Multiple arbitrarily inflated negative binomial regression model and its application

Methodologic Challenges in the Analysis of Count Data in Radiology Health Services Research

The two most popular models inwell-known count regression models are Poisson and negative binomial regression models. Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. Negative binomial regression is similar to regular multiple regression except that the dependent (Y) variables an observed count that follows the negative binomial distribution. This research studies some factors affecting divorce using Poisson and negative binomial regression models. The factors are unemployment rate, inflation and Gini coefficient. The data were taken from the website of the Statistics Center for the years 2002 to 2023.Under the Poisson regression model, each factor has been reported to have an effect on the divorce rate. The two factors of inflation and unemployment had a direct effect and income inequality factors had an inverse effect on the divorce rate. But, under the negative binomial regression model, only inflation has an effect on the number of divorces. It is worth noting that according to the AIC values, the negative binomial regression model has a better fit than the Poisson regression model because its AIC value is lower.

Introduction: The need to model the impact of some demographic indicators on the frequency of household visits to healthcare centres in Nigeria's community is very important for preventing and spreading community diseases. This study aimed to investigate the effect of the patents' age, gender, marital status, type of illness and amount spent on the frequency of visits to community health care centres in Nigeria and to compared Negative Binomial Regression (NBR) and Generalized Poisson Regression (GPR) models to determine the preferred count regression model for the number of household visits to health centres in some communities in Nigeria. Methods: Survey of 132640 households in some Nigeria communities obtained from the 2018/2019 Nigeria Living Standard Survey (NLSS) were extracted from the National Bureau of Statistics (NBS) in collaboration with the World Bank. The Negative Binomial and Generalised Poisson regression models were used to investigate the five demographic variables on the frequency of visit to the community health centres. The performance of the count regression model was assessed using the Chi-square -2log Likelihood Statistic (2logL), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) selection criteria. Results: Findings from the study showed that the type of illness and amount spent has a significantly positive effect on the number of household members' visits to the community health care centres in Nigeria while age, gender, and marital status was discovered to have a negative effect on the number of household members' visits to the community health care centres in Nigeria. Conclusion: The Nigeria Government, health centre management and community healthcare service providers' need to be aware that the amount spent and the nature of illness determines the level of health care services utilisation in the Nigeria community, hence the need for the drastic reduction in charges to encourage a household visit to the community health centres whenever the need arises.

COVID-19 is currently threatening countries in the world. Presently in Nigeria, there are about 29,286 confirmed cases, 11,828 discharged and 654 deaths as of 6th July 2020. It is against this background that this study was targeted at modeling daily cases of COVID-19’s deaths in Nigeria using count regression models like; Poisson Regression (PR), Negative Binomial Regression (NBR) and Generalized Poisson Regression (GPR) model. The study aim at fitting an appropriate count Regression model to the confirmed, active and critical cases of COVID-19 in Nigeria after 118 days. The data for the study was extracted from the daily COVID-19 cases update released by the Nigeria Centre for Disease Control (NCDC) online database from February 28th, 2020 – 6th, July 2020. The extracted data were used in the simulation of Poisson, Negative Binomial, and Generalized Poisson Regression model with a program written in STATA version 14 and fitted to the data at a 5% significance level. The best model was selected based on the values of -2logL, AIC, and BIC selection test/criteria. The results obtained from the analysis revealed that the Poisson regression could not capture over-dispersion, so other forms of Poisson Regression models such as the Negative Binomial Regression and Generalized Poisson Regression were used in the estimation. Of the three count Regression models, Generalized Poisson Regression was the best model for fitting daily cumulative confirmed, active and critical COVID-19 cases in Nigeria when overdispersion is present in the predictors because it had the least -2log-Likelihood, AIC, and BIC. It was also discovered that active and critical cases have a positive and significant effect on the number of COVID-19 related deaths in Nigeria.

Sequence count data are commonly modelled using the negative binomial (NB) distribution. Several empirical studies, however, have demonstrated that methods based on the NB-assumption do not always succeed in controlling the false discovery rate (FDR) at its nominal level. In this paper, we propose a dedicated statistical goodness of fit test for the NB distribution in regression models and demonstrate that the NB-assumption is violated in many publicly available RNA-Seq and 16S rRNA microbiome datasets. The zero-inflated NB distribution was not found to give a substantially better fit. We also show that the NB-based tests perform worse on the features for which the NB-assumption was violated than on the features for which no significant deviation was detected. This gives an explanation for the poor behaviour of NB-based tests in many published evaluation studies. We conclude that nonparametric tests should be preferred over parametric methods.

