Excess Zeros Research Articles

A zero-inflated endemic-epidemic model with an application to measles time series in Germany.

Count data with an excess of zeros are often encountered when modeling infectious disease occurrence. The degree of zero inflation can vary over time due to nonepidemic periods as well as by age group or region. A well-established approach to analyze multivariate incidence time series is the endemic-epidemic modeling framework, also known as the HHH approach. However, it assumes Poisson or negative binomial distributions and is thus not tailored to surveillance data with excess zeros. Here, we propose a multivariate zero-inflated endemic-epidemic model with random effects that extends HHH. Parameters of both the zero-inflation probability and the HHH part of this mixture model can be estimated jointly and efficiently via (penalized) maximum likelihood inference using analytical derivatives. We found proper convergence and good coverage of confidence intervals in simulation studies. An application to measles counts in the 16 German states, 2005-2018, showed that zero inflation is more pronounced in the Eastern states characterized by a higher vaccination coverage. Probabilistic forecasts of measles cases improved when accounting for zero inflation. We anticipate zero-inflated HHH models to be a useful extension also for other applications and provide an implementation in anRpackage.

Spatial accessibility of pre-exposure prophylaxis (PrEP): different measure choices and the implications for detecting shortage areas and examining its association with social determinants of health

PurposeWe examine how various pre-exposure prophylaxis (PrEP) accessibility measures impact the detection of PrEP shortage areas and the relation of shortage areas to social determinants of health (SDOH). MethodsUsing ZIP Code Tabulation Areas (ZCTAs) in New York City as a case study, we compared 25 measures of spatial PrEP accessibility across four categories, including density, proximity, two-step floating catchment area (2SFCA), and Gaussian 2SFCA (G2SFCA). Bayesian spatial regression models were used to examine how PrEP accessibility is associated with SDOH. ResultsUsing density to measure PrEP accessibility for small areas such as ZCTAs poses challenges to statistical modeling because the measured accessibility values are highly skewed with excess zeros, leading to the necessity of using complex models such as the two-part mixture model. When G2SFCA measures are used, which account for distance decay effects and the competition from the PrEP demand side, findings on PrEP shortage area detection and the association between PrEP accessibility and SDOH were more consistent and less sensitive to spatial scales (i.e., varying from 10- to 30-minute driving). ConclusionsThis research adds to the nascent research on PrEP accessibility measurement and sheds light on selecting an appropriate measure to assess spatial disparities in PrEP accessibility and its associations with SDOH.

Investigating the Associations Between Socioeconomic Factors and Unhealthy Days among Adults Using Zero-inflated Negative Binomial Regression

Poor social and economic circumstances affect the health of individuals throughout the life cycle. The purpose of the study was to examine whether state-level and individual-level socioeconomic factors are associated with mentally or physically unhealthy days in the general U.S. population of adults. The Behavioral Risk Factor Surveillance System and the American Community Survey in 2016 were used to examine state-level social determinants of health and the number of self-reported mentally unhealthy days in the last 30 days using Zero-Inflated Negative Binomial (ZINB) regression models. Men, older individuals, minorities, persons with higher educational attainment levels, persons who were employed, persons who were married, or with a partner, and persons with one or zero chronic condition were more likely to report excessive zeros for responses to the mentally, and physically unhealthy days. The negative binomial regression results indicated that higher state-level poverty rates, higher income inequity, lower median income, and higher unemployment rates were related to the higher number of reported mentally, and physically unhealthy days. Persons with higher educational attainment, and who were employed reported lower mentally, and physically unhealthy days. The findings show significant relationships between socioeconomic contexts and general health status. Health planners and policymakers may use the results to allocate resources and guide public policies and programs.

Predicting potential underreporting of firearm ownership in a nationally representative sample.

