Abstract: The prevalence of sleep apnea problem have rise since twenty years ago. Sleep apnea disrupts the quality of sleep and may influence quality of life. The purpose of this study was to find relationship between occurrence of apnea and occurrence of rapid eye movement (REm) sleep stages. The empirical Bayes method was used to estimates the rates of apnea and rates of REm among 13 patients that were suffering of sleep apnea problem. The data was extracted from PhysioBank website that consists of apnea events and sleep stages. In this study, The parameter estimates of Poisson-gamma model was considered. The estimation of parameter was done using three method which is moment (mom), maximum likelihood (mLE) and alternate method (mLM). The results indicated that the estimates of parameter was almost similar between three methods. The estimates of rates of apnea was not related to rates of REm. The rates of apnea and rates of REm was differed between the 1st and 2nd half period of sleep. Furthermore, there was no relationship between apnea and sleep stages of REm when the time of sleep was partition into 1st and 2nd period of sleep. Based on the bootstrapping method the estimates of parameter was found to be acceptable for a particular patients.