model is inadequate to (1) capture over-dispersion, and (2) distinguish between excess zeros arising from non-susceptible and susceptible populations. In this study, we develop zero-inflated (ZI) mixture spatially varying coefficient (SVC) models to (1) distinguish between the sources of the excess zeros and (2) uncover the spatially varying effects of precipitation and temperature (LST) on cholera. We demonstrate the potential of the models using cholera data from Ghana. A striking observation is that the Poisson model outperformed the ZI mixture models in terms of fit. The ZI Negative Binomial (ZINB) outperformed the ZI Poisson (ZIP) model. Subject to our objectives, we make inferences using the ZINB model. The proportion of zeros estimated with the ZINB model is 0.41 and exceeded what would have been estimated using a Poisson model which is 0.35. We observed the spatial trends of the effects of precipitation and LST to have both increasing and decreasing gradients; an observation implying that the use of only the global coefficients would lead to wrong inferences. We conclude that (1) the use of ZI mixture models has epidemiological significance. Therefore, its choice over the Poisson model should be based on an epidemiological concept rather than model fit and, (2) the extension of ZI mixture models to accommodate spatially varying coefficients uncovered remarkable varying effects of the covariates. These findings have significant implications for public health monitoring of cholera.

Sample size calculation for cluster randomized trials with zero-inflated count outcomes.

Cluster randomized trials (CRT) have been widely employed in medical and public health research. Many clinical count outcomes, such as the number of falls in nursing homes, exhibit excessive zero values. In the presence of zero inflation, traditional power analysis methods for count data based on Poisson or negative binomial distribution may be inadequate. In this study, we present a sample size method for CRTs with zero-inflated count outcomes. It is developed based on GEE regression directly modeling the marginal mean of a zero-inflated Poisson outcome, which avoids the challenge of testing two intervention effects under traditional modeling approaches. A closed-form sample size formula is derived which properly accounts for zero inflation, ICCs due to clustering, unbalanced randomization, and variability in cluster size. Robust approaches, including t-distribution-based approximation and Jackknife re-sampling variance estimator, are employed to enhance trial properties under small sample sizes. Extensive simulations are conducted to evaluate the performance of the proposed method. An application example is presented in a real clinical trial setting.

Re-analyzing the SARS-CoV-2 series using an extended integer-valued time series models: A situational assessment of the COVID-19 in Mauritius.

This paper proposes some high-ordered integer-valued auto-regressive time series process of order p (INAR(p)) with Zero-Inflated and Poisson-mixtures innovation distributions, wherein the predictor functions in these mentioned distributions allow for covariate specification, in particular, time-dependent covariates. The proposed time series structures are tested suitable to model the SARs-CoV-2 series in Mauritius which demonstrates excess zeros and hence significant over-dispersion with non-stationary trend. In addition, the INAR models allow the assessment of possible causes of COVID-19 in Mauritius. The results illustrate that the event of Vaccination and COVID-19 Stringency index are the most influential factors that can reduce the locally acquired COVID-19 cases and ultimately, the associated death cases. Moreover, the INAR(7) with Zero-inflated Negative Binomial innovations provides the best fitting and reliable Root Mean Square Errors, based on some short term forecasts. Undeniably, these information will hugely be useful to Mauritian authorities for implementation of comprehensive policies.

Generalized zero-inated Poisson regression mixture model for fitting health-related data

In many bioscience studies, it is common to encounter count data with a large number of zeros that Poisson regression model or standard zero-inflated Poisson (ZIP) regression model do not fit well. Generalized zero-inflated Poisson (GZIP) regression mixture model can handle the data with excess zeros and overdispersion caused by unobserved heterogeneity. For the parameter estimation, expectation-maximization (EM) algorithm with iteratively reweighted least sqaures (IRLS) method is used. We applied GZIP regression mixture model into two health-related data, Behavioral Risk Factor Surveillance System (BRFSS) data and Integrated Public Use Microdata Series (IPUMS) census data, and compared the performance of the models using AIC and BIC to find the best mixture model.

