Bayesian Analysis Based On Zero-inflated Poisson Model And Its Application In Medicine

With the deepening of medical reform and the development of "3521project", there aways exist a large number of zero in the number of observed events in the Clinical medicine、Public Health and Community Medicine Information surveys.The research about Count Data model analysis also gradually causes the attention of more researchers. In medical research, many individuals were not observed the occurrence of the observed events during the observation period, its value may be zero, in which the proportion of zero is far more than predicition ability of zero of Poission regression. If we still fit basic Poisson model, it would result the occurrence of bias.The zero-inflated Poisson regression (ZIP) model is proposed to solve the problems which establish mixed regression model by using the zero count and the nonzero count. It is important for us to select the model by judging whether there are too many zero data in the actual research. If Zero expansion does exist, we use the ZIP regression model to analysis it.When ZIP model parameters are estimated, another important problem is the relationship between the different method of estimation and the sample size. We proposed the scope of application of different estiamation methods by discussing the theory and simulation study of classical approach (Maximum Likelihood Method) and Bayesian Estimation Method.By using MCMC methods, combined with Data Augmentation skills of enumeration, and using the Gibbs sampling algorithm of MH on the basis of conditional distribution, then we can finally obtain the posterior distribution of the parameters and estimate of parameter. We explicit the accuracy of the Maximum Likelihood Method and Bayes Estimation by introducing the theory、simuation and instance analysis. When the sample size is small, Bayesian parameter estimation results are better than the Maximum Likelihood Method, especially for the parameter estimation results of "zero" process. When n≥100,the parameter estimation results by using the ZIP model、MLE and Bayes estimation are all close to the true value. Only by choosing the appropriate prior distribution, setting appropriate initial value, having sufficient number of iterations when we using Bayesian analysis based on Zero-inflated Poisson model, we can obtain more satisfaction parameters estimated values. Meanwhile, we verify the two parameter estimation methods by analysing82patients with coronary heart disease who relapse after PCI operation within a year. The analysis showed that the Maximum Likelihood Estimation Method can not select meaningful impact factors in the process of "zero" when the sample is relatively small. However the results of Bayesian parameter estimation are accurater and more reasonable.In summary, this paper introduce Score test in detail of judging zero expansion of the count data of medical and health fields. If the count data contains too many zero which are more than the forecasting ability of the Poisson regression for zero, we can use the ZIP model. In this paper, we also expound the theory of MLE and Bayes estimation based on zero-inflated Poisson model, and further proceed simulation study and medical example analysis which the sample size is smaller. The result shows that the estimate of parameter are better than MLE, we can obtain estimate of parameter and the CI of posterior distribution, so the ZIP model is better when the sample is small.