This study utilized demographic and intrapersonal variables to identify individuals who may have falsely denied firearm ownership and determined if individuals can be divided into meaningful subgroups. Participants were United States residents (N = 3500) recruited from January to June 2020. matched to the 2010 census data for age, race, sex, income, and education level. A Zero-Inflated Negative Binomial (ZINB) regression was utilized to determine potential underreporting of firearm ownership, and a latent class analysis was utilized to determine unique subgroups of those who were identified as underreporting firearm ownership in the ZINB. Participants (N = 1306) were identified as underreporting firearm ownership (excess zeros) based on a model that included demographic and intrapersonal variables. A latent class analysis indicated that among excess zeros, three unique subgroups exist. Determining who may be underreporting firearm ownership will allow for a more comprehensive understanding of firearm ownership in the US and more targeted safe storage messages that may reach those who own firearms and are at risk for firearm-related injury and death.

Evaluating the performance of different Bayesian count models in modelling childhood vaccine uptake among children aged 12–23 months in Nigeria

BackgroundChoosing appropriate models for count health outcomes remains a challenge to public health researchers and the validity of the findings thereof. For count data, the mean–variance relationship and proportion of zeros is a major determinant of model choice. This study aims to compare and identify the best Bayesian count modelling technique for the number of childhood vaccine uptake in Nigeria.MethodsWe explored the performances of Poisson, negative binomial and their zero-inflated forms in the Bayesian framework using cross-sectional data pooled from the Nigeria Demographic and Health Survey conducted between 2003 and 2018. In multivariable analysis, these Bayesian models were used to identify factors associated with the number of vaccine uptake among children. Model selection was based on the -2 Log-Likelihood (-2 Log LL), Leave-One-Out Cross-Validation Information Criterion (LOOIC) and Watanabe-Akaike/Widely Applicable Information Criterion (WAIC).ResultsExploratory analysis showed the presence of excess zeros and overdispersion with a mean of 4.36 and a variance of 12.86. Observably, there was a significant increase in vaccine uptake over time. Significant factors included the mother’s age, level of education, religion, occupation, desire for last-child, place of delivery, exposure to media, birth order of the child, wealth status, number of antenatal care visits, postnatal attendance, healthcare decision maker, community poverty, community illiteracy, community unemployment, rural proportion and number of health facilities per 100,000. The zero-inflated negative binomial model was best fit with -2Log LL of -27171.47, LOOIC of 54464.2, and WAIC of 54588.0.ConclusionThe Bayesian zero-inflated negative binomial model was most appropriate to identify factors associated with the number of childhood vaccines received in Nigeria due to the presence of excess zeros and overdispersion. Improving vaccine uptake by addressing the associated risk factors should be promptly embraced.

Zero-inflated Poisson-Akash distribution for count data with excessive zeros

Zero-inflated Poisson-Akash distribution for count data with excessive zeros

Determinants of Conflict-Related Sexual Violence: A Meta-Reanalysis Distinguishing Two Classes of Zero Observations

Abstract Existing databases on conflict-related sexual violence (CRSV) feature a disproportionate number of “zero” observations, which conflate a true absence of CRSV with an unknown presence of CRSV. Empirical studies model such zeros as solely indicating a lack of CRSV, thereby obscuring what needs to be known about its determinants and patterns. In this article, I present a comprehensive meta-reanalysis of quantitative CRSV studies that have disregarded the two-fold nature of excessive zeros in their data. To redress this neglect, I differentiate the two types of zeros probabilistically and then estimate the prevalence of CRSV conditional on the statistical partitioning of its two zero types. My meta-reanalysis refines previous findings, restoring confidence in intuitive theoretical expectations and resolving inconclusive and unexpected results in the field. It also dispels potential misconceptions by providing alternative evidence and explanations. Overall, distinguishing the two classes of zeros in estimation yields more informed results, making substantial contributions to scholarly understanding of CRSV while avoiding spurious confirmations and disconfirmations.

