Testing violations of the exponential assumption in cancer clinical trials with survival endpoints.

Personalized cancer therapy requires clinical trials with smaller sample sizes compared to trials involving unselected populations that have not been divided into biomarker subgroups. The use of exponential survival modeling for survival endpoints has the potential of gaining 35% efficiency or saving 28% required sample size (Miller, 1983), making personalized therapy trials more feasible. However, the use of exponential survival has not been fully accepted in cancer research practice due to uncertainty about whether or not the exponential assumption holds. We propose a test for identifying violations of the exponential assumption using a reduced piecewise exponential approach. Compared with an alternative goodness-of-fit test, which suffers from inflation of type I error rate under various censoring mechanisms, the proposed test maintains the correct type I error rate. We conduct power analysis using simulated data based on different types of cancer survival distribution in the SEER registry database, and demonstrate the implementation of this approach in existing cancer clinical trials.

On powerful exact nonrandomized tests for the Poisson two-sample setting.

In the case of two independent samples from Poisson distributions, the natural target parameter for hypothesis testing is the ratio of the two population means. The conditional tests which have been derived for this class of problems already in the 1940s are well known to be optimal in terms of power only when randomized decisions between hypotheses are admitted at the boundary of the respective rejection regions. The major objective of this contribution is to show how the approach used by Boschloo in 1970 for constructing a powerful nonrandomized version of Fisher's exact test for hypotheses about the odds ratio between two binomial parameters can successfully be adapted for the Poisson case. The resulting procedure, which we propose to term Poisson-Boschloo test, depends on some cutoff for the observed total number of events, the variable upon which conditioning has to be done. We show that for any fixed specific alternative, this cutoff can be chosen in such a way that the resulting nonrandomized test falls short in power of the randomized UMPU test only by a negligible amount. Thus, sample size calculation for the Poisson-Boschloo test can be carried out nearly exactly by means of the same computational procedure as has to be used for the randomized UMPU test. Since the power of the latter is accessible to elementary computational tools, this result makes approximate methods of sample size calculation for the Poisson-Boschloo test dispensable. It is furthermore shown how the construction of a Poisson-Boschloo type test extends to the case that interest is in establishing equivalence in the strict, two-sided sense rather than noninferiority. Although proceeding to two-sided equivalence considerably complicates the construction, comparing the resulting test procedure in terms of power with the exact randomized UMPU test leads essentially to the same conclusions as in the noninferiority case.

Comparing Two Exponential Distributions Using the Exact Likelihood Ratio Test.

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.