Zero-inflated Regression Models Research Articles

A new discrete distribution with applications to radiation, smoking, and health data

In this study, a flexible discrete distribution is introduced by compounding Epanechnikov-exponential and Poisson distributions. Many mathematical features of the distribution are obtained. Several point estimators of the unknown parameter are proposed. The Monte Carlo simulation study is carried out to compare these estimators. Three methods are proposed to construct the approximate confidence intervals for the distribution parameter. A novel zero-inflated regression model is given based on the proposed discrete distribution as an alternative to zero-inflated geometric and zero-inflated Poisson models. The usability of the distribution and the count regression model is demonstrated by some practical data analyses, such as the number of dicentric chromosomes observed after exposure to radiation at doses of 0.600, survey data on health, and smoking habits.

Comparison of different statistical models for the analysis of fracture events: findings from the Prevention of Falls Injury Trial (PreFIT)

BackgroundFractures are rare events and can occur because of a fall. Fracture counts are distinct from other count data in that these data are positively skewed, inflated by excess zero counts, and events can recur over time. Analytical methods used to assess fracture data and account for these characteristics are limited in the literature.MethodsCommonly used models for count data include Poisson regression, negative binomial regression, hurdle regression, and zero-inflated regression models. In this paper, we compare four alternative statistical models to fit fracture counts using data from a large UK based clinical trial evaluating the clinical and cost-effectiveness of alternative falls prevention interventions in older people (Prevention of Falls Injury Trial; PreFIT).ResultsThe values of Akaike information criterion and Bayesian information criterion, the goodness-of-fit statistics, were the lowest for negative binomial model. The likelihood ratio test of no dispersion in the data showed strong evidence of dispersion (chi-square = 225.68, p-value < 0.001). This indicates that the negative binomial model fits the data better compared to the Poisson regression model. We also compared the standard negative binomial regression and mixed effects negative binomial models. The LR test showed no gain in fitting the data using mixed effects negative binomial model (chi-square = 1.67, p-value = 0.098) compared to standard negative binomial model.ConclusionsThe negative binomial regression model was the most appropriate and optimal fit model for fracture count analyses.Trial registrationThe PreFIT trial was registered as ISRCTN71002650.

Evaluation of negative binomial and zero-inflated negative binomial models for the analysis of zero-inflated count data: application to the telemedicine for children with medical complexity trial

BackgroundTwo characteristics of commonly used outcomes in medical research are zero inflation and non-negative integers; examples include the number of hospital admissions or emergency department visits, where the majority of patients will have zero counts. Zero-inflated regression models were devised to analyze this type of data. However, the performance of zero-inflated regression models or the properties of data best suited for these analyses have not been thoroughly investigated.MethodsWe conducted a simulation study to evaluate the performance of two generalized linear models, negative binomial and zero-inflated negative binomial, for analyzing zero-inflated count data. Simulation scenarios assumed a randomized controlled trial design and varied the true underlying distribution, sample size, and rate of zero inflation. We compared the models in terms of bias, mean squared error, and coverage. Additionally, we used logistic regression to determine which data properties are most important for predicting the best-fitting model.ResultsWe first found that, regardless of the rate of zero inflation, there was little difference between the conventional negative binomial and its zero-inflated counterpart in terms of bias of the marginal treatment group coefficient. Second, even when the outcome was simulated from a zero-inflated distribution, a negative binomial model was favored above its ZI counterpart in terms of the Akaike Information Criterion. Third, the mean and skewness of the non-zero part of the data were stronger predictors of model preference than the percentage of zero counts. These results were not affected by the sample size, which ranged from 60 to 800.ConclusionsWe recommend that the rate of zero inflation and overdispersion in the outcome should not be the sole and main justification for choosing zero-inflated regression models. Investigators should also consider other data characteristics when choosing a model for count data. In addition, if the performance of the NB and ZINB regression models is reasonably comparable even with ZI outcomes, we advocate the use of the NB regression model due to its clear and straightforward interpretation of the results.

Real-World Evidence of Aripiprazole Tablets with Sensor: Treatment Patterns and Impacts on Psychiatric Healthcare Resource Utilization.