Truncated rank-based tests for two-part models with excessive zeros and applications to microbiome data

Truncated rank-based tests for two-part models with excessive zeros and applications to microbiome data

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 novel causal mediation analysis approach for zero-inflated mediators.

Mediation analyses play important roles in making causal inference in biomedical research to examine causal pathways that may be mediated by one or more intermediate variables (ie, mediators). Although mediation frameworks have been well established such as counterfactual-outcomes (ie, potential-outcomes) models and traditional linear mediation models, little effort has been devoted to dealing with mediators with zero-inflated structures due to challenges associated with excessive zeros. We develop a novel mediation modeling approach to address zero-inflated mediators containing true zeros and false zeros. The new approach can decompose the total mediation effect into two components induced by zero-inflated structures: the first component is attributable to the change in the mediator on its numerical scale which is a sum of two causal pathways and the second component is attributable only to its binary change from zero to a non-zero status. An extensive simulation study is conducted to assess the performance and it shows that the proposed approach outperforms existing standard causal mediation analysis approaches. We also showcase the application of the proposed approach to a real study in comparison with a standard causal mediation analysis approach.

Improving trends estimates for specific work-related ill-health conditions when excess zeros are present in a voluntary health reporting scheme

BackgroundTrends in occupational disease incidence are estimated in voluntary reporting schemes such as The Health and Occupational Reporting (THOR) Network in the UK. Voluntary reporting schemes request responses even if...

Effects of design consistency on run-off-road crashes: An application of a Random Parameters Negative Binomial Lindley model

Run-off-road crashes are one of the most common crash types, especially in rural roadway environments contributing significantly to fatalities and severe injuries. These crashes are complex and multi-dimensional events, and factors like road geometry, driver behaviour, traffic characteristics and roadside features contribute to their occurrence, separately or interactively. Sudden changes in road geometry, in particular, can influence driver behaviour, and therefore, in developing a micro-level crash risk model for run-off-road crashes, one of the challenges is incorporating the effects of driver behaviour (disaggregated information) that may arise from the variations in road geometry (aggregated information). This study aims to examine the interaction between road geometry and driver behaviour through a set of measures for design consistency on two-lane rural roads. Multiple data sources, including crash data for 2014–18, traffic data, probe speed data and roadway geometric data, for twenty-three highways in Queensland, Australia, have been fused for this study. Seventeen types of design consistency measures with regard to alignment consistency, operating speed consistency and driving dynamics are tested. A run-off-road crash risk model is estimated by employing the Random Parameters Negative Binomial Lindley regression framework, which accounts for excess zeros in the crash counts and captures the effects of unobserved heterogeneity in the parameter estimates. Results indicate that the geometric design consistency capturing the interaction between driver behaviour and operational factors better predicts run-off-road crashes along rural highways. In addition, roadside attributes like clear zone width, infrastructures, terrain, and roadway remoteness also contribute to run-off-road crashes. The findings of the study provide a comprehensive understanding of the influence of variations in roadway geometry on driver behaviour and run-off-road crashes along rural highways.

Emotional complexity under high stress: Do protective associations for risk behaviors persist even during a pandemic?

Risk behaviors like substance use and binge eating are often used to cope with negative emotions. Engagement in these behaviors has been exacerbated by the COVID-19 pandemic. Past research suggests that complex emotion conceptualizations captured as emotion differentiation (ability to discriminate between emotional states) and polarity (ability to integrate positive and negative features of emotional experience) may be protective. We examined associations of mean affect intensity, emotion differentiation, and emotion polarity with frequency of daily substance use and binge eating across 10 days in a demographically diverse sample of U.S. adults (N = 353) recruited between March 24 and April 9, 2020, when stay-at-home orders were initiated. Owing to the nested data structure and excessive zero values, analyses were conducted using multilevel zero-inflated negative binomial regression. Consistent with past research, negative affect was positively associated with frequency of substance use and binge eating. Importantly, results indicated that negative emotion differentiation was protective, predicting greater likelihood of not using substances and binge eating at all across the sampling period. These effects remained even after controlling for mean affect intensity, emotion polarity, and positive emotion differentiation. Neither positive emotion differentiation nor emotion polarity were significantly associated with either behavior. Our results suggest that greater complexity in conceptualization of negative emotions facilitates some protection against risk behaviors such as substance use and binge eating, even during periods of high environmental stress. These findings have important implications for optimizing interventions to reduce engagement in risk behaviors. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Disparities in oesophageal cancer risk by age, sex, and nativity in Kuwait:1980–2019

