A Modified Inverse Gaussian Poisson Regression with an Exposure Variable to Model Infant Mortality

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.

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.

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.

A crash-prediction model for multilane roads

Weather Variability and the Incidence of Cryptosporidiosis: Comparison of Time Series Poisson Regression and SARIMA Models

Objectives: The aim of this study was to identify the risk factors associated with number of crime committed by youth (Youth Delinquency) between ages 10-17, using Ordinary Least Square (OLS), Poisson Regression model (PRM), Negative Binomial Regression model (NBRM)& Zero Inflated Negative Binomial (ZINB) with the aim to choose the most appropriate model for the observed count data. Methodology: The data in the study was collected from youth whose mothers enrolled in Philadelphia Collaborative Perinatal Project (CPP). School and delinquency record (between ages 10-17) was obtained by the Centre for studies in Criminology and Criminal Law. Literature search suggest that factors associated with child delinquency can be divided into four main factors as Individual, Family, School and Peer. Therefore we included variables in the analysis accordingly. Result: For OLS scatter plot of residuals versus estimated counts showed definite pattern of heterogeneity (non-constant variance). The likelihood-ratio (LR) test of over dispersion yields the significant p-value, which implied that the outcome variable is overdispersed. The plot of the difference between the actual probabilities and the mean predicted probabilities for each model showed that PRM has poor predictions for low counts (0-2). Conclusion: NBRM and ZINB both performed well, however fit statistics revealed that NBRM has provided more closed predication as compare ZINB.NB modeling techniques provides much more compelling and accurate results instead of basic PRM or those available through simple linear or log-linear modeling techniques

The Poisson regression model is often used as a first model for count data with covariates. Since this model is a GLM with canonical link, regression parameters can be easily fitted using standard software. However the model requires equidispersion, which might not be valid for the data set under consideration. There have been many models proposed in the literature to allow for overdispersion. One such model is the negative binomial regression model. In addition, score tests have been commonly used to detect overdispersion in the data. However these tests do not allow to quantify the effects of overdispersion. In this paper we propose easily interpretable discrepancy measures which allow to quantify the overdispersion effects when comparing a negative binomial regression to Poisson regression. We propose asymptotic $\alpha$-level tests for testing the size of overdispersion effects in terms of the developed discrepancy measures. A graphical display of p-values curves can then be used to allow for an exact quantification of the overdispersion effects. This can lead to a validation of the Poisson regression or a discrimination of the Poisson regression with respect to the negative binomial regression. The proposed asymptotic tests are investigated in small samples using simulation and applied to two examples.

Nepal has experienced the glacial reduction of under-five mortality in recent years which portends greater challenges to achieve the global target outlined in the Sustainable Development Goals (SDGs) for reducing childhood mortality. To resolve this inevitable adversity and safeguard newborns' lives, additional scientific studies are necessary to plan for evidence-based interventions. This study aimed to develop a suitable statistical model using the associated factors to predict the number of under-five mortality a mother in Nepal encountered throughout her lifetime. The nationally representative Nepal Demographic and Health Survey (NDHS) 2022 data were used to conduct this study. The response variable was the number of under-five mortality a mother has experienced throughout her lifetime. Factors related to different circumstances, including maternal, paternal, socioeconomic, child, environmental, and the utilization of health care services were considered as independent variables. The zero-inflated negative binomial regression (ZINBR) model was fitted as the most plausible model to analyze the number of under-five mortality by its covariates after assessing the different count models including the Poisson regression (PR) model, negative binomial regression (NBR) model, zero-inflated negative binomial regression (ZINBR) model, and hurdle negative binomial regression (HNBR) model. The analysis of the data revealed that 8.6% of the mothers in Nepal have endured at least one under-five mortality. The mean number of deaths before attaining five years was found to be 0.11 (95% CI: 0.10-0.11). The ecological region, smoking habit of mothers, total CEB, source of drinking water, preceding birth interval, and birth order number were obtained as significant covariates of the number of under-five mortality. Mothers from the mountain region (IRR: 1.1756, 95% CI: 1.0095-1.369, p-value = 0.0418) in contrast to hilly region, smoker mothers (IRR: 1.2067, 95% CI: 1.0392-1.4011, p-value = 0.0141) as compared to non-smoker mothers, mothers with total CEB 3 or more (IRR: 1.588, 95% CI: 1.3116-1.9226, p-value = 0.0353) as compared to 2 or less, preceding birth interval less than 24 months (IRR: 1.2061, 95% CI: 1.0788-1.3485, p-value = 0.0018) as compared to 24 months or more, and birth order number 4th or above (IRR: 3.5681, 95% CI: 3.1512-4.0401, p-value < 0.001) as compared to 1st-3rd were associated with the increased incidence of number of under-five mortality. Furthermore, the mothers who drink water from the tube well (IRR: 0.7719, 95% CI: 0.6191-0.9623, p-value = 0.0323) as compared to those who drink water from other sources have a decreased incidence of the number of under-five mortality. The ecological region, mother smokes cigarettes, total CEB, source of drinking water, preceding birth interval, and the birth order number appeared as the important predictors of under-five mortality. The high under-five mortality prevalent in the mountain and terai areas of Nepal presents a significant hurdle in efforts to decrease overall under-five mortality. Thus, improving existing healthcare services, raising the quality of life, and introducing effective health education initiatives are crucial to reducing under-five mortality.