Maintaining adherence to antipsychotic (AP) medication is often challenging. Aripiprazole tablets with sensor (AS) contain an ingestible event marker and communicate with wearable patches and a smartphone app to provide objective medication ingestion data. This study evaluated real-world treatment patterns of AS usage and its impact on psychiatric healthcare resource utilization (HCRU). This retrospective, observational cohort study identified individuals who initiated AS between 1/1/2019 and 6/30/2020 with 3 months baseline and 6 months of follow-up data using a commercial medical and pharmacy claims database (Clarivate). Controls were propensity score-matched (4:1) to AS initiators based on age (±2 years), sex, diagnosis (major depressive disorder [MDD], schizophrenia, bipolar I disorder [BP-I], other), insurance, and baseline oral AP use (yes/no). Days of AP supply were evaluated using a general regression model. The frequency of psychiatric HCRU during follow-up was compared between groups using a zero-inflated regression model. Most AS initiators were diagnosed with MDD (61.2%) and were women (61.2%); mean age was 37.7 years (standard deviation: 14.1). Most AS initiators (53.1%) continued treatment for >60 days (mean days of supply = 77). After adjusting for covariates, AS initiators had 41% more days of AP supply during follow-up compared with controls (P <0.0001) and significantly lower adjusted odds ratios (ORs) for psychiatric outpatient visits (adjusted OR = 0.80; P <0.05), emergency department visits (adjusted OR = 0.11; P <0.05), inpatient visits (adjusted OR = 0.42; P <0.05), and other medical services (adjusted OR = 0.25; P <0.05). Participants who implemented AS had significantly more days of AP supply and fewer psychiatric care visits. These preliminary results suggest AS usage can help build regular medication-taking habits and holds promise for reducing psychiatric HCRU. Additional studies with larger sample sizes are warranted to inform clinical practice and coverage decisions.

Geo-spatial risk factor analysis for drug overdose death in South Florida from 2014 to 2019, and the independent contribution of social determinants of health

PurposeThe physical environment and social determinants of health have been shown to influence health behaviors including drug use and fatal drug overdose. The current research examines the effects of the built environment, social determinants of health measures and aggregated risk from the built environment at neighborhood-level on drug overdose death locations in Miami-Dade County, Florida. MethodsRisk Terrain Modeling (RTM) was used to assess the place features risk factors that significantly increase the risk of drug overdose death spatially in Miami-Dade County ZIP Code Tabulation Areas, Florida from 2014 to 2019. An aggregated neighborhood risk of fatal drug overdose measure was developed by averaging the risk per grid cell from the RTM within census block groups each year. Six logistic and zero-inflated regression models were built to examine the effects of three indices of incident-specific social determinants of health (IS-SDH) measures and aggregated risk measures separately, and simultaneously on drug overdose death locations each year. ResultsSeven place features including parks, bus stops, restaurants and grocery stores were significantly related to the occurrence of fatal drug overdoses. When examined separately, one or more indices of the IS-SDH were significant covariates of drug overdose locations in some years. When examined simultaneously, the three indices of the IS-SDH and aggregated risk of fatal drug overdose measure could be all significant in certain years. ConclusionsThe patterns of high-risk areas and place features identified from the RTM related to drug overdose deaths may be used to inform the placement of treatment and prevention resources. A multi-factor approach that combines an aggregated neighborhood risk measure reflecting the risk from the built environment and the incident-specific social determinants of health measures can be used to identify the drug overdose death locations in certain years.

Association of climate factors with dengue incidence in Bangladesh, Dhaka City: A count regression approach