Modeling COVID-19 daily cases in Senegal using a generalized Waring regression model

The coronavirus disease 2019 (COVID-19) pandemic was defined by the World Health Organization (WHO) as a global epidemic on March 11, 2020, as the infectious disease that threatens public health fatally. In this study, the main aim is to model the impact of various air pollution causes on mortality data due to the COVID-19 pandemic by Generalized Linear Mixed Model (GLMM) approach to make global statistical inferences about 174 WHO member countries as subjects in the six WHO regions. “Total number of deaths by these countries due to the COVID-19 pandemic” until July 27, 2022, is taken as the response variable. The explanatory variables are taken as the WHO regions, the number of deaths from air pollution causes per 100.000 population as “household air pollution from solid fuels,” “ambient particulate matter pollution,” and “ambient ozone pollution.” In this study, Poisson, geometric, and negative binomial (NB) regression models with “country” taken as fixed and random effects, as special cases of GLMM, are fitted to model the response variable in the aspect of the above-mentioned explanatory variables. In the Poisson, geometric, and NB regression models, Iteratively Reweighted Least Squares parameter estimation method with the Fisher-Scoring iterative algorithm under the log-link function as canonical link function is used. In the GLMM approach, Laplace approximation is also used in the prediction of random effects. In this study, six different Poisson, geometric, and NB regression models with fixed and random effects are established for 174 countries all over the world to make global statistical inferences for investigating the relationships between “total number of deaths” by these countries due to the COVID-19 pandemic and “air pollution causes.” As a result of this study, “NB mixed-effects regression model” as the most appropriate GLMM is used to make global statistical inferences about the impact of the various air pollution causes on the mortality data due to the COVID-19 pandemic.

Background: It may take a long time to diagnose multiple sclerosis (MS) since the emergence of primary symptoms. This study aimed to use count regression models to compare their fit and to identify factors affecting delay in the diagnosis of MS. Methods: Data were collected from the Nationwide MS Registry of Iran (NMSRI) for Mazandaran Province, Iran, using census sampling until April 2022. The four models of Poisson regression, negative binomial (NB) regression, zero-inflated Poisson (ZIP) regression, and zero-inflated negative binomial (ZINB) regression were used in this study. Results: In this study on 2894 patients, 74.0% were women, and 8.5% had a family history of MS. The mean ± standard deviation (SD) of the patients' age was 34.96 ± 9.41 years, and the mean delay in diagnosis was 12.32 ± 33.26 months, with a median of 0 (Q1-Q3: 0-9). The NB regression model showed the best performance, and factors, including a history of hospitalization and the year of symptom onset, had significant effects on a delayed diagnosis. Besides, the Expanded Disability Status Scale (EDSS) score was significantly different before and after 2017; it was also associated with sex, type of MS, and history of hospitalization. Conclusion: The mean diagnostic delay and the mean age of MS diagnosis are critical in Mazandaran Province. Patients with MS develop the disease at an early age and are diagnosed with a long delay. The time of symptom onset is a significant factor in the diagnosis of MS, and in recent years, there have been improvements in the diagnostic process.

Effectiveness of sampling plans by attributes based on mixture distributions characterising microbial clustering in food

Processes that occasionally, but not always, produce extreme values are notoriously difficult to model, as a small number of extreme observations may have a large impact on the results. Existing methods for handling extreme values are often arbitrary and leave researchers without guidance regarding this problem. In this paper, we propose an extreme value and zero-inflated negative binomial (EVZINB) regression model, which allows for separate modeling of extreme and nonextreme observations to solve this problem. The EVZINB model offers an elegant solution to modeling data with extreme values and allows researchers to draw additional inferences about both extreme and nonextreme observations. We illustrate the usefulness of the EVZINB model by replicating a study on the effects of the deployment of UN peacekeepers on one-sided violence against civilians.

Count variables are common in behavioral science as an outcome.Count regression models, such as Poisson regression, are recommended when analyzing count variables but can be challenging to interpret given their non-linear functional form.I recommend relative importance analysis as a method to use in interpreting count regression model results.This work extends on past research by describing an approach to determining the importance of independent variables in count regression models using dominance analysis.Herein, dominance analysis is reviewed as a relative importance method, recommend a pseudo-R 2 to use with count regression model-based dominance analysis, and outline the results of an analysis with simulated data that uses the recommended methodology.This work contributes to the literature by extending dominance analysis to count regression models and provides a thoroughly documented example analysis that researchers can use to implement the methodology in their research.

