Background & Aim: Statistical modeling is one of the most suitable methods for analyzing the relationship between health and medical issues. In the situation of analysis of zero-inflated data, there are different methods. In this study, the models Poisson, Poisson gamma, and Poisson lognormal regression were compared.Methods & Materials: This cross-sectional study was conducted to determine the influential factors on decay-missing-filled (DMF) index by the three mentioned models using the data of 808 first-grade children of the primary school in Kerman, Iran. The command PROC NLMIXED in SAS software was applied for fitting the models on data. For comparing the models, we applied the Akaike’s criterion (AIC), mean square error (MSE) criterion and confidence interval (CI).Results: The AIC and CI showed that the Poisson lognormal model was better than the others due to a level of significance. The variables of the students’ place of living, mothers’ jobs, fathers’ jobs, the region, sex, optic problems, and behavioral problems had a significant effect on DMF index.Conclusion: Poisson lognormal was better than the other models in dental health data.

Multivariate normal-Poisson model has been recently introduced as a special case of normal stable Tweedie models. The model is composed of a univariate Poisson variable, and the remaining variables given the Poisson one are independent Gaussian variables with variance the value of the Poisson component. Two characterizations of this model are shown, first by variance function and then by generalized variance function which is the determinant of the variance function. The latter provides an explicit solution of a particular Monge-Ampère equation.

BACKGROUND AND OBJECTIVE: Different statistical methods can be used to analyze fertility data. In cases that dependent variable is count, Poisson model is applied. If Poisson model is not applicable in a specific situation, it is better to apply generalized Poisson model and in cases that multilevel variable exists, it is better to use multilevel Poisson model. Our goal in this study is to compare both generalized and multilevel Poisson regression model with Poisson regression model in estimating of coefficient of the effective factors on the number of children.METHODS: This is a cross-sectional study. A sample of 1019 women (15-49 years old) from rural area was selected by stratified sampling. The women were categorized into seven groups and in each group the intended samples were selected equally by systematic sampling. Data were analyzed by Poisson regression model, generalized and multilevel Poisson regression model.FINDINGS: The sample mean and sample variance of the number of children were 4.3 and 8.3, respectively. There was a significant relationship between educational status of the spouses, age of marriage, feeding period, economical status and the interval between the children in generalized and multilevel Poisson regression model.CONCLUSION: According to the results of this study, generalized and multilevel Poisson regression models were more suitable for data analysis and it can estimate coefficient effective of factors on the number of children exactly.

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the e ects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively a ects the variance of the maximum likelihood estimator (MLE) of the Poisson regression coe cients. To address this problem, a Poisson Liu estimator has been proposed by numerous researchers. In this paper, a Jackknifed Liu-type Poisson estimator (JPLTE) is proposed and derived. The idea behind the JPLTE is to decrease the shrinkage parameter and, therefore, improve the resultant estimator by reducing the amount of bias. Our Monte Carlo simulation results suggest that the JPLTE estimator can bring significant improvements relative to other existing estimators. In addition, the results of a real application demonstrate that the JPLTE estimator outperforms both the Poisson Liu estimator and the maximum likelihood estimator in terms of predictive performance.

Background: Malaria is the third most important infectious disease in the world. WHO propose programs for controlling and elimination of the disease. Malaria elimination program has begun in first phase in Iran from 2010. Climate factors play an important role in transmission and occurrence of malaria infection. The main goal is to investigate the spatial distribution of incidence of malaria during April 2011 to March 2018 in Hormozgan Province and its association with climate covariates. Methods: The data included 882 confirmed cases gathered from CDC in Hormozgan University of Medical Sciences. A Poisson-Gamma Random field model with Bayesian approach was used for modeling the data and produces the smoothed standardized incidence rate (SIR). Results: The SIR for malaria ranged from 0 (Abu Musa and Haji Abad districts) to 280. 57 (Bandar– e-Jask). Based on model, temperature (RR= 2. 29; 95% credible interval: (1. 92– 2. 78)) and humidity (RR= 1. 04; 95% credible interval: (1. 03– 1. 06)) had positive effect on malaria incidence, but rainfall (RR= 0. 92; 95% credible interval: (0. 90– 0. 95)) had negative impact. Also, smoothed map represent hot spots in the east of the province and in Qeshm Island. Conclusion: Based on the analysis of the study results, it was found that the ecological conditions of the region (temperature, humidity and rainfall) and population displacement play an important role in the incidence of malaria. Therefore, the malaria surveillance system should continue to be active in the region, focusing on high-risk areas of malaria.