BackgroundIn Bangladesh, particularly in Dhaka city, dengue fever is a major factor in serious sickness and hospitalization. The weather influences the temporal and geographical spread of the vector-borne disease dengue in Dhaka. As a result, rainfall and ambient temperature are considered macro factors influencing dengue since they have a direct impact on Aedes aegypti population density, which changes seasonally dependent on these critical variables. This study aimed to clarify the relationship between climatic variables and the incidence of dengue disease. MethodsA total of 2253 dengue and climate data were used for this study. Maximum and minimum temperature (°C), humidity (grams of water vapor per kilogram of air g.kg−1), rainfall (mm), sunshine hour (in (average) hours per day), and wind speed (knots (kt)) in Dhaka were considered as the independent variables for this study which trigger the dengue incidence in Dhaka city, Bangladesh. Missing values were imputed using multiple imputation techniques. Descriptive and correlation analyses were performed for each variable and stationary tests were observed using Dicky Fuller test. However, initially, the Poisson model, zero-inflated regression model, and negative binomial model were fitted for this problem. Finally, the negative binomial model is considered the final model for this study based on minimum AIC values. ResultsThe mean of maximum and minimum temperature, wind speed, sunshine hour, and rainfall showed some fluctuations over the years. However, a mean number of dengue cases reported a higher incidence in recent years. Maximum and minimum temperature, humidity, and wind speed were positively correlated with dengue cases. However, rainfall and sunshine hours were negatively associated with dengue cases. The findings showed that factors such as maximum temperature, minimum temperature, humidity, and windspeed are crucial in the transmission cycles of dengue disease. On the other hand, dengue cases decreased with higher levels of rainfall. ConclusionThe findings of this study will be helpful for policymakers to develop a climate-based warning system in Bangladesh.

Dispersion insensitive truncated models for inflated count data with upper bound

Zero-inflated regression models are generally accepted for modeling data with inflated amounts of zeros. The principle used in constructing the distribution for these models has been extended to modeling certain types of data with inflation at the upper bound of the support. An excellent example of this is the zero and κ-inflated truncated Poisson regression model which utilizes the Poisson distribution. However, the equi-dispersion nature of the Poisson distribution makes the model less suitable for data that are under-dispersed and over-dispersed. Models based on exponentiated exponential geometric distribution (EEGD) are presented as alternatives for modeling any count data with an upper bound, irrespective of the nature of dispersion. The models are obtained by truncating the EEGD at the top and inflating at either or both zero and κ. A simulation study is conducted to examine the performances of the models under certain conditions. The result shows that the closer the dispersion parameter c is from the equi-dispersion line, the better the estimates for over-dispersed data, while the farther the dispersion parameter from the equi-dispersed line, the better the estimates for an under-dispersed model. The application of the models is illustrated using data from the Behavioral Risk Factor Surveillance System 2011.

A new zero–inflated discrete Lindley regression model

Recently, providing a new count regression model is very popular for many researchers. These count regression models are constructed by using a new discrete distribution or one of the existing distributions in the literature. In this paper, we consider a new zero-inflated regression model as an alternative to the zero-inflated regression models. We present two real data applications to illustrate the usefulness of the suggested regression model in modeling data, and compare the competitor models such as Poisson, discrete Lindley, and zero-inflated regression models. We provide a new count regression model which is useful in modeling overdispersed data.

Migrant and native women’s perceptions of prenatal care communication quality: the role of host-country language proficiency

BackgroundDespite the potentially significant impact of women-prenatal care provider communication quality (WPCQ) on women’s perinatal health, evidence on the determinants of those perceptions is still lacking, particularly among migrant women.MethodsWe aimed to examine the effect of women’s host-country language proficiency on their perceived WPCQ. We analyzed the data of 1210 migrant and 1400 native women who gave birth at Portuguese public hospitals between 2017 and 2019 and participated in the baMBINO cohort study. Migrants’ language proficiency was self-rated. Perceived WPCQ was measured as a composite score of 9 different aspects of self-reported communication quality and ranged from 0 (optimal) to 27.ResultsA high percentage of women (29%) rated communication quality as “optimal”. Zero-inflated regression models were fitted to estimate the association between language proficiency and perceived WPCQ. Women with full (aIRR 1.35; 95% CI 1.22,1.50), intermediate (aIRR 1.41; 95% CI 1.23,1.61), and limited (aIRR 1.72; 95% CI 1.45,2.05) language proficiencies were increasingly more likely to have lower WPCQ when compared to natives.ConclusionsFacilitating communication with migrant women experiencing language barriers in prenatal care could provide an important contribution to improving prenatal care quality and addressing potential subsequent disparities in perinatal health outcomes.

Artificial Intelligence-based CT Assessment of Bronchiectasis: The COPDGene Study.

