Statistical Test For Zero-Inflated Poisson With Censored And Its Application

The zero-inflated problem with censoring often occurs in many fields such as public health,biomedicine,economics,and agriculture.When additional count data with a value of zero is observed,if we still use the traditional Poisson model for fitting,Then the prediction of the count data will have a large error,resulting in a zero-inflated model,and the more commonly used zero-inflated Poisson model.In practice,the situation is often complex and diverse,and the data may be ”censored” due to detection limitations.Censoring is divided into ”left-censored” and ”right-censored”.For zero-inflated models,”right-censored” is often discussed.Condition.In terms of estimation method,for the zero-inflated Poisson model with censoring,the existing literature mainly estimates its parameters,and the test of zero-inflated is relatively lacking.The predecessors in this paper migrated the zero-inflated test method on the Poisson model,established a new statistic based on the difference between the observed number of zeros and the expected number of zeros,and compared with the traditional zero-inflated test methods Wald test,LR test and Score test Do a performance comparison.This paper mainly consists of four parts.The first zero-inflated part is the research background and literature review of this paper.It introduces the significance of this paper and the previous explorations on the zero-inflated Poisson model with censoring and the zero-inflated test.The second part introduces the model and constructs a new test statistic,and derives its asymptotic properties based on estimating equations.The conclusion shows that the new The proposed test statistic obeys the standard normal distribution,and when the data is the Censored Poisson model,the mean When the value is a constant,the new test statistic is identical to the Score test statistic.The third part conducts a random simulation study to test whether there is zero inflation in the generated censored data.The new test is compared with the traditional test,and the performance of the test is evaluated in terms of both type 1 error and power.For different parameters in this paper Cases,in the absence of zero-inflated data,the performance of the new test is the best,and the Wald and LR tests fail when the mean is large and the censoring bound is small;when the mean is constant,the performance of the new test is consistent with the Score test.When there is zero-inflated data,the test performance depends on the parameters,and the overall performance of the new test is better.The fourth part includes the application of the test method in real data,and further illustrates the feasibility of the new test method.