A deep generative approach for crash frequency model with heterogeneous imbalanced data

Crash frequency model is often subject to excessive zero observation because of the rare nature of crashes. To address the problem of imbalanced crash data, a deep generative approach – augmented variational autoencoder – was proposed to generate synthetic crash data for the association measure between crash and possible explanatory factors. This approach was characterized by a factorized generative model and refined objective function. For instance, the generative model can handle heterogeneous data including real-valued, nominal and ordinal distributions. On the other hand, the refined objective function can control for the random effect by better recognizing both the zero-crash and non-zero crash cases. In this study, comprehensive traffic and crash data of multiple distribution types in Hong Kong in the period between 2014 and 2016 were used. To assess the data generation performance of the proposed augmented variational autoencoder method, a conventional data synthesis technique (synthetic minority oversampling technique-nominal continuous) was also considered. Performances of crash frequency models of total crashes and fatal and severe injury crashes are assessed. For total crashes, the results of parameter estimation, in terms of statistical fit, prediction accuracy, and explanatory factors identified, of the crash frequency model based on synthetic data using the augmented variational autoencoder method adhered closer to that based on original data, compared to that based on synthetic data using the synthetic minority oversampling technique-nominal continuous method. For fatal and severe injury crashes, zero-crash observations were prevalent, with the ratio of zero-crash to non-zero crash cases of 9 to 1. Crash data was first balanced using the proposed augmented variational autoencoder method. Then, fatal and severe injury crash frequency models using correlated random parameter models based on original data and balanced data were estimated respectively. Results indicate that fatal and severe injury crash frequency model based on balanced data outperforms its counterpart, with the lowest root mean square error, lowest mean absolute error, and highest number of crash explanatory factors identified. More importantly, correlation between the random parameters can be revealed. Findings of this study should shed light to both researchers and practitioners for the development of crash frequency models, with which the problem of excessive zero observations is prevalent when highly disaggregated traffic and crash data by time and space are used.

Application of the Truncated Zero-Inflated Double Poisson for Determining of the Effecting Factors on the Number of Coronary Artery Stenosis

Background Risk factors of coronary heart disease have been discussed in the literature; however, conventional statistical models are not appropriate when the outcome of interest is number of vessels with obstructive coronary artery disease. In this paper, a novel statistical model is discussed to investigate the risk factors of number of vessels with obstructive coronary artery disease. Methods This cross-sectional study was conducted on 633 elderly cardiovascular patients at Ghaem Hospital, Mashhad, Iran from September 2011 to May 2013. Clinical outcome is number of vessels with obstructive coronary artery disease (=0, 1, 2, 3), and predictor variables are baseline demographics and clinical features. A right-truncated zero-inflated double Poisson regression model is performed which can accommodate both underdispersion and excess zeros in the outcome. The goodness-of-fit of the proposed model is compared with conventional regression models. Results Out of 633 cardiovascular patients, 327 were male (51.7%). Mean age was ~65 ± 7 years (for individuals with zero, one ,and two coronary artery stenosis) and ~66 ± 7 years (for individuals with three coronary artery stenosis). BMI (0.04 ± 0.01, p = 0.011) and female gender (0.19 ± 0.09, p = 0.032) were significant associated with the count part of the model, and only BMI (−0.47 ± 0.2, p = 0.011) was significantly predictive of logit part of the model. The goodness-of-fit measurements indicate that the proposed model outperforms the conventional regression models. Conclusion The proposal regression model shows a better fit compared to the standard regression analysis in modeling number of vessels with obstructive coronary artery disease. Hence, using truncated zero-inflated double Poisson regression model—as an alternative model—is advised to study the risk factors of number of involved vessels of coronary artery stenosis.

Nonparametric percentile curve estimation for a nonnegative marker with excessive zeros

Norm curves for the head circumference, height, and weight of newborns and infants are widely known examples of percentile curves over age, and early accounts date back 50 years. The advent of the Agatston score for coronary calcification based on coronary computed tomography in 1990 heralded the era of a new marker in preventive medicine, in addition to well-known cardiovascular risk factors. A peculiarity of the nonnegative Agatston score in populations that are free of coronary artery disease is the overexpression of zeros. In a case study, we have demonstrated a nonparametric approach for percentile curve estimation using markers such as the Agatston score. This method is based on lowess smoothing of marker-positive scores on age, and the resulting percentile curves are subsequently transposed according to the estimated proportions of zeros. The approach does not involve any parametric assumptions, is robust against outliers, and fulfills the noncrossing property for percentile curves. A simulation study using samples of N=1,000, 2,000, 5,000, and 10,000 subjects illuminates the closeness of the estimated 50th, 75th, and 90th percentile curves to the respective true curves, assuming an exponentially distributed marker and a proportion of zero scores that increase with age.•The method is applicable to highly skewed data and exemplified here with subgroup data of the referenced procedure.•The consistency and general performance of the method is shown by means of simulation.•The method is an explicit, transferable, and reproducible procedure that is applicable to a wide spectrum of markers and scores across various scientific disciplines, far beyond cardiovascular medicine.

Economic analysis of out-of-pocket costs among people in opioid agonist treatment: A cross-sectional survey in three Australian jurisdictions.

