Gray R J, Tsiatis A A
Department of Biostatistics, Dana-Farber Cancer Institute, Boston, Massachusetts.
Biometrics. 1989 Sep;45(3):899-904.
For diseases with a positive probability of being cured, a family of alternatives to the null hypothesis of equality of survival distributions is introduced, which is designed to focus power against alternatives with differences in cure rates. The optimal linear rank test for this alternative is derived, and found to be substantially more efficient than the log-rank test for this alternative when cure rates are less than 50%, while there is little difference between the tests if the cure rates are 50% or greater. The simple test based on the difference of Kaplan-Meier estimates of the proportion cured is also examined, and found to be fully efficient for this alternative with no censoring, while its efficiency rapidly drops as censoring is increased. The new test is not a pure test of equality of cure rates when the data are censored, but rather is a test of equality of survival distributions that focuses power against late differences in the survival curves.
对于有治愈可能性的疾病，引入了一族原假设生存分布相等的备择假设，其目的是将检验功效集中于针对治愈率存在差异的备择假设。推导了针对此备择假设的最优线性秩检验，并发现当治愈率小于50%时，该检验比针对此备择假设的对数秩检验效率显著更高，而当治愈率为50%或更高时，两种检验之间差异不大。还研究了基于治愈比例的Kaplan-Meier估计值之差的简单检验，发现对于无删失的此备择假设，该检验是完全有效的，而随着删失增加，其效率迅速下降。当数据存在删失时，新检验并非纯粹的治愈率相等检验，而是一种生存分布相等检验，它将检验功效集中于针对生存曲线后期差异。
