Normal approximation methods under the null hypothesis of no difference are frequently used to test the two independent proportions in non-inferiority trials. However, these tests are not appropriate under the null hypothesis of non-zero difference. We review the likelihood score methods proposed by Miettinen and Nurminen, Farrington and Manning, and Gart and Nam and compare the performance of these tests. The simulation study shows that the likelihood score tests under the null hypothesis of non-zero difference have better performance at a Type I error and power than usual normal approximation methods.