Out-of-pocket costs for opioid agonist treatment (OAT) constitute a barrier to treatment entry and retention.This study examines OAT clients' total out-of-pocket costs (including dispensing fees, travel costs and OAT-related appointment costs) in different treatment settings (public clinics, community pharmacies, and private clinics). Cross-sectional survey of 402 people with opioid drug use (OUD) in New South Wales (NSW), Victoria (VIC), Tasmania (TAS), Australia; 266 clients (66%) currently receiving methadone, buprenorphine or buprenorphine-naloxone treatment were asked about dispensing fees, travel costs and OAT-related appointment costs in the past 28 days. A two-part regression model was used to deal with non-normal distributions of costing data (right skew and excess zeros). Among clients currently receiving OAT, 87% paid out-of-pocket costs. Among those who paid out-of-pocket costs (N=194), travel costs accounted for more than half of total costs (52%), followed by dispensing fees (44%). The mean monthly total out-of-pocket costs were AU$135 (SD: AU$121) for public clinics, AU$161 (SD: AU$110) to AU$214 (SD: AU$166) for community pharmacies and AU$355 (SD: AU$159) for private clinics. Compared to participants in NSW private clinics, those at public clinics paid one third the total out-of-pocket costs (coefficient=0.33; 95%CI=0.23-0.48) and those at NSW, TAS, VIC pharmacies paid approximately half the costs (coefficient=0.58; 95%CI=0.42-0.79; coefficient=0.51; 95%CI=0.36-0.72; coefficient=0.47; 95%CI=0.34-0.66, respectively). People in OAT for more than a year paid half the total out-of-pocket costs, compared with those in OAT less than a year (coefficient=0.49, 95%CI=0.31-0.77). Participants in the current study spent one-eighth of their income on out-of-pocket costs associated with OAT representing a substantial financial burden. Total out-of-pocket costs disproportionately affects those who are newer in treatment and receiving fewer unsupervised doses. Considering and addressing total out-of-pocket costs, especially travel costs and dispensing fees, to clients is critical to prevent cost from being a barrier from receiving effective care.

Performance of the Ridge and Liu Estimators in the zero‐inflated Bell Regression Model

The Poisson regression model is popularly used to model count data. However, the model suffers drawbacks when there is overdispersion—when the mean of the Poisson distribution is not the same as the variance. In this situation, the Bell regression model fits well to the data. Also, there is a high tendency of excess zeros in the count data. In this case, the zero‐inflated Bell regression model is an alternative to the Bell regression model. The parameters of the zero‐inflated Bell regression model are mostly estimated using the method of maximum likelihood. Linear dependency is a threat in a real‐life application when modeling the relationship between the response variable and two or more explanatory variables in a generalized linear model such as the zero‐inflated Bell regression model. It reduced the efficiency of the maximum likelihood estimator. Therefore, we developed the ridge and Liu estimators for the zero‐inflated Bell regression model to deal with this issue. The simulation and application results support the dominance of the proposed methods over the conventional maximum likelihood estimator.

إستخدام توزيع بواسون ذى الاصفار الزائدة وتوزيع هاردل بواسون في نمذجة تکرار المطالبات في تأمين السيارات

Abstract The aim of this paper is to highlight the use of Zero inflated Poisson distribution and Hurdle Poisson distribution to improve goodness of fit of data with excess zeros. Claim frequency data were used for the Singapore motor insurance database available on the internet. The data are tested for the detection of excess zeros. Parameters of Zero inflated Poisson distribution are estimated using method of moments and method of maximum likelihood. Mean and variance formulas are derived for the distribution of Hurdle Poisson and estimators of method of moment and maximum likelihood of unknown parameters are derived. Parameters of Hurdle Poisson are estimated. The data are modeled using Poisson distribution, Zero inflated Poisson distribution and Hurdle Poisson distribution. Goodness of fit are tested using Chi Square test. The best distribution in the study is selected using AIC & BIC criteria. Hurdle Poisson is the best distribution for modeling the data.

A New Bivariate Random Coefficient INAR(1) Model with Applications

Excess zeros is a common phenomenon in time series of counts, but it is not well studied in asymmetrically structured bivariate cases. To fill this gap, we first considered a new first-order, bivariate, random coefficient, integer-valued autoregressive model with a bivariate innovation, which follows the asymmetric Hermite distuibution with five parameters. An attractive advantage of the new model is that the dependence between series is achieved by innovative parts and the cross-dependence of the series. In addition, the time series of counts are modeled with excess zeros, low counts and low over-dispersion. Next, we established the stationarity and ergodicity of the new model and found its stochastic properties. We discuss the conditional maximum likelihood (CML) estimate and its asymptotic property. We assessed finite sample performances of estimators through a simulation study. Finally, we demonstrate the superiority of the proposed model by analyzing an artificial dataset and a real dataset.

