二存活函數之對等性檢定

Abstract

In oncology, increasing number of active control trials have been conducted to compare a test therapy to a standard therapy. These new therapies are developed for less invasive or easy administration, or for reduced toxicity and thus to improve the quality of life at the minimal expense of survival. Therefore, evaluation of equivalence or non-inferiority based on censored endpoints such as overall survivals between test and active control becomes an important and practical issue. Under the assumption of proportional hazards, Wellek (1993) proposed a log-rank test for assessment of equivalence of two survival functions. In this paper, an explicit form of the asymptotic variance of the maximum likelihood estimator for the treatment eect is derived. It follows that the asymptotic power and sample size formulae can also be obtained. Alternatively, a two one-sided test (TOST) is proposed to evaluate the equivalence of two survival functions. The critical values of the proposed TOST depend upon only the asymptotic variance and the standard normal percentiles, which greatly simplify the sample size determination. In addition, a procedure for testing non-inferiority based on censored endpoint is derived and the corresponding sample size formula is also provided. It can be shown that when the sample size is large, the same sample size formulae can be derived for both the log-rank test and TOST when two survival functions are assumed to be equal. The sample size formulas for both procedures take into account the accrual pattern and the duration of the study. A simulation is conducted to empirically investigate the performance on size, power, and sample size of the proposed procedures and the log-rank test. Numerical examples are provided to illustrate the proposed procedures.