Poisson Binomial Research Articles

Semi-parametric approach for modelling overdispersed count data with application to Industry 4.0

The paper deals with a test for the goodness-of-fit of a model for count data, in the framework of Generalized Linear Models. The motivating example concerns the study on the effectiveness of policy incentives for the adoption of 4.0 technologies by Small and Medium Enterprises. According to the literature, openness to Industry 4.0 should be measured in terms of the number of 4.0 technologies adopted, represented by a count variable. To investigate the effectiveness of public policy interventions to encourage the adoption of 4.0 technologies, we propose the application of a model for count data with a permutation ANOVA to test the goodness-of-fit and for the model selection. When the distribution of the response is neither Poisson nor Negative Binomial, and in the quite common situation in which the response variance is much greater than the mean, the classic Poisson regression and Negative Binomial regression are not valid. The proposed testing method is based on the combination of permutation tests on the significance of the regression coefficient estimates. The power behaviour of the proposed semi-parametric solution is investigated through a comparative Monte Carlo simulation study. The performance of such a method is compared to those of the two main parametric competitors. The application of the permutation test to an interesting case study is presented. The dataset is original, and related to a sample survey carried out in Italy, about the adoption of Industry 4.0 technologies by Italian enterprises.

An Integrated Predictive Maintenance and Operations Scheduling Framework for Power Systems Under Failure Uncertainty

Maintenance planning plays a key role in power system operations under uncertainty as it helps providers and operators ensure a reliable and secure power grid. This paper studies a short-term condition-based integrated maintenance planning with operations scheduling problem while considering the possible unexpected failure of generators as well as transmission lines. We formulate this problem as a two-stage stochastic mixed-integer program with failure scenarios sampled from the sensor-driven remaining lifetime distributions of the individual system elements whereas a joint chance constraint consisting of Poisson Binomial random variables is introduced to account for failure risks. Because of its intractability, we develop a cutting-plane method to obtain an exact reformulation of the joint chance constraint by proposing a separation subroutine and deriving stronger cuts as part of this procedure. We also derive a second-order cone programming-based safe approximation of this constraint to solve large-scale instances. Furthermore, we propose a decomposition algorithm implemented in parallel fashion for solving the resulting stochastic program, which exploits the features of the integer L-shaped method and the special structure of the maintenance and operations scheduling problem to derive valid and stronger sets of optimality cuts. We further present preprocessing steps over transmission line flow constraints to identify redundancies. To illustrate the computational performance and efficiency of our algorithm compared with more conventional maintenance approaches, we design a computational study focusing on a weekly plan with daily maintenance and hourly operational decisions involving detailed unit commitment subproblems. Our computational results on various IEEE instances demonstrate the computational efficiency of the proposed approach with reliable and cost-effective maintenance and operational schedules. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0154 .

A Novel Method for Assessing Risk-Adjusted Diagnostic Coding Specificity for Depression Using a U.S. Cohort of over One Million Patients.

Depression is a prevalent and debilitating mental health condition that poses significant challenges for healthcare providers, researchers, and policymakers. The diagnostic coding specificity of depression is crucial for improving patient care, resource allocation, and health outcomes. We propose a novel approach to assess risk-adjusted coding specificity for individuals diagnosed with depression using a vast cohort of over one million inpatient hospitalizations in the United States. Considering various clinical, demographic, and socioeconomic characteristics, we develop a risk-adjusted model that assesses diagnostic coding specificity. Results demonstrate that risk-adjustment is necessary and useful to explain variability in the coding specificity of principal (AUC = 0.76) and secondary (AUC = 0.69) diagnoses. Our approach combines a multivariate logistic regression at the patient hospitalization level to extract risk-adjusted probabilities of specificity with a Poisson Binomial approach at the facility level. This method can be used to identify healthcare facilities that over- and under-specify diagnostic coding when compared to peer-defined standards of practice.

Geographically Weighted Zero-Inflated Negative Binomial Regression: A general case for count data

Poisson and Negative Binomial Regression Models are often used to describe the relationship between a count dependent variable and a set of independent variables. However, these models fail to analyze data with an excess of zeros, being Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) models the most appropriate to fit this kind of data. To Incorporate the spatial dimension into the count data models, Geographically Weighted Poisson Regression (GWPR), Geographically Weighted Negative Binomial Regression (GWNBR) and Geographically Weighted Zero-Inflated Poisson Regression (GWZIPR) have been developed, but the zero-inflation part of the negative binomial distribution is undeveloped in order to incorporate the overdispersion and the excess of zeros, as was at the beginning of the COVID-19 pandemic, whereas some places were having an outbreak of cases and in others places, there were no cases yet. Therefore, we propose a Geographically Weighted Zero-Inflated Negative Binomial Regression (GWZINBR) model which can be considered a general case for count data, since locally it can become a GWZIPR, GWNBR or a GWPR model. We applied this model to simulated data and to the cases of COVID-19 in South Korea at the beginning of the pandemic in 2020 and the results showed a better understanding of the phenomenon compared to the GWNBR model.