Symptom Presence and Symptom Severity as Unique Indicators of Psychopathology: An Application of Multidimensional Zero-Inflated and Hurdle Graded Response Models.

Questionnaires inquiring about psychopathology symptoms often produce data with excess zeros or the equivalent (e.g., none, never, and not at all). This type of zero inflation is especially common in nonclinical samples in which many people do not exhibit psychopathology, and if unaccounted for, can result in biased parameter estimates when fitting latent variable models. In the present research, we adopt a maximum likelihood approach in fitting multidimensional zero-inflated and hurdle graded response models to data from a psychological distress measure. These models include two latent variables: susceptibility, which relates to the probability of endorsing the symptom at all, and severity, which relates to the frequency of the symptom, given its presence. After estimating model parameters, we compute susceptibility and severity scale scores and include them as explanatory variables in modeling health-related criterion measures (e.g., suicide attempts, diagnosis of major depressive disorder). Results indicate that susceptibility and severity uniquely and differentially predict other health outcomes, which suggests that symptom presence and symptom severity are unique indicators of psychopathology and both may be clinically useful. Psychometric and clinical implications are discussed, including scale score reliability.

Generalized Confidence Intervals for Zero-Inflated Pareto Distribution

This paper considers interval estimations for the mean of Pareto distribution with excess zeros. Three approaches for interval estimation are proposed based on fiducial generalized pivotal quantities (FGPQs), respectively. Simulation studies are performed to assess the performance of the proposed methods, along with three measurements to determine comparisons with competing approaches. The advantages and disadvantages of each method are provided. The methods are illustrated using a real phone call dataset.

Improved shrinkage estimators in zero-inflated negative binomial regression model

‎Zero-inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. ‎This paper addressed parameter estimation in the zero-inflated negative binomial model when there are many parameters, ‎so that some of them have not influence on the response variable. ‎We proposed parameter estimation based on the linear shrinkage, ‎pretest, ‎shrinkage pretest, ‎Stein-type, ‎and positive Stein-type estimators. ‎We obtained the asymptotic distributional biases and risks of the suggested estimators theoretically. ‎‎We also conducted a Monte Carlo simulation study ‎to compare the performance of each estimator with the unrestricted estimator using simulated relative efficiency (SRE) criterion.‎‎ ‎The results reveal that the SREs of proposed estimators are higher than the unrestricted estimator. ‎The suggested estimators were applied to the wildlife fish data to appraise their performance.

Bayesian spatio-temporal distributed lag modeling for delayed climatic effects on sparse malaria incidence data

BackgroundIn many areas of the Greater Mekong Subregion (GMS), malaria endemic regions have shrunk to patches of predominantly low-transmission. With a regional goal of elimination by 2030, it is important to use appropriate methods to analyze and predict trends in incidence in these remaining transmission foci to inform planning efforts. Climatic variables have been associated with malaria incidence to varying degrees across the globe but the relationship is less clear in the GMS and standard methodologies may not be appropriate to account for the lag between climate and incidence and for locations with low numbers of cases.MethodsIn this study, a methodology was developed to estimate the spatio-temporal lag effect of climatic factors on malaria incidence in Thailand within a Bayesian framework. A simulation was conducted based on ground truth of lagged effect curves representing the delayed relation with sparse malaria cases as seen in our study population. A case study to estimate the delayed effect of environmental variables was used with malaria incidence at a fine geographic scale of sub-districts in a western province of Thailand.ResultsFrom the simulation study, the model assumptions which accommodated both delayed effects and excessive zeros appeared to have the best overall performance across evaluation metrics and scenarios. The case study demonstrated lagged climatic effect estimation of the proposed modeling with real data. The models appeared to be useful to estimate the shape of association with malaria incidence.ConclusionsA new method to estimate the spatiotemporal effect of climate on malaria trends in low transmission settings is presented. The developed methodology has potential to improve understanding and estimation of past and future trends in malaria incidence. With further development, this could assist policy makers with decisions on how to more effectively distribute resources and plan strategies for malaria elimination.