Background: Under-five mortality rate, often known by its acronym U5MR, indicates the probability of dying between birth and five years of age, expressed per 1,000 live births. Globally, 16,000 children under-five still die every day. Especially in Sub-Saharan Africa every 1 child in 12, dying before his or her fifth birthday. This study aims to identify the determinants of under-five mortality among women in child bearing age group of Tach-Armachiho district using count regression models. Methods: For achieving the objective, a two-stage random sampling technique (simple random sampling and systematic random sampling techniques in the first and second stages respectively) was used to select women respondents. The sample survey conducted in Tach-Armachiho district considered a total of 3815 households of women aged 15 to 49 years out of which the information was collected from 446 selected women through interviewer administrated questionnaire. Results: The descriptive statistics result showed that in the district 16.6% of mothers have faced the problem of at least one under-five death. In this study, Poisson regression, negative binomial, zero-inflated Poisson and zero-inflated negative binomial regression models were applied for data analysis. Each of these count models were compared by different statistical tests. So that, zero-inflated poisson regression model was found to be the best fit for the collected data. Results of the zero-inflated Poisson regression model showed that education of husband, source of water, mother occupation, kebele of mother, prenatal care, place of delivery, place of residence, wealth of house hold, average birth interval and average breast feeding were found to be statistically significant determinants of under-five mortality. Conclusions: In this study, it was found that the factors like average birth interval and average breast feeding were found to be statistically significant factors in both groups (not always zero category and always zero category) with under-five child deathwhereas education of husband, source of water, place of delivery, mother occupation and wealth index of the household have significant effect on under-five mortality under not always zero group. Place of residence, kebele of mother and prenatal care have a significant effect on under-five mortality in TachArmachiho district on inflated group

Tujuan: Untuk menjelaskan gambaran faktor lingkungan fisik meliputi: suhu, kelembaban, kecepatan angin dan curah hujan, dan menganalisis secara spasial dan temporal pengaruhnya terhadap kejadian malaria di Kabupaten Banjarnegara tahun 2011-2015. Metode: Penelitian ini menggunakan desain studi ekologi dengan pendekatan spasial-temporal. Data yang digunakan adalah data time series bulan kejadian malaria dan faktor lingkungan fisik di Kabupaten Banjarnegara tahun 2011-2015. Model regresi poisson dan binomial negatif digunakan untuk menganalisis pengaruh faktor lingkungan fisik dengan kejadian malaria berdasrakan hasil pemilihan model terbaik dengan melihat nilai Akaike’s Information Criteria (AIC) dan Bayesian Information Criteria (BIC). Data faktor lingkungan fisik dilakukan interpolasi menggunakan metode IDW ( Inverse Distance Weighting ) pada software Sistem Informasi Geografis. Hasil: Rata-rata suhu udara dan kelembaban udara dari tahun 2011-2015 berturut-turut 25,79 o C dan 87,37%, sedangkan rata-rata kecepatan angin dan curah hujan berturut-turut 26,07 km/h, 276,02 mm. Analisis statistik, grafik/ time trend , dan spasial menunjukkan bahwa ada hubungan antara suhu, kelembaban, kecepatan angin dan curah hujan dengan kejadian malaria di Kabupaten Banjarnegara. Hasil analisis regresi binomial negatif menunjukkan bahwa secara bermakna suhu pada bulan yang sama (P= 0,036), suhu pada dua bulan sebelumnya (P=0,022) berkorelasi negatif berturut-turut dengan Estimate Value (-0,273, -0,319) sedangkan curah hujan pada satu bulan sebelumnya (P=0,0001) berkorelasi positif dengan Estimate value (0,002) terhadap kejadian malaria di Kabupaten Banjarnegara Tahun 2011-2015. Hasil analisis spasial menunjukkan bahwa kasus tertinggi malaria berada di Kecamatan Banjarmangu, Punggelan dan Pagedongan dengan kisaran suhu 25,64 o C-26,77 o C, kisaran kelembaban 86,07%-88,41%, kisaran kecepatan angin 18,71km/h-28,30km/h, dan kisaran curah hujan 225,25mm-318,24mm. Simpulan: Suhu pada bulan yang sama, dan suhu pada dua bulan sebelumnya memiliki pengaruh yang negatif terhadap kejadian malaria sedangkan curah hujan pada satu bulan sebelumnya memiliki pengaruh yang positif terhadap kejadian malaria di Kabupaten Banjarnegara. Maka, untuk mengatasi masalah kejadian malaria dan melaksanakan program penanggulangannya maka Pemerintah Daerah Kabupaten Banjarnegara perlu mempertimbangan faktor lingkungan fisik.