Count regression models analysis of factors affecting antenatal care utilization in Ethiopia: original article.

Antenatal care (ANC) reduces maternal and newborn mortalities and makes it easier to find infections early and prevent them from progressing. This study aimed to identify factors affecting ANC utilization in Ethiopia via the count regression model. The data for the study was drawn from the 2019 Ethiopian Mini Demographic and Health Survey dataset. Count regression models, such as Poisson, Negative Binomial (NB), Zero-Inflated Poisson (ZIP), and Zero-Inflated Negative Binomial (ZINB) models, were used to determine the factors influencing ANC utilization. A total of 3962 women were included in the study. Only about 42% of women used the WHO-recommended number of ANC of a minimum of four visits. The ZIP model was outperforming to fit the data as compared to other count regression models. Rural residence (IRR=0.8832, 95% CI: 0.8264-0.9440), being resident of the Somalia region (IRR=0.4762, 95% CI: 0.3919-0.5785), SNNPR (IRR=0.8716, 95% CI: 0.7913-0.9600), and Gambela Region (IRR=0.7830, 95% CI: 0.7063-0.8680), being Muslim (IRR=0.9384, 95% CI: 0.8876-0.9921) decrease the ANC utilization. Contrarily, Addis Ababa residence (IRR=1.1171, 95% CI: 1.0181-1.2259), primary education (IRR=1.1278, 95% CI: 1.0728-1.1855), secondary and higher education (IRR=1.2357, 95% CI: 1.1550-1.3220), middle wealth index (IRR=1.0855, 95% CI: 1.0095-1.1671) and rich wealth index (IRR=1.0941, 95% CI: 1.0152-1.1790) increase the ANC utilization. The ZIP model best fitted the data compared to others. The study revealed that being poor, rural resident, uneducated, Somalia region resident, SNNPR resident, Gambela region resident, and Muslim were factors associated with lower ANC utilization. Thus, health education is needed to be given for mothers with no education. In addition, building a strong awareness-creation program regarding ANC is required for rural residents so as to improve the level of ANC utilization in Ethiopia.

Improving performance of hurdle models using rare-event weighted logistic regression: an application to maternal mortality data.

In this paper, performance of hurdle models in rare events data is improved by modifying their binary component. The rare-event weighted logistic regression model is adopted in place of logistic regression to deal with class imbalance due to rare events. Poisson Hurdle Rare Event Weighted Logistic Regression (REWLR) and Negative Binomial Hurdle (NBH) REWLR are developed as two-part models which use the REWLR model to estimate the probability of a positive count and a Poisson or NB zero-truncated count model to estimate non-zero counts. This research aimed to develop and assess the performance of the Poisson and Negative Binomial (NB) Hurdle Rare Event Weighted Logistic Regression (REWLR) models, applied to simulated data with various degrees of zero inflation and to Nairobi county's maternal mortality data. The study data on maternal mortality were pulled from JPHES. The data contain the number of maternal deaths, which is the outcome variable, and other obstetric and demographic factors recorded in MNCH facilities in Nairobi between October 2021 and January 2022. The models were also fit and evaluated based on simulated data with varying degrees of zero inflation. The obtained results are numerically validated and then discussed from both the mathematical and the maternal mortality perspective. Numerical simulations are also presented to give a more complete representation of the model dynamics. Results obtained suggest that NB Hurdle REWLR is the best performing model for zero inflated count data due to rare events.

How many strong earthquakes will there be tomorrow?

