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

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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.