On a Characterization of Zero-Inflated Negative Binomial Distribution

Zero-inflated negative binomial distribution is characterized in this paper through a linear differential equation satisfied by its probability generating function.

Study of Zero-Inflated Regression Models in a Large-Scale Population Survey of Sub-Health Status and Its Influencing Factors

Objective Sub-health status has progressively gained more attention from both medical professionals and the publics. Treating the number of sub-health symptoms as count data rather than dichotomous data helps to completely and accurately analyze findings in sub-healthy population. This study aims to compare the goodness of fit for count outcome models to identify the optimum model for sub-health study.Methods The sample of the study derived from a large-scale population survey on physiological and psychological constants from 2007 to 2011 in 4 provinces and 2 autonomous regions in China. We constructed four count outcome models using SAS: Poisson model, negative binomial (NB) model, zero-inflated Poisson (ZIP) model and zero-inflated negative binomial (ZINB) model. The number of sub-health symptoms was used as the main outcome measure. The alpha dispersion parameter and O test were used to identify over-dispersed data, and Vuong test was used to evaluate the excessive zero count. The goodness of fit of regression models were determined by predictive probability curves and statistics of likelihood ratio test.Results Of all 78 307 respondents, 38.53% reported no sub-health symptoms. The mean number of sub-health symptoms was 2.98, and the standard deviation was 3.72. The statistic O in over-dispersion test was 720.995 (P<0.001); the estimated alpha was 0.618 (95% CI: 0.600-0.636) comparing ZINB model and ZIP model; Vuong test statistic Z was 45.487. These results indicated over-dispersion of the data and excessive zero counts in this sub-health study. ZINB model had the largest log likelihood (-167 519), the smallest Akaike’s Information Criterion coefficient (335 112) and the smallest Bayesian information criterion coefficient (335455),indicating its best goodness of fit. The predictive probabilities for most counts in ZINB model fitted the observed counts best. The logit section of ZINB model analysis showed that age, sex, occupation, smoking, alcohol drinking, ethnicity and obesity were determinants for presence of sub-health symptoms; the binomial negative section of ZINB model analysis showed that sex, occupation, smoking, alcohol drinking, ethnicity, marital status and obesity had significant effect on the severity of sub-health.Conclusions All tests for goodness of fit and the predictive probability curve produced the same finding that ZINB model was the optimum model for exploring the influencing factors of sub-health symptoms.

The Impacts of Mosquito Density and Meteorological Factors on Dengue Fever Epidemics in Guangzhou, China, 2006-2014: a Time-series Analysis

Objective To explore the associations between the monthly number of dengue fever（DF） cases and possible risk factors in Guangzhou, a subtropical city of China. Methods The monthly number of DF cases, Breteau Index （BI）, and meteorological measures during 2006-2014 recorded in Guangzhou, China, were assessed. A negative binomial regression model was used to evaluate the relationships between BI, meteorological factors, and the monthly number of DF cases. Results A total of 39,697 DF cases were detected in Guangzhou during the study period. DF incidence presented an obvious seasonal pattern, with most cases occurring from June to November. The current month＇s BI, average temperature （Tare）, previous month＇s minimum temperature （Train）, and Tare were positively associated with DF incidence. A threshold of 18.25℃ was found in the relationship between the current month＇s Tmin and DF incidence. Conclusion Mosquito density, Tove, and Tmin play a critical role in DF transmission in Guangzhou. These findings could be useful in the development of a DF early warning system and assist in effective control and prevention strategies in the DF epidemic.

Comparison of six generalized linear models for occurrence of lightning-induced fires in northern Daxing'an Mountains,China

The occurrence of lightning-induced forest fires during a time period is count data featuring over-dispersion （i.e., variance is larger than mean） and a high frequency of zero counts. In this study, we used six generalized linear models to examine the relationship between the occurrence of lightning-induced forest fires and meteorological factors in the Northern Daxing＇an Mountains of China. The six models included Poisson, negative binomial （NB）, zero- inflated Poisson （ZIP）, zero-inflated negative binomial （ZINB）, Poisson hurdle （PH）, and negative binomial hurdle （NBH） models. Goodness-of-fit was compared and tested among the six models using Akaike information criterion （AIC）, sum of squared errors, likelihood ratio test, and Vuong test. The predictive performance of the models was assessed and compared using independent validation data by the data-splitting method. Based on the model AIC, the ZINB model best fitted the fire occurrence data, followed by （in order of smaller AIC） NBH, ZIP, NB, PH, and Poisson models. The ZINB model was also best for pre- dicting either zero counts or positive counts （〉1）. The two Hurdle models （PH and NBH） were better than ZIP, Poisson, and NB models for predicting positive counts, but worse than these three models for predicting zero counts. Thus, the ZINB model was the first choice for modeling the occurrence of lightning-induced forest fires in this study, which implied that the excessive zero counts of lightning- induced fires came from both structure and sampling zeros.