This study investigates the determinants of smoking behavior among young adults in Khuzestan province, southwest Iran, using two-level count regression models. Given the high prevalence of smoking-related diseases and the social impact of smoking, understanding the factors influencing smoking habits is crucial for effective public health interventions. We conducted a cross-sectional analysis of 1,973 individuals aged 18-35 years, using data from the Daily Smoking Consumption Survey (DSCS) in Khuzestan province collected in 2023. A variety of count regression models, including Poisson, Negative Binomial, Conway-Maxwell Poisson, and their zero-inflated counterparts, were evaluated. The best-fitting model was selected based on goodness-of-fit indices. Approximately 90% of participants were non-smokers. Among smokers, the prevalence of light, moderate, and heavy smoking was 47.7, 19.0, and 33.3%, respectively. The two-level Zero-Inflated Conway-Maxwell Poisson (ZICMP) model provided the appropriate fit for the data. Key determinants of daily cigarette consumption included gender, age, education, and Body Mass Index (BMI). Men consumed 3.24 times more cigarettes per day than women. Higher education levels were inversely related to smoking intensity, with MSc/PhD holders having significantly lower smoking rates. Age and BMI also significantly influenced smoking behavior, with younger and obese individuals showing lower smoking rates. The use of advanced count models capable of handling numerous zeros and overdispersion is crucial for accurately analyzing trends in cigarette consumption across different population groups. The results indicate that factors such as older age, lower education levels, and gender differences influence smoking behavior. Therefore, prevention strategies aimed at delaying the onset of smoking, particularly among men, and promoting education among adolescents can effectively reduce smoking rates. However, further research should consider additional socioeconomic variables and encompass a broader age range to enhance the understanding of smoking behavior.

In the present work we compared different calculation approaches for their ability to accurately define microbiological control levels based on historical data. To that end, real microbiological data were used for simulation experiments. The results of our study confirmed that assuming a normal distribution is not appropriate for that purpose. In addition, assumption of a Poisson distribution generally underestimated the control level, and the predictive power for future values was highly insufficient. The non-parametric Excel percentile strongly predicted future values in our simulation experiments (although not as good as some of the parametric models). With the limited amount of data used in the simulations, the calculated control levels for the upper percentiles were on average higher and more variable compared to the parametric models. This was due to the fact that the largest observed value was generally defined as the control level. Accordingly, the Excel percentile is less robust towards outliers and requires more data to accurately define control levels as compared to parametric models. The negative binomial as well as the zero-inflated negative binomial distribution, both parametric models, had good predictive power for future values. Nonetheless, on basis of our simulation experiments, we saw no evidence to generally prefer the zero-inflated model over the non-inflated one. Finally, with our data, the gamma distribution on average had at least as good predictive power as the negative binomial distribution and zero-inflated negative binomial distribution for percentiles ≥98%, indicating that it may represent a viable option for calculating microbiological control levels at high percentiles. Presumably, this was based on the fact that the gamma distribution fitted the upper end of the distribution better than other models. Since in general microbiological control levels would be based on the upper percentiles, microbiologists may exclusively rely on the gamma distribution for calculation of their control levels. As the gamma distribution can conveniently be calculated in standard office calculation software, it may represent a superior alternative to the widely used percentile functions or other distribution models. During the manufacturing of pharmaceutical drug products, the counts of microorganisms are monitored in the cleanroom environment, water, the product's raw materials, and the final product. This enables manufacturers to ensure that high numbers of microorganisms that may impair the product's microbiological quality are detected before the product is released to the patient. Microbiological control levels must be set to determine at which number a count is considered too high. Exceeding such levels may require an investigation to determine the root cause explaining why such high numbers of microorganisms occurred, and a set of actions should be performed with the aim of eliminating this root cause. In order to really differentiate higher-than-usual counts, microbiological control levels should be based on historical data. In the present work we analyzed different calculation approaches towards that purpose. We used real microbiological data and performed simulation experiments to determine which statistical method could calculate the most realistic control levels that would provide the best prediction for future routine testing. Better predictions would ensure that only significant contaminations lead to an excursion of the microbiological control level, which would avoid wasting resources by investigating non-issues or normal/controlled conditions.