For trials developed in rare or serious diseases, unequal randomization ratios are often used to maximize the patients' benefits of receiving treatments. The sample sizes calculated using the pooled variance estimates and unpooled variance estimates both from normal approximation are noticeably different especially with unequal rand ratios. This research studied 10 methods of sizing difference in proportion under the rand ratios of 1:1,2:1 and 3:1,including the normal approximation, Fisher's exact test,likelihood ratio test, Newcombe's Wilson score with continuity correction, Miettinen&Nurminen, Chan&Zhang, Agresti&Min and Santner&Snell methods. The method performances were compared via power assessment and type I error assessment, based on simulated datasets with selected effect sizes containing low placebo rate. We identified methods that inflate the type I error especially under unequal rand ratios. We recommend normal approximation with pooled variance estimates and Miettinen&Nurminen method to be powerful but not to inflate type I error. For the methods not readily available in common used statistical softwares, R codes have been developed for sizing trials with simulations.