Crash Frequency Analysis

Modeling highway traffic crash frequency is an important approach for identifying high crash risk areas that can help transportation agencies allocate limited resources more efficiently, and find preventive measures. This paper applies a Poisson regression model, Negative Binomial regression model and then proposes an Artificial Neural Network model to analyze the 2008-2012 crash data for the Interstate I-90 in the State of Minnesota in the US. By comparing the prediction performance between these three models, this study demonstrates that the Neural Network is an effective alternative method for predicting highway crash frequency.

Safety Analysis of Riding at Intersection Entrance Using Video Recognition Technology

To study riding safety at intersection entrance,video recognition technology is used to build vehicle-bicycle conflict models based on the Bayesian method.It is analyzed the relationship among the width of nonmotorized lanes at the entrance lane of the intersection,the vehicle-bicycle soft isolation form of the entrance lane of intersection,the traffic volume of right-turning motor vehicles and straight-going non-motor vehicles,the speed of right-turning motor vehicles,and straight-going non-motor vehicles,and the conflict between right-turning motor vehicles and straight-going nonmotor vehicles.Due to the traditional statistical methods,to overcome the discreteness of vehicle-bicycle conflict data and the differences of influencing factors,the Bayesian random effect Poisson-log-normal model and random effect negative binomial regression model are established.The results show that the random effect Poisson-log-normal model is better than the negative binomial distribution of random effects;The width of non-motorized lanes,the form of vehicle-bicycle soft isolation,the traffic volume of right-turning motor vehicles,and the coefficients of straight traffic volume obey a normal distribution.Among them,the type of vehicle-bicycle soft isolation facilities and the vehicle-bicycle traffic volumes are significantly positively correlated with the number of vehicle-bicycle conflicts.The width of non-motorized lanes is significantly negatively correlated with the number of vehicle-bicycle conflicts.Peak periods and flat periods,the average speed of right-turning motor vehicles,and the average speed of straight-going non-motor vehicles have no significant influence on the number of vehicle-bicycle conflicts.

Impact of the Changes in Women’s Characteristics over Time on Antenatal Health Care Utilization in Egypt (2000-2008)

Objectives: This study empirically assesses the impact of the changes in women’s characteristics, empowerment, availability and quality of health services on woman’s decision to use antenatal care (ANC) and the frequency of that use during the period 2000-2008. Study Design: The study is a cross-sectional analytical study using 2000 and 2008 Egypt Demographic and Health Surveys. Methods: The assessment of the studied impact is conducted using the Zero-inflated Negative Binomial Regression. In addition, Factor Analysis technique is used to construct some of the explanatory variables such as women’s empowerment, the availability and quality of health services indicators. Results: Utilization of antenatal health care services is greatly improved from 2000 to 2008. Availability of health services is one of the main determinants that affect the number of antenatal care visits in 2008. Wealth index and quality of health services play an important role in raising the level of antenatal care utilization in 2000 and 2008. However, the impact of the terminated pregnancy on receiving ANC increased over time. Conclusions: Further research of the determinants of antenatal health care utilization is needed, using more updated measures of women’s empowerment, availability and quality of health services. In order to improve the provision of antenatal health care services, it is important to understand barriers to antenatal health care utilization. Therefore, it is advisable to collect information from women about the reasons for not receiving antenatal care.

Predictors of the Aggregate of COVID-19 Cases and Its Case-Fatality: A Global Investigation Involving 120 Countries

Objective: Since the identification of COVID-19 in December 2019 as a pandemic, over 4500 research papers were published with the term “COVID-19” contained in its title. Many of these reports on the COVID-19 pandemic suggested that the coronavirus was associated with more serious chronic diseases and mortality particularly in patients with chronic diseases regardless of country and age. Therefore, there is a need to understand how common comorbidities and other factors are associated with the risk of death due to COVID-19 infection. Our investigation aims at exploring this relationship. Specifically, our analysis aimed to explore the relationship between the total number of COVID-19 cases and mortality associated with COVID-19 infection accounting for other risk factors. Methods: Due to the presence of over dispersion, the Negative Binomial Regression is used to model the aggregate number of COVID-19 cases. Case-fatality associated with this infection is modeled as an outcome variable using machine learning predictive multivariable regression. The data we used are the COVID-19 cases and associated deaths from the start of the pandemic up to December 02-2020, the day Pfizer was granted approval for their new COVID-19 vaccine. Results: Our analysis found significant regional variation in case fatality. Moreover, the aggregate number of cases had several risk factors including chronic kidney disease, population density and the percentage of gross domestic product spent on healthcare. The Conclusions: There are important regional variations in COVID-19 case fatality. We identified three factors to be significantly correlated with case fatality.