A resampling approach to disaggregate analysis of bus-involved crashes using panel data with excessive zeros

Public bus constitutes more than 70% of the overall road-based public transport patronage in Hong Kong, and its crash involvement rate has been the highest among all public transport modes. Though previous studies had identified explanatory factors that affect the crash risk of buses, use of considerably imbalanced crash data with excessive zero observations could lead to inaccurate parameter estimation. This study aims to resolve the excess zero problem of disaggregate analysis of bus-involved crashes based on synthetic data using a Synthetic Minority Over-Sampling Technique for panel data (SMOTE-P). Dataset comprising crash, traffic, and road inventory data of 88 road segments in Hong Kong during the period from 2014 to 2017 is used. To assess the data balancing performance, other common data generation approaches such as Random Under-sampling of the Majority Class (RUMC) technique, Cluster-Based Under-Sampling (CBUS), and mixed resampling, are also considered. Random effect Poisson (REP) models based on synthetic data and random effect zero-inflated Poisson (REZIP) model based on original data are estimated. Results indicate that REP model based on synthetic data using SMOTE-P outperforms REZIP model based on original data and REP models based on synthetic data using RUMC, CBUS and mixed approaches, in terms of statistical fit, prediction error, and explanatory factors identified. Results of model estimation based on SMOTE-P suggest that factors including morning peak, evening peak, hourly traffic flow, average lane width, road length, bus stop density, percentage of bus in the traffic stream, and presence of bus priority lane all affect the bus-involved crash frequency. More importantly, this study provides a feasible solution for disaggregate crash analysis with imbalanced panel data.

Precisely modeling zero-inflated count phenotype for rare variants.

Count data with excessive zeros are increasingly ubiquitous in genetic association studies, such as neuritic plaques in brain pathology for Alzheimer's disease. Here, we developed gene-based association tests to model such data by a mixture of two distributions, one for the structural zeros contributed by the Binomial distribution, and the other for the counts from the Poisson distribution. We derived the score statistics of the corresponding parameter of the rare variants in the zero-inflated Poisson regression model, and then constructed burden (ZIP-b) and kernel (ZIP-k) tests for the association tests. We evaluated omnibus tests that combined both ZIP-b and ZIP-k tests. Through simulated sequence data, we illustrated the potential power gain of our proposed method over a two-stage method that analyzes binary and non-zero continuous data separately for both burden and kernel tests. The ZIP burden test outperformed the kernel test as expected in all scenarios except for the scenario of variants with a mixture of directions in the genetic effects. We further demonstrated its applications to analyses of the neuritic plaque data in the ROSMAP cohort. We expect our proposed test to be useful in practice as more powerful than or complementary to the two-stage method.

Multivariate zero-inflated Bell distribution and its inference and applications

In this paper we introduce a multivariate family of distributions for multivariate count data with excess zeros, which is a multivariate extension of the univariate zero-inflated Bell distribution. We derive various general properties of this multivariate distribution. In particular, the marginal distributions are univariate zero-inflated Bell distributions. The model parameters are estimated using the traditional maximum likelihood estimation method. In addition, we develop a simple EM algorithm to compute the maximum likelihood estimates of the parameters of the new multivariate distribution with closed-form expressions for the maximum likelihood estimators. Empirical applications that employ real multivariate count data are considered to illustrate the usefulness of the new class of multivariate distributions, and comparisons with the multivariate zero-inflated Poisson distribution, multivariate zero-adjusted Poisson distributions, and multivariate zero-inflated generalized Poisson distribution are made.

Type I multivariate zero-inflated COM-Poisson regression model.

In this paper, we present the Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution, whose development is based on the extension of the Type I multivariate zero-inflated Poisson distribution. We developed important properties of the distribution and present a regression model. The AIC and BIC criteria are used to select the best fitted model. Two real data sets have been used to illustrate the proposed model. Moreover, we conclude by stating that the Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution produces a better fitted model for multivariate count data with excess of zeros.

Modelling Excess Zeros in Count Data: A New Perspective on Modelling Approaches

SummaryWe consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: over‐dispersion (OD) models and zero‐inflation (ZI) models, both of which can be seen as generalisations of the Poisson distribution; we refer to these as implicit and explicit ZI models, respectively. Although sometimes seen as competing approaches, they can be complementary; OD is a consequence of ZI modelling, and ZI is a by‐product of OD modelling. The central objective in such analyses is often concerned with inference on the effect of covariates on the mean, in light of the apparent excess of zeros in the counts. Typically, the modelling of the excess zerosper seis a secondary objective, and there are choices to be made between, and within, the OD and ZI approaches. The contribution of this paper is primarily conceptual. We contrast, descriptively, the impact on zeros of the two approaches. We further offer a novel descriptive characterisation of alternative ZI models, including the classic hurdle and mixture models, by providing a unifying theoretical framework for their comparison. This in turn leads to a novel and technically simpler ZI model. We develop the underlying theory for univariate counts and touch on its implication for multivariate count data.