Sooriyarachchi M R, Whitehead J
Department of Statistics and Computer Science, University of Colombo, Sri Lanka.
Biometrics. 1998 Sep;54(3):1072-84.
Two tests are proposed for comparing the survival curves of patients randomised between an experimental treatment and a control treatment when it is anticipated that the two survival curves may not satisfy the assumption of proportional hazards. The tests are particularly useful for the situation in which the survival curves are coincident or cross over early in the follow-up period and then diverge. The tests compare the probabilities of survival for longer than some fixed time since randomisation for the two groups of patients. Both methods take account of the right-censored observations, and both are associated with methods for estimating and setting confidence limits for treatment differences. The first method is a mathematically direct approach based on the derivation of the efficient score statistic and Fisher's information. The second method is simpler, being based on Kaplan-Meier estimates and their variances. Conventional methods of sample size determination require the assumption of proportional hazards. Here a sequential approach is used, as it is difficult to set the sample size in advance without strong assumptions about the relationship between the two survival curves. Simulation results giving information on the size and power of the proposed tests are provided and the tests are applied to data from a clinical trial in breast cancer.
当预计两种生存曲线可能不满足比例风险假设时，提出了两种检验方法，用于比较接受实验性治疗和对照治疗的随机分组患者的生存曲线。这些检验对于生存曲线在随访期早期重合或交叉然后分开的情况特别有用。检验比较两组患者自随机分组以来超过某个固定时间的生存概率。两种方法都考虑了右删失观测值，并且都与估计治疗差异和设定其置信限的方法相关。第一种方法是基于有效得分统计量和费舍尔信息推导的数学直接方法。第二种方法更简单，基于Kaplan-Meier估计及其方差。传统的样本量确定方法需要比例风险假设。这里使用一种序贯方法，因为在没有关于两条生存曲线之间关系的强假设的情况下，很难预先设定样本量。提供了关于所提出检验的大小和功效的模拟结果，并将这些检验应用于乳腺癌临床试验的数据。