BackgroundThis cross-sectional cohort study assessed the inequalities in oesophageal carcinoma risk by age, sex and nativity in Kuwait: 1980–2019.MethodsUsing oesophageal cancer incidence data from the Kuwait National Cancer Registry, relevant Kuwaiti population data and World Standard Population as a reference, age-standardized incidence rates (ASIR) (per 100,000 person-years) overall and by subcohorts were computed. The incident oesophageal cancer cases count was overdispersed with excessive structural zeros, therefore, it was analyzed using multivariable zero-inflated negative binomial (ZINB) model.ResultsOverall ASIR of oesophageal cancer was 10.51 (95% CI: 6.62-14.41). The multivariable ZINB model showed that compared with the younger age category (< 30 years), the individuals in higher age groups showed a significant (p < 0.001) increasing tendency to develop the oesophageal cancer. Furthermore, compared with the non-Kuwaiti residents, the Kuwaiti nationals were significantly (p < 0.001) more likely to develop oesophageal cancer during the study period. Moreover, compared with 1980-84 period, ASIRs steadily and significantly (p < 0.005) declined in subsequent periods till 2015-19.ConclusionsA high incidence of oesophageal cancer was recorded in Kuwait, which consistently declined from 1980 to 2019. Older adults (aged ≥ 60 years) and, Kuwaiti nationals were at high risk of oesophageal cancer. Focused educational intervention may minimize oesophageal cancer incidence in high-risk groups in this and other similar settings. Future studies may contemplate to evaluate such an intervention.

Reducing bias and mitigating the influence of excess of zeros in regression covariates with multi-outcome adaptive LAD-lasso

Zero-inflated explanatory variables, as opposed to outcome variables, are common, for example, in environmental sciences. In this article, we address the problem of having excess of zero values in some continuous explanatory variables, which are subject to multi-outcome lasso-regularized variable selection. In short, the problem results from the failure of the lasso-type of shrinkage methods to recognize any difference between zero value occurring either in the regression coefficient or in the corresponding value of the explanatory variable. This kind of confounding will obviously increase the number of false positives – all non-zero regression coefficients do not necessarily represent true outcome effects. We present here the adaptive LAD-lasso for multiple outcomes, which extends the earlier work of multi-outcome LAD-lasso with adaptive penalization. In addition to well-known property of having less biased regression coefficients, we show that the adaptivity also improves method’s ability to recover from influences of excess of zero values measured in continuous covariates.

BZINB Model-Based Pathway Analysis and Module Identification Facilitates Integration of Microbiome and Metabolome Data.