Background CT is the standard method used to assess bronchiectasis. A higher airway-to-artery diameter ratio (AAR) is typically used to identify enlarged bronchi and bronchiectasis; however, current imaging methods are limited in assessing the extent of this metric in CT scans. Purpose To determine the extent of AARs using an artificial intelligence-based chest CT and assess the association of AARs with exacerbations over time. Materials and Methods In a secondary analysis of ever-smokers from the prospective, observational, multicenter COPDGene study, AARs were quantified using an artificial intelligence tool. The percentage of airways with AAR greater than 1 (a measure of airway dilatation) in each participant on chest CT scans was determined. Pulmonary exacerbations were prospectively determined through biannual follow-up (from July 2009 to September 2021). Multivariable zero-inflated regression models were used to assess the association between the percentage of airways with AAR greater than 1 and the total number of pulmonary exacerbations over follow-up. Covariates included demographics, lung function, and conventional CT parameters. Results Among 4192 participants (median age, 59 years; IQR, 52-67 years; 1878 men [45%]), 1834 had chronic obstructive pulmonary disease (COPD). During a 10-year follow-up and in adjusted models, the percentage of airways with AARs greater than 1 (quartile 4 vs 1) was associated with a higher total number of exacerbations (risk ratio [RR], 1.08; 95% CI: 1.02, 1.15; P = .01). In participants meeting clinical and imaging criteria of bronchiectasis (ie, clinical manifestations with ≥3% of AARs >1) versus those who did not, the RR was 1.37 (95% CI: 1.31, 1.43; P < .001). Among participants with COPD, the corresponding RRs were 1.10 (95% CI: 1.02, 1.18; P = .02) and 1.32 (95% CI: 1.26, 1.39; P < .001), respectively. Conclusion In ever-smokers with chronic obstructive pulmonary disease, artificial intelligence-based CT measures of bronchiectasis were associated with more exacerbations over time. Clinical trial registration no. NCT00608764 © RSNA, 2022 Supplemental material is available for this article. See also the editorial by Schiebler and Seo in this issue.

New zero-inflated regression models with a variant of censoring

There is ever growing demand of modeling overdispersed count data generated by various disiplines. Excessive number of zeros and heterogeneity in the population are two main sources of the overdispersion problem. Development of new count models that are more flexible than conventional Poisson model is thus necessary in order to address such sources. This study fullfils this need by proposing a new heterogeneous Poisson model with a capture of excess zeros, namely zero-inflated Poisson–Ailamujia (ZIPA) model. In line with the aim of curing overdispersion, a censored variant of this newly suggested model is also here developed. An extensive simulation study is conducted to assess the performances of both forms of new models in terms of bias, precision and accuracy measures. Additionally, two real world applications are presented to illustrate practical implications of zero-inflated (censored) Poisson–Ailamujia models in comparison to some alternatives.

Distribution models calibrated with independent field data predict two million ancient and veteran trees in England.

Large, citizen-science species databases are powerful resources for predictive species distribution modeling (SDM), yet they are often subject to sampling bias. Many methods have been proposed to correct for this, but there exists little consensus as to which is most effective, not least because the true value of model predictions is hard to evaluate without extensive independent field sampling. We present here a nationwide, independent field validation of distribution models of ancient and veteran trees, a group of organisms of high conservation importance, built using a large and internationally unique citizen-science database: the Ancient Tree Inventory (ATI). This validation exercise presents an opportunity to test the performance of different methods of correcting for sampling bias, in the search for the best possible prediction of ancient and veteran tree distributions in England. We fitted a variety of distribution models of ancient and veteran tree records in England in relation to environmental predictors and applied different bias correction methods, including spatial filtering, background manipulation, the use of bias files, and, finally, zero-inflated (ZI) regression models, a new method with great potential to investigate and remove sampling bias in species data. We then collected new independent field data through systematic surveys of 52 randomly selected 1-km2 grid squares across England to obtain abundance estimates of ancient and veteran trees. Calibration of the distribution models against the field data suggests that there are around eight to 10 times as many ancient and veteran trees present in England than the records currently suggest, with estimates ranging from 1.7 to 2.1 million trees compared to the 200,000 currently recorded in the ATI. The most successful bias correction method was systematic sampling of occurrence records, although the ZI models also performed well, significantly predicting field observations and highlighting both likely causes of undersampling and areas of the country in which many unrecorded trees are likely to be found. Our findings provide the first robust nationwide estimate of ancient and veteran tree abundance and demonstrate the enormous potential for distribution modeling based on citizen-science data combined with independent field validation to inform conservation planning.