The novel coronavirus causing the COVID-19 pandemic and morbidity and mortality around the world has left unprecedented repercussions on all aspects of life. Estimation of the incidence of coronavirus patients will reimburse planning and preparation for new waves. The link between COVID-19 and air pollution data can allow us to estimate COVID cases. In this study, count data models; Poisson regression and negative binomial regressions models and machine learning methods; support vector regression and random forest are used to investigate the link between new COVID-19 cases and the air pollution data in Bangkok, Thailand. The root means square error and means absolute percentage error are used as the criterions to compare the efficiency from each method. The results from the real data showed that the support vector regression outperforms random forest and also Poisson regression and negative binomial regression models.

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

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.

Many positive trends in the health of Americans continued into 1997. In 1997, the preliminary birth rate declined slightly to 14.6 births per 1000 population, and the fertility rate, births per 1000 women 15 to 44 years of age, was unchanged from the previous year (65.3). These indicators suggest that the downward trend in births observed since the early 1990s may have abated. Fertility rates for white, black, and Native American women were essentially unchanged between 1996 and 1997. Fertility among Hispanic women declined 2% in 1997 to 103.1, the lowest level reported since national data for this group have been available. For the sixth consecutive year, birth rates dropped for teens. Birth rates for women 30 years or older continued to increase. The proportion of births to unmarried women (32.4%) was unchanged in 1997. The trend toward earlier utilization of prenatal care continued for 1997; 82.5% of women began prenatal care in the first trimester. There was no change in the percentage with late (third trimester) or no care in 1997. The cesarean delivery rate rose slightly to 20.8% in 1997, a reversal of the downward trend observed since 1989. The percentage of low birth weight (LBW) infants rose again in 1997 to 7.5%. The percentage of very low birth weight was up only slightly to 1.41%. Among births to white mothers, LBW increased for the fifth consecutive year, to 6.5%, whereas the rate for black mothers remained unchanged at 13%. Much, but not all, of the rise in LBW for white mothers during the 1990s can be attributed to an increase in multiple births. In 1996, the multiple birth rate rose again by 5%, and the higher-order multiple birth rate climbed by 20%. Infant mortality reached an all time low level of 7.1 deaths per 1000 births, based on preliminary 1997 data. Both neonatal and postneonatal mortality rates declined. In 1996, 64% of all infant deaths occurred to the 7.4% of infants born at LBW. Infant mortality rates continue to be more than two times greater for black than for white infants. Among all the states in 1996, Maine, Massachusetts, and New Hampshire had the lowest infant mortality rates. Despite declines in infant mortality, the United States continues to rank poorly in international comparisons of infant mortality. Expectation of life at birth reached a new high in 1997 of 76.5 years for all gender and race groups combined. Age-adjusted death rates declined in 1997 for diseases of the heart, accidents and adverse affects (unintentional injuries), homicide, suicide, malignant neoplasms, cerebrovascular disease, chronic liver disease and cirrhosis, and diabetes. In 1997, mortality due to HIV infection declined by 47%. Death rates for children from all major causes declined again in 1997. Motor vehicle traffic injuries and firearm injuries were the two major causes of traumatic death. A large proportion of childhood deaths continue to occur as a result of preventable injuries.

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.

Predicting Censored Count Data with COM-Poisson Regression

Tuberculosis (TB) remains a major public health concern in many parts of the world, including Benue State, Nigeria, where agricultural communities are particularly vulnerable. This study aims to model the monthly mortality incidence of tuberculosis (TB) among farmers in Benue State, Nigeria, focusing on serologically confirmed, active, severe, recovered, and mortality cases using count data regression models. Three count data regression models: Poisson Regression (PR), Negative Binomial Regression (NBR), and Generalized Poisson Regression (GPR) were employed to predict TB-related mortality based on these variables. Secondary data from the Benue State Epidemiological Unit, Makurdi, spanning from January 2010 to December 2023, served as the basis for analysis. The study found the presence of over-dispersion in the Poisson Regression model which necessitated the use of NBR and GPR. Model performance was evaluated using -2 Log-Likelihood (-2 logL), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Among the three competing models, NBR provided the best fit, with a -2 logL value of -901.92, an AIC of 1203.85, and a BIC of 1223.70, effectively addressing the over-dispersion in the data. The analysis identified confirmed, active, and severe TB cases as significant predictors of TB-related mortality in Benue State. Additionally, a strong negative and significant relationship was observed between recovered cases and mortality, indicating that an increase in recoveries correlates with a decline in TB-related deaths. The study recommends that policymakers and researchers should prioritize the Negative Binomial Regression model for TB analysis, enhance TB case management and treatment adherence, improve TB data collection, and design targeted interventions to reduce severe cases and increase recovery rates among vulnerable populations like farmers.