Loss of Power with Tests for Treatment Effects in Clinical Trials due to Patients' Heterogeneity and Countermeasure

logrank试验在临床试验中常用来评价治疗效果，以患者生存时间为主要反应指标。获得临床试验所需患者数量的常用公式与患者自然预后的异质性程度无关；因此，医学研究人员在进行测试时并未过多关注患者的异质性。然而，最近，异质性对测试结果的影响已经被广泛研究。本研究的目的是描述癌症患者的异质性，估计异质性对分层logrank检验的功效的影响，并研究应用“分段线性风险模型”的Cox回归方法，该方法使我们能够将数据拟合到任何形式的协变量向量指定的风险中。利用一项由6000多名患者组成的胃癌临床试验的数据估计了层内患者的异质性：从模拟研究中发现，由于观察到患者的异质性，分层logrank试验可能会遭受严重的功率损失。另一方面，带有错误危险模型的Cox回归方法也可能导致大量的功率损失。因此，我们开发了Cox回归方法，采用考虑预后因素的“分段线性风险模型”来建模风险。证实了PL模型在肿瘤临床试验中普遍优于其他模型。

The logrank test is commonly used to evaluate the treatment effect in clinical trials with patients survival times as the main response measure. The usual formula to obtain the number of patients required in a clinical trial is independent of the degree of heterogeneity regarding natural prognoses of patients ; accordingly, medical researchers have not paid much attention to heterogeneity of patients in conducting the test. Recently, however, the effects of heterogeneity on the results of the test have been extensively studied.The objective of this study is to describe the heterogeneity of cancer patients, to estimate the effects of the heterogeneity on the power of the stratified logrank tests and to study the Cox regression method with "piecewise linear hazard model" in application, which enables us to fit data to hazards specified for any forms of the covariate vector.The heterogeneity of patients within stratum was estimated using the data of a gastric cancer clinical trial consisiting of over 6000 patients : It is revealed then from simulation studies that the stratified logrank tests may suffer serious power loss due to the observed heterogeneity of the patients. On the other hand, the Cox regression method with a misspecified hazards model may also result in a substantial loss of power. And thus, we have developed Cox regression method with "piecewise linear hazard model" of modeling hazards which takes into account the prognostic factors. It is confirmed the PL model is universally sperior to the other models in cancer clinical trials.