In this note, we study the distribution of earthquake numbers in both worldwide and regional catalogs: in the Global Centroid Moment Tensor catalog, from 1980 to 2019 for magnitudes Mw 5. 5+ and 6.5+ in the first case, and in the Italian instrumental catalog from 1960 to 2021 for magnitudes Mw 4.0+ and 5.5+ in the second case. A subset of the global catalog is also used to study the Japanese region. We will focus our attention on short-term time windows of 1, 7, and 30 days, which have been poorly explored in previous studies. We model the earthquake numbers using two discrete probability distributions, i.e., Poisson and Negative Binomial. Using the classical chi-squared statistical test, we found that the Poisson distribution, widely used in seismological studies, is always rejected when tested against observations, while the Negative Binomial distribution cannot be disproved for magnitudes Mw 6.5+ in all time windows of the global catalog. However, if we consider the Japanese or the Italian regions, it cannot be proven that the Negative Binomial distribution performs better than the Poisson distribution using the chi-squared test. When instead we compared the performances of the two distributions using the Akaike Information Criterion, we found that the Negative Binomial distribution always performs better than the Poisson one. The results of this study suggest that the Negative Binomial distribution, largely ignored in seismological studies, should replace the Poisson distribution in modeling the number of earthquakes.

Risk Adjustment of ICD-10-CM Coded Potential Inpatient Complications Using Administrative Data.

To risk-adjust the Potential Inpatient Complication (PIC) measure set and propose a method to identify large deviations between observed and expected PIC counts. Acute inpatient stays from the Premier Healthcare Database from January 1, 2019 to December 31, 2021. In 2014, the PIC list was developed to identify a broader set of potential complications that can occur as a result of care decisions. Risk adjustment for 111 PIC measures is performed across 3 age-based strata. Using patient-level risk factors and PIC occurrences, PIC-specific probabilities of occurrence are estimated through multivariate logistic regression models. Poisson Binomial cumulative mass function estimates identify deviations between observed and expected PIC counts across levels of patient-visit aggregation. Area under the curve (AUC) estimates are used to demonstrate PIC predictive performance in an 80:20 derivation-validation split framework. We used N=3,363,149 administrative hospitalizations between 2019 and 2021 from the Premier Healthcare Database. PIC-specific model predictive performance was strong across PICs and age strata. Average area under the curve estimates across PICs were 0.95 (95% CI: 0.93-0.96), 0.91 (95% CI: 0.90-0.93), and 0.90 (95% CI: 0.89-0.91) for the neonate and infant, pediatric, and adult strata, respectively. The proposed method provides a consistent quality metric that adjusts for the population's case mix. Age-specific risk stratification further addresses currently ignored heterogeneity in PIC prevalence across age groups. Finally, the proposed aggregation method identifies large PIC-specific deviations between observed and expected counts, flagging areas with a potential need for quality improvements.

Estimation of crash type frequency accounting for misclassification in crash data

Crash misclassification (MC) – e.g., a crash of one type or severity being mistakenly miscategorized as another – is a relatively common problem in transportation safety. Crash frequency models for individual crash categories estimated using datasets with MC errors could result in biased parameter estimates and thus lead to ineffective countermeasure planning. This study proposes a novel methodological formulation to directly account for this MC error and incorporates it into the two most common count data models used for crash frequency prediction: Poisson and Negative Binomial (NB) regression. The proposed framework introduces probabilistic MC rates among different crash types and modifies the likelihood function of the count models accordingly. The paper also demonstrates how this approach can be integrated into reformulated models that express each count model as a discrete choice model. The capability of the proposed models to estimate true parameters, given the existence of MC error, is examined via simulation analysis. Then, the proposed models are applied to empirical data to examine the presence of MC in crash data and further examine the robustness of the proposed models. Although the MC rates are found to be very low in the empirical data, the fit of proposed models are found to be better compared to the models that ignore MC error and thus likely provide more reliable parameter estimates.

A Conway–Maxwell–Poisson Type Generalization of Hypergeometric Distribution

The hypergeometric distribution has gained its importance in practice as it pertains to sampling without replacement from a finite population. It has been used to estimate the population size of rare species in ecology, discrete failure rate in reliability, fraction defective in quality control, and the number of initial faults present in software coding. Recently, Borges et al. considered a COM type generalization of the binomial distribution, called COM–Poisson–Binomial (CMPB) and investigated many of its characteristics and some interesting applications. In the same spirit, we develop here a generalization of the hypergeometric distribution, called the COM–hypergeometric distribution. We discuss many of its characteristics such as the limiting forms, the over- and underdispersion, and the behavior of its failure rate. We write its probability-generating function (pgf) in the form of Kemp’s family of distributions when the newly introduced shape parameter is a positive integer. In this form, closed-form expressions are derived for its mean and variance. Finally, we develop statistical inference procedures for the model parameters and illustrate the results by extensive Monte Carlo simulations.