Introduction: Different statistical methods can be used to analyze fertility data. When the response variable is discrete, Poisson model is applied. If the condition does not hold for the Poisson model, its generalized model will be applied.The goal of this study was to compare the efficiency of generalized Poisson regression model with the standard Poisson regression model in estimating the coefficient of effective factors in the number of children.Methods: This is a cross-sectional study carried out on a population of married women with the age range of 15-49 years old in Kashan, Iran. The cluster sampling method was used for data collection. Clusters consisted of the urban blocks determined by the municipality. The total number of 10 clusters each of 30 households was selected according to the health center's framework. The necessary data were then collected through a self-made questionnaire and direct interviews with women under study. Further, the data analysis was performed by using the standard and generalized Poisson regression models through the R software.Results: The average number of children for each woman was 1.45 with a variance of 1.073.A significant relationship was observed between the husband's age, number of unwanted pregnancies, and the average duration of breastfeeding with the present number of children in the two standard and generalized Poisson regression models (p<0.05). The mean age of women participating in this study was 33.1±7.57 years (from 25.53 years to 40.67) and the mean age of marriage was 20.09±3.82 (from16.27 years to23.91), and the mean age of their husbands was 37.9±8.4years (from 29.5 years to 46.3). In the current study, the majority of women were in the age range of 30-35 years old with the median of 32 years old, however, most of men were in the age range of 35-40 years old with the median of 37 years old. While 236 of women did not have unwanted pregnancies, most participants of the present study had one unwanted pregnancy.Conclusion: According to the achieved results, the generalized Poisson regression model is more suitable for data analysis and can estimate the coefficient of effective factors on the number of children more precisely.

Variable selection in Poisson regression with high dimensional data has been widely used in recent years. we proposed in this paper using a penalty function that depends on a function named a penalty. An Atan estimator was compared with  Lasso and adaptive lasso. A simulation and application show that an Atan estimator has the advantage in the estimation of coefficient and variables selection.

Background & Aim: The excess hazard rate proposed by Andersen and Vaeth may underestimate the long-term excess hazard rate for cancer survival. Zahl explained the phenomenon by continuous selection of the most robust individuals after diagnosis. He applied correlated inverse Gaussian and gamma frailty models to estimate excess intensity and reached a better estimate of the rate and called it the corrected excess hazard. The compound Poisson distribution has more parameters and therefore owns more flexibility and includes gamma and inverse Gaussian distributions as special cases. Therefore, the aim of this study was to estimate the excess hazard using compound poisson frailty model Methods & Materials: Both shared and correlated frailty (CF) variables based on compound Poisson distribution were used to model unobserved common covariates. A data set of patients diagnosed with localized or regional gastrointestinal tract cancer collected at the Mazandaran province of Iran was studied. As registration systems in Iran are so affected by omission and various errors, a number of five West Coale- Demeny life tables for men and four for women were constructed corresponding to each birth cohort, which was considered as the reference life tables. Thus, population-based mortality rates [h1 (t)] were simply replaced by the appropriate values of the West tables depending on the sex (male or female) and birth cohort of the patient.Results: The CF model with unequal variances could best estimate the long-term excess hazard.Conclusion: This study advocates the CF models can best estimate the long-term excess hazard rates regardless of the distribution of the frailty variable.