Odds Ratio Estimation for Small Count in Zero-Inflated Poisson

Abstract

The odds ratio estimation when observed frequencies are very small usually causes difficulty in calculation. In this paper, we proposed the estimator of odds ratio for small count using Empirical Bayes (EB) in Zero-inflated Poisson distribution, where the hyper-parameters can be estimated via the posterior marginal distribution function. We compare the proposed estimator of odds ratio based on EB in Zero-inflated Poisson distribution with moments method estimator (MME) and modified maximum likelihood estimator (MMLE) using the Estimated Relative Error (ERE) as criterion of comparison. The result of a simulated study indicates that the EB estimator is more efficient than MME and MMLE. For application, the EB odds ratio estimation is implemented in AIDS-related data which the response was the self-reported number of times that respondents having a risky sexual partners, classified by gender. The estimation based EB also yields consistent result as those in simulation, resulting in smallest ERE when compared to MME and MMLE.INDEX TERMS Empirical Bayes, zero-inflated Poisson distribution, moments method estimation, modified maximum likelihood estimator.