Count-Data Mixed Models of Topical Tweets: A Case of Indonesia Flood Events

Examining topic-level variability in modeling Twitter data can potentially yield more comprehensive insights into public perception during critical periods, thereby enhancing natural disaster mitigation and surveillance efforts. In this study, we utilized generalized linear mixed models (GLMMs) to illustrate the variability in tweet counts related to specific topics in Indonesia during the flood events that occurred in February 2021. The glmmTMB library in R was employed for this purpose. The data were assumed to follow two distinct exponential distributions: Poisson and Negative Binomial. To incorporate random effects, random intercepts and random slopes were introduced, allowing them to vary randomly across topics in the initial two models. Additionally, the final model addressed issues related to dispersion and zero-inflation. By evaluating the Akaike Information Criteria scores, we determined that a model based on the Negative Binomial distribution with random zero-inflation intercepts best fit the data. The chosen model formulation and the estimated parameters have the potential to forecast topic-specific trends in Indonesian flood-related Twitter data.

Modelling of vertical integration in commercial poultry production of Ghana: A count data model analysis

Poultry production has significant potential to reduce protein deficiency, food insecurity and poverty in Ghana. However, limited vertical integration and high cost of production in the sector have stifled growth and exposed poultry farms in the country to many risks, leading to poor business performance. This study uses cross-sectional data from 102 commercial poultry farms to assess the determinants of vertical integration in the Ghanaian poultry industry by employing zero-inflated Poisson (ZIP) and Zero-inflated Negative Binomial (ZINB) models. The results show that one in every four poultry farms in the country are vertically integrated, either partially or fully. The ZINB model, which best fits the data, reveals that the degree of vertical integration in the poultry business is significantly influenced by a set of personal (education, occupation, and farming experience) and farm level (land tenure, flock size, production cost, and farm revenue) characteristics as well as institutional factors (credit access, extension access and membership of association). The paper discusses the implications of these findings and provides appropriate recommendations for strengthening the poultry industry in Ghana.

Bayesian temporal, spatial and spatio-temporal models of dengue in a small area with INLA

ABSTRACT Understanding spatio-temporal patterns of communicable diseases and their dependency structure is crucial for assessing the potential mitigation and control measures. This paper presents various Bayesian models of dengue and studies the models with Integrated Nested Laplace Approximation (INLA) approach. Several structure models, as the combination of two temporal models of Autoregressive (AR) and Random Walk (RW), and three likelihoods of Gaussian, Poisson and Negative Binomial, are developed and utilised. The study further formulates a spatial model and four types of spatio-temporal models, as the combination of spatial and temporal random effects. All proposed models are applied to the dengue counts in the small city of Kendari, Indonesia. Based on the DIC and WAIC values, the level counts of dengue for each county are well described by AR(1)-Poisson. The best performances of the single-trend model and the multiple-trend model are achieved with AR(1)-Negative Binomial and AR(2)-Poisson, respectively. The multiple-trend model performs better than the single-trend model. Both spatial and spatio-temporal models show a significant spatial and temporal impact on the area-specific relative risk. The spatio-temporal model of Type I performs better than the other types on the dengue dataset, and followed by Type IV as the second best model.

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


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

A Semi-Parametric Integer-Valued Autoregressive Model with Covariates

AbstractWe consider a low count data INAR (Integer Autoregressive Regression) model in which the arrivals are modelled non-parametrically and are allowed to contain covariates. Accommodating possible covariates is important as exogenous variability, such as seasonality, often needs to be catered for. The main challenge is to maintain the axiomatic properties of the arrivals non-parametric mass function while, at the same time, incorporating covariates directly into the associated probabilities. Compared with models that impose standard distributions such as Poisson or Negative Binomial for the arrivals, our approach is more flexible and provides a general arrival specification. The dependence structure is parametric and uses the standard binomial thinning operator. The parameters are estimated by the Maximum Likelihood. Monte Carlo simulations show that our proposed model performs very well with good finite sample results. Two empirical issues are addressed where incorporating covariates is a prerequisite for successful modelling. The first incorporates seasonal covariates into a semi-parametric model for forecasting the numbers of claimants of wage loss benefits in the logging industry in British Columbia, Canada. The second investigates if macro-economic indicators in an economy may be useful in predicting the number of bank failures in the US financial sector.

Use of medical services in Chile: How sensitive are the results to different econometric models?