Simultaneous confidence bands in a zero-inflated regression model for binary data

Abstract The logistic regression model has become a standard tool to investigate the relationship between a binary outcome and a set of potential predictors. When analyzing binary data, it often arises, however, that the observed proportion of zeros is greater than expected under the postulated logistic model. Zero-inflated binomial (ZIB) models have been developed to fit binary data that contain too many zeros. Maximum likelihood estimators in these models have been proposed, and their asymptotic properties were recently established. In this paper, we use these asymptotic properties to construct simultaneous confidence bands for the probability of a positive outcome in a ZIB regression model. Simultaneous confidence bands are especially attractive since they allow inference to be made over the whole regressor space. We construct two types of confidence bands, based on: (i) the Scheffé method for the linear regression model; (ii) Monte Carlo simulations to approximate the distribution of the supremum of a Gaussian field indexed by the regressor. The finite-samples properties of these two types of bands are investigated and compared in a simulation study.

Zero-inflated Modified Borel-Tanner Regression Model for Count Data

By starting from the one-parameter Modified Borel-Tanner distribution proposed recently in the statistic literature, we introduce the zero-inflated Modified Borel-Tanner distribution. Additionally, on the basis of the proposed zero-inflated distribution, a novel zero-inflated regression model is proposed, which is quite simple and may be an interesting alternative to usual zero-inflated regression models for count data. The parameters of the proposed model are estimated by Maximum Likelihood Estimation technique. To check the potentiality of the zero inflated Modified Borel-Tanner regression, an application to the count of infected blood cells is taken. The results suggest that the new zero inflated Modified Borel-Tanner regression is more appropriate to model these count data than other familiar zero-inflated (or not) regression models commonly used in practice.

Goodness of fit test for a zero-inflated Bernoulli regression model

The goodness of fit (GOF) test is an intensely crucial and meaningful issue in scientific research because it is widely applied in sciences such as statistics, applied mathematics, economics, finance, engineering, and so on. To the extent of this article, we first revisit the GOF test for the logistic model, and then we propose the GOF test for the zero-inflated Bernoulli (ZIBer) model. We seek to establish Karl Pearson’s chi-square test and unweighted residual sum of square test for this model. Afterward, we demonstrate that both tests have an asymptotic normal distribution with a mean and standard deviation that they derived. Simulation studies and an actual data set are also studied to illustrate the effectiveness of the proposed method.

Environmental Injustice and Industrial Chicken Farming in Maryland.

Maryland’s growing chicken industry, including concentrated animal feeding operations (CAFOs) and meat processing plants, raises a number of concerns regarding public health and environmental justice. Using hot spot analysis, we analyzed the totality of Maryland’s CAFOs and meat processing plants and those restricted to the Eastern Shore to assess whether communities of color and/or low socioeconomic status communities disproportionately hosted these types of facilities at the census tract level. We used zero-inflated regression modeling to determine the strength of the associations between environmental justice variables and the location of CAFOs and meatpacking facilities at the State level and on the Eastern Shore. Hot spot analyses demonstrated that CAFO hot spots on the Eastern Shore were located in counties with some of the lowest wealth in the State, including the lowest ranking county—Somerset. Zero-inflated regression models demonstrated that increases in median household income across the state were associated with a 0.04-unit reduction in CAFOs. For every unit increase in the percentage of people of color (POC), there was a 0.02-unit increase in meat processing facilities across the state. The distribution of CAFOs and meat processing plants across Maryland may contribute to poor health outcomes in areas affected by such production, and contribute to health disparities and health inequity.

