Models For Zero-inflated Count Data And Its Medical Applications

Count data refers to the number of times a medical event occurs in unit time, space, area. The outcome is the realization of a nonnegative integer-valued random variable,for example is 0,1,2,3, ... and so on. It is a discrete-continuous numerical variable. Poisson regression is the basic model for count data. Poisson regression is assumed the event rate is invariant, and the mean of event is equal to the variance. In practical applications this assumption is often too strict. Negative binomial regression is an expansion of Poisson regression in these cases.There are always a large number of zero observed in count data, When the proportion of zero is far more than that of predictive capability of Poisson regression or negative binomial regression, it is refered as zero-inflated. Actually zero-inflated Poisson regression is a mixed model, It can solute the extra-zero problem well, and we extended zero-inflated Poisson regression to zero inflated negative binomial regression model. We studied the overdispersion test, resoning of zero-inflated model, simulation study, models selection. and analysis of examples was carried out to compare basic model with zero-inflated models. The conclusions were as follows:1. Count models had some advantages related to classical logistic or linear regression modelCompared to logistic regression and multiple linear regression which were sometimes applied to count data mistakely, Count model was much better in line with the nature of count data.2. Models selection when overdispersionPoisson regression could be as an exploratory analysis when overdispersion, it was more appropriate to select negative binomial regression model.3. The BHHH estimate of zero-inflated count modelThe BHHH estimate of variance of zero-inflated count model was simpler and more easily implemented than that of Hessian matrix in most cases. However the two estimates were asymptotically equivalent, in finite samples they might give different results, the real examples confirmed this. 4. Vuong test for count data model selectionSimulation studies showed that Vuong test had high enough power, But at the same time the results showed it seemed to be inclined to complex models, this needed further to be done.5. Bootstrap estimateBootstrap estimates showed it could not guarantee that the maximum likelihood estimate of ZIM converged in the global maximum in practical count data, the stability and consistency of maximum likelihood estimate could be evaluated based on Bootstrap sample.