We compared different econometric specifications to model the use of medical services in Chile, focussing on visits to general practitioners and specialist physicians. The evaluated models are the Poisson, Negative Binomial, Zero Inflated Poisson and Negative Binomial, two-step Hurdle model, sample-selection Poisson, and Latent Class model. These models were estimated using Chilean data for the years 2009 and 2015, separated by gender. Unlike previous literature that supported the use of the latent class model, our results show that the latent class model is not always the model with the best goodness of fit. Furthermore, the model with the best fit is not necessarily the model with the best predictive power. For instance, depending on the year and medical services, either the latent class model or the sample-selection Poisson model performs better than the other models. The results also show that the selection of the econometric model may have implications for the estimated influence that variables such as age, income, or affiliation to the public versus private sector have on the use of medical services. Using Chilean data, we have tested that the selection of an econometric method to model the use of medical services is not a problem with a unique answer. We recommend performing a sensitivity analysis of goodness of fit and predictive power between gender, healthcare services, or different years of datasets in future applications to be sure about the best model specification in each context.

An explainable artificial intelligence approach for predicting cardiovascular outcomes using electronic health records.

Understanding the conditionally-dependent clinical variables that drive cardiovascular health outcomes is a major challenge for precision medicine. Here, we deploy a recently developed massively scalable comorbidity discovery method called Poisson Binomial based Comorbidity discovery (PBC), to analyze Electronic Health Records (EHRs) from the University of Utah and Primary Children’s Hospital (over 1.6 million patients and 77 million visits) for comorbid diagnoses, procedures, and medications. Using explainable Artificial Intelligence (AI) methodologies, we then tease apart the intertwined, conditionally-dependent impacts of comorbid conditions and demography upon cardiovascular health, focusing on the key areas of heart transplant, sinoatrial node dysfunction and various forms of congenital heart disease. The resulting multimorbidity networks make possible wide-ranging explorations of the comorbid and demographic landscapes surrounding these cardiovascular outcomes, and can be distributed as web-based tools for further community-based outcomes research. The ability to transform enormous collections of EHRs into compact, portable tools devoid of Protected Health Information solves many of the legal, technological, and data-scientific challenges associated with large-scale EHR analyses.

Role of peer support in a hepatitis C elimination programme.

Many people with chronic hepatitis C infection don't engage in treatment. To eliminate hepatitis C and avoid health inequalities therapy must be provided to everyone. In other diseases peers with lived experience of the condition have improved care but, for hepatitis C, studies have not shown unequivocal benefit. We completed a retrospective analysis of the English National Health Service treatment registry comparing treatment networks with and without peers using Bayesian Poisson (for count outcomes) or Bayesian Binomial (for proportion outcomes) mixed effects models with time fixed effects. For each outcome, we estimated relative ratio (RR-Poisson model) or odds ratio (Odds Ratio (OR)-Binomial model) between peer and non-peer networks. We analysed 30,729 patients within 20 operational delivery networks. In networks with peers there was an increase in the number of people initiating therapy (RR 1.12 95%, credible interval 1.02-1.21) and an increase in the proportion completing therapy (OR 2.45 95%, credible interval 1.49-3.84). However, we saw no change in proportions of people using drugs who initiated therapy nor any significant change in virological response (OR 1.14 95% credible interval 0.979-1.36). We repeated the analysis looking at the impact of peers two months after they had been introduced, when they had established networks of contacts, and saw an increase in the proportion of people treated in addiction services. In treating patients with chronic hepatitis C infection the inclusion of peer supporters may increase the number of people who initiate and complete antiviral therapy.

Rediscover: an R package to identify mutually exclusive mutations.

Discover is an algorithm developed to identify mutually exclusive genomic events. Its main contribution is a statistical analysis based on the Poisson-Binomial (PB) distribution to take into account the mutation rate of genes and samples. Discover is very effective for identifying mutually exclusive mutations at the expense of speed in large datasets: the PB is computationally costly to estimate, and checking all the potential mutually exclusive alterations requires millions of tests. We have implemented a new version of the package called Rediscover that implements exact and approximate computations of the PB. Rediscover exact implementation is slightly faster than Discover for large and medium-sized datasets. The approximation is 100-1000 times faster for them making it possible to get results in less than a minute with a standard desktop. The memory footprint is also smaller in Rediscover. The new package is available at CRAN and provides some functions to integrate its usage with other R packages such as maftools and TCGAbiolinks. Rediscover is available at CRAN (https://cran.r-project.org/web/packages/Rediscover/index.html). Supplementary data are available at Bioinformatics online.

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

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