Modelling Healthcare Demand Count Data with Excessive Zeros and Overdispersion

ABSTRACT In healthcare economics count datasets often exhibit excessive zeros or right-skewed tails. When covariates are available, such datasets are typically modelled using the zero-inflated (ZI) or finite mixture (FM) regression models. However, neither model performs adequately when the dataset has both excessive zeros and a long tail, which is often the case in practice. In this paper we combine these two models to create a more flexible, versatile class of ZIFM models. With this model we perform a comprehensive analysis on the number of visits to a physician’s office using the US healthcare demand dataset that has been used in numerous healthcare studies in the literature. After comparing to other existing models which have been reported to perform well on this dataset, we find that the ZIFM model substantially outperforms alternative models. In addition, the model offers a new interpretation that is in contrast to previous empirical findings regarding the factors associated with the demand for the physicians, which can shed a fresh light on the healthcare utilisation policies.

ASYMPTOTIC PROPERTIES IN THE PROBIT-ZERO-INFLATED BINOMIAL REGRESSION MODEL

Zero-inflated regression models have had wide application recently and have provenuseful in modeling data with many zeros. Zero-inflated Binomial (ZIB) regression model is an extension of the ordinary binomial distribution that takes into account the excess of zeros. In comparing the probit model to the logistic model, many authors believe that there is little theoretical justification in choosing one formulation over the other in most circumstances involving binary responses. The logit model is considered to be computationally simpler but it is based on a more restrictive assumption of error independence, although many other generalizations have dealt with that assumption as well. By contrast, the probit model assumes that random errors have a multivariate normal distribution. This assumption makes the probit model attractive because the normal distribution provides a good approximation to many other distributions. In this paper, we develop a maximum likelihood estimation procedure for the parameters of a zero-inflated Binomial regression model with probit link function for both component of the model. We establish the existency, consistency and asymptotic normality of the proposed estimator.

Modeling Longitudinal Microbiome Compositional Data: A Two-Part Linear Mixed Model with Shared Random Effects

Longitudinal microbiome studies have been widely used to unveil the dynamics in the complex host-microbial ecosystems. Modeling the longitudinal microbiome compositional data, which is semi-continuous in nature, is challenging in several aspects: the overabundance of zeros, the heavy skewness of non-zero values that are bounded in (0, 1), and the dependence between the binary and non-zero parts. To deal with these challenges, we first extended the work of Chen and Li [1] and proposed a two-part zero-inflated Beta regression model with shared random effects (ZIBR-SRE), which characterize the dependence between the binary and the continuous parts. Besides, the microbiome compositional data have unit-sum constraint, indicating the existence of negative correlations among taxa. As ZIBR-SRE models each taxon separately, it does not satisfy the sum-to-one constraint. We then proposed a two-part linear mixed model (TPLMM) with shared random effects to formulate the log-transformed standardized relative abundances rather than the original ones. Such transformation is called “additive logistic transformation”, initially developed for cross-sectional compositional data. We extended it to analyze the longitudinal microbiome compositions and showed that the unit-sum constraint can be automatically satisfied under the TPLMM framework. Model performances of TPLMM and ZIBR-SRE were compared with existing methods in simulation studies. Under settings adopted from real data, TPLMM had the best performance and is recommended for practical use. An oral microbiome application further showed that TPLMM and ZIBR-SRE estimated a strong correlation structure in the binary and the continuous parts, suggesting models without accounting for this dependence would lead to biased inferences.

An Application Comparison of Two Poisson Models on Zero Count Data

Counting data (including zero counts) appear in a variety of applications, so counting models have become popular in many fields. In statistical fields, count data can be defined as observation types that use only non-negative integer values. Sometimes researchers may Counts more zeros than the expected. You may describe Excess zero as Zero-Inflation, excess zeros cause over-dispersion. So, the objective of this paper is use zero-inflated regression models (Poisson Regression model, Zero-Inflated Poisson (ZIP), and Zero-Altered Poisson (ZAP)) to analyse rainfall data and select the best model that deal with these type of data. It has been shown through the study and practical application that the advantage and quality of the Zero-Altered Poisson Regression (ZAPR) where the Zero-Altered Poisson regression model was the best count data model for our data, Although it is hard to distinguish Zero-Inflated Poisson (ZIP) regression model, it is better than Poisson regression model.