Determinants of Antenatal Health Care Utilization in Egypt (2000-2014) Using Binary and Count Outcomes

Aim: This study seeks to investigate the factors determining the utilization of antenatal care services, the frequency of that use, and the timing of receiving antenatal care among Egyptian women utilizing a national representative data from Egypt Demographic and Health Surveys (EDHS) in 2000 and 2014. Methods: The paper estimates the logistic regression model, zero-inflated negative binomial model (ZINB), and negative binomial regression model (NB) to identify the most important determinants of antenatal health care utilization. Results: The findings indicate that the period 2000-2014 has experienced a significant increase in the use of antenatal health care services. The use of the public sector antenatal care services relative to that of the private sector has been decreasing over time. Moreover, wealth index, women’s education and quality of health services play significant roles in increasing accessibility of antenatal health care services. On the other hand, women’s empowerment has shown a positive effect in 2000 only. Conclusion: The study highlights the most vulnerable groups that are less likely to have access to antenatal health care services, mainly women who are less educated, poor and living in rural areas especially Upper Egypt. This certainly requires a more targeted health strategy with an equity lens.

Road Crash Prediction Models: Different Statistical Modeling Approaches

Road crash prediction models are very useful tools in highway safety, given their potential for determining both the crash frequency occurrence and the degree severity of crashes. Crash frequency refers to the prediction of the number of crashes that would occur on a specific road segment or intersection in a time period, while crash severity models generally explore the relationship between crash severity injury and the contributing factors such as driver behavior, vehicle characteristics, roadway geometry, and road-environment conditions. Effective interventions to reduce crash toll include design of safer infrastructure and incorporation of road safety features into land-use and transportation planning;improvement of vehicle safety features;improvement of post-crash care for victims of road crashes;and improvement of driver behavior, such as setting and enforcing laws relating to key risk factors, and raising public awareness. Despite the great efforts that transportation agencies put into preventive measures, the annual number of traffic crashes has not yet significantly decreased. For in-stance, 35,092 traffic fatalities were recorded in the US in 2015, an increase of 7.2% as compared to the previous year. With such a trend, this paper presents an overview of road crash prediction models used by transportation agencies and researchers to gain a better understanding of the techniques used in predicting road accidents and the risk factors that contribute to crash occurrence.

Statistical Modeling of Malaria Incidences in Apac District, Uganda

Malaria is a major cause of morbidity and mortality in Apac district, Northern Uganda. Hence, the study aimed to model malaria incidences with respect to climate variables for the period 2007 to 2016 in Apac district. Data on monthly malaria incidence in Apac district for the period January 2007 to December 2016 was obtained from the Ministry of health, Uganda whereas climate data was obtained from Uganda National Meteorological Authority. Generalized linear models, Poisson and negative binomial regression models were employed to analyze the data. These models were used to fit monthly malaria incidences as a function of monthly rainfall and average temperature. Negative binomial model provided a better fit as compared to the Poisson regression model as indicated by the residual plots and residual deviances. The Pearson correlation test indicated a strong positive association between rainfall and malaria incidences. High malaria incidences were observed in the months of August, September and November. This study showed a significant association between monthly malaria incidence and climate variables that is rainfall and temperature. This study provided useful information for predicting malaria incidence and developing the future warning system. This is an important tool for policy makers to put in place effective control measures for malaria early enough.

Dynamic road crime risk prediction with urban open data

Crime risk prediction is helpful for urban safety and citizens’life quality.However,existing crime studies focused on coarse-grained prediction,and usually failed to capture the dynamics of urban crimes.The key challenge is data sparsity,since that 1)not all crimes have been recorded,and 2)crimes usually occur with low frequency.In this paper,we propose an effective framework to predict fine-grained and dynamic crime risks in each road using heterogeneous urban data.First,to address the issue of unreported crimes,we propose a cross-aggregation soft-impute(CASI)method to deal with possible unreported crimes.Then,we use a novel crime risk measurement to capture the crime dynamics from the perspective of influence propagation,taking into consideration of both time-varying and location-varying risk propagation.Based on the dynamically calculated crime risks,we design contextual features(i.e.,POI distributions,taxi mobility,demographic features)from various urban data sources,and propose a zero-inflated negative binomial regression(ZINBR)model to predict future crime risks in roads.The experiments using the real-world data from New York City show that our framework can accurately predict road crime risks,and outperform other baseline methods.

1995-2015年中国老年人口迁移的空间格局与影响因素

Although China was one of the countries with the fastest-growing aging population in the world,limited scholarly attention has been paid to migration among older adults in China.The full picture of their migration in the entire country over time remains unknown.This study examines the spatial patterns of older interprovincial migration flows and their drivers in China over the period 1995 to 2015,using four waves of census data and intercensal population sample survey data.Results from eigenvector spatial filtering negative binomial regressions indicate that older adults tend to migrate away from low cost-of-living rural areas to high cost-of-living urban and rural areas,moving away from areas with extreme temperature differences.The location of their grandchildren is among the most important attractions.Our findings suggest that family-oriented migration is more common than amenity-led migration among retired Chinese older adults,and the cost-of-living is an indicator of economic opportunities for adult children and the quality of senior care services.