The paper provides estimation of the odds ratio between two independent groups using two types of Moving Extreme Ranked Set Sampling (MERSS). Theoretical properties of the suggested estimator are derived and compared with its counterpart estimator using simple random sampling (SRS). It is found that the estimator based on MERSS is always valid and has some advantages over that based on SRS. Real data from a level I Trauma center are used to illustrate the procedures developed in this paper.