Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We dis...Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.展开更多
Background: Cardiovascular diseases (CVDs) are the leading cause of death globally. An estimated 17.9 million people died from CVDs in 2019, representing 32% of all global deaths. Of these deaths, 85% were due to hear...Background: Cardiovascular diseases (CVDs) are the leading cause of death globally. An estimated 17.9 million people died from CVDs in 2019, representing 32% of all global deaths. Of these deaths, 85% were due to heart attack and stroke. Over three quarters of CVD deaths take place in low- and middle-income countries. We have studied the pattern of mortality due to cardiovascular in the six countries of the Arabian Gulf and its association with obesity over the 29 years 1990 to 2019. Methods: We used the linear mixed effect models to investigate the pattern of CVD mortality over the year 1990 to 2019, together with the pattern of change in one of the most important risk factors that is obesity, and its association with CVD mortality over the same period. Conclusions: Although there were fluctuations in the pattern of mortality and the prevalence of obesity over the specified period, there has been a steady decline in the per-100,000 number of deaths and the prevalence of obesity. However, there was a strong association between the two variables. From the fitted models we estimated that a one percent increase in obesity is associated with an average increase in cardiovascular deaths of 2.7 deaths per 100,000.展开更多
文摘Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.
文摘Background: Cardiovascular diseases (CVDs) are the leading cause of death globally. An estimated 17.9 million people died from CVDs in 2019, representing 32% of all global deaths. Of these deaths, 85% were due to heart attack and stroke. Over three quarters of CVD deaths take place in low- and middle-income countries. We have studied the pattern of mortality due to cardiovascular in the six countries of the Arabian Gulf and its association with obesity over the 29 years 1990 to 2019. Methods: We used the linear mixed effect models to investigate the pattern of CVD mortality over the year 1990 to 2019, together with the pattern of change in one of the most important risk factors that is obesity, and its association with CVD mortality over the same period. Conclusions: Although there were fluctuations in the pattern of mortality and the prevalence of obesity over the specified period, there has been a steady decline in the per-100,000 number of deaths and the prevalence of obesity. However, there was a strong association between the two variables. From the fitted models we estimated that a one percent increase in obesity is associated with an average increase in cardiovascular deaths of 2.7 deaths per 100,000.