Integration of multi-omics data is a challenging but necessary step to advance our understanding of the biology underlying human health and disease processes. To date, investigations seeking to integrate multi-omics (e.g., microbiome and metabolome) employ simple correlation-based network analyses; however, these methods are not always well-suited for microbiome analyses because they do not accommodate the excess zeros typically present in these data. In this paper, we introduce a bivariate zero-inflated negative binomial (BZINB) model-based network and module analysis method that addresses this limitation and improves microbiome-metabolome correlation-based model fitting by accommodating excess zeros. We use real and simulated data based on a multi-omics study of childhood oral health (ZOE 2.0; investigating early childhood dental caries, ECC) and find that the accuracy of the BZINB model-based correlation method is superior compared to Spearman's rank and Pearson correlations in terms of approximating the underlying relationships between microbial taxa and metabolites. The new method, BZINB-iMMPath, facilitates the construction of metabolite-species and species-species correlation networks using BZINB and identifies modules of (i.e., correlated) species by combining BZINB and similarity-based clustering. Perturbations in correlation networks and modules can be efficiently tested between groups (i.e., healthy and diseased study participants). Upon application of the new method in the ZOE 2.0 study microbiome-metabolome data, we identify that several biologically-relevant correlations of ECC-associated microbial taxa with carbohydrate metabolites differ between healthy and dental caries-affected participants. In sum, we find that the BZINB model is a useful alternative to Spearman or Pearson correlations for estimating the underlying correlation of zero-inflated bivariate count data and thus is suitable for integrative analyses of multi-omics data such as those encountered in microbiome and metabolome studies.

A general averaging method for count data with overdispersion and/or excess zeros in biomedicine.

With the aim of providing better estimation for count data with overdispersion and/or excess zeros, we develop a novel estimation method-optimal weighting based on cross-validation-for the zero-inflated negative binomial model, where the Poisson, negative binomial, and zero-inflated Poisson models are all included as its special cases. To facilitate the selection of the optimal weight vector, a -fold cross-validation technique is adopted. Unlike the jackknife model averaging discussed in Hansen and Racine (2012), the proposed method deletes one group of observations rather than only one observation to enhance the computational efficiency. Furthermore, we also theoretically prove the asymptotic optimality of the newly developed optimal weighting based on cross-validation method. Simulation studies and three empirical applications indicate the superiority of the presented optimal weighting based on cross-validation method when compared with the three commonly used information-based model selection methods and their model averaging counterparts.

A Bayesian zero-inflated Dirichlet-multinomial regression model for multivariate compositional count data.

The Dirichlet-multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data generated by high-throughput sequencing technology in omics research due to its ability to accommodate the compositional structure of the data as well as overdispersion. A major limitation of the DM distribution is that it is unable to handle excess zeros typically found in practice which may bias inference. To fill this gap, we propose a novel Bayesian zero-inflated DM model for multivariate compositional count data with excess zeros. We then extend our approach to regression settings and embed sparsity-inducing priors to perform variable selection for high-dimensional covariate spaces. Throughout, modeling decisions are made to boost scalability without sacrificing interpretability or imposing limiting assumptions. Extensive simulations and an application to a human gut microbiome dataset are presented to compare the performance of the proposed method to existing approaches. We provide an accompanying R package with a user-friendly vignette to apply our method to otherdatasets.

Hurdle-QAP models overcome dependency and sparsity in scientific collaboration count networks

ABSTRACT Spatial proximity may facilitate scientific collaboration. We regress its impact within two German research institutions, defining collaboration strength and proximity by the number of joint publications and spatial distance between work places. The methodological focus lies on accounting for (i) the dependency structure in network data and (ii) excess zeros in the sparse target matrix. The former can be addressed by a quadratic assignment procedure (QAP), the second by a hurdle model. To offer a joint solution, we combine the methods to novel parametric and non-parametric hurdle-QAP models. The analysis reveals that proximity can facilitate collaboration, but significant effects get lost within building structures. Outcomes of this study may inform about how to target the promotion of interdisciplinary research.

Modelling zero inflated and under-reported count data

Poisson distribution is a classic choice for modelling unbounded count data. However, count data arising in various fields of scientific research often have excess zeros and are under-reported. In such situations, Poisson distribution gives a poor fit and Poisson model based inferences lead to biased estimators and inaccurate confidence intervals. In this paper we develop a flexible model which can accommodate excess zeros and undercount. Internal validation data has been used for making likelihood based inferences. The impact of ignoring undercount and excess zeros are studied through extensive simulations. The finite sample behaviour of the estimators are investigated through bootstrap methodology. Finally, a real life data which is supposedly under-reported and known to have excess zeros is analysed.