The exact two-sided likelihood ratio test for testing the equality of two exponential means is proposed and proved to be the uniformly most powerful unbiased test. This exact test has advantages over two alternative approaches in that it is unbiased and more powerful while maintaining the type I error. The use of the proposed test is demonstrated in a non-small cell lung cancer clinical trial design.
Keywords: Survival analysis; exponential family; power calculation; uniformly most powerful unbiased test.