藥物劑量反應研究中一個重要的問題便是鑑別優於零劑量對照組的最低劑量水準，亦稱為最低有效劑量(minimum effective dose)。本文首先就右設限存活資料，根據加權對數秩統計量(weighted logrank statistics)建構類似對比形式的統計量，以封閉降階檢定程序(closed step-down testing procedure)鑑別最低有效劑量。當收集的資料除存活時間外，亦包含與病人生理狀態和病情相關的共變數時，此一最低有效劑量可能與研究中的共變數相關。為鑑別與共變數相關的最低有效劑量，我們分別在分層或不分層的Cox風險模式下，建立兩個處理組病人的存活中位數差異及限制平均壽命差異之信賴區間，並且應用於封閉降階的檢定之中。本文進一步使用蒙地卡羅(Monte Carlo)方法模擬風險函數(hazard function)成比例，及風險函數差異發生在早期的右設限存活資料，藉以研究所提檢定方法在小樣本情形下的誤差率及檢定力表現。我們也研究上述信賴區間在兩樣本問題中的覆蓋機率和區間寬度，並且探求及其應用於最低有效劑量的效率。最後，藉分析右設限存活資料說明本文所提各種方法的應用。

Dose-response studies are frequently conducted to evaluate the treatment effects of a drug in animal experiments or clinical trials for drug development, where subjects or patients are randomly allocated to groups to receive several increasing dose levels of the drug and a zero-dose control. One factor of interest in such studies is to identify the minimum effective dose (MED) of the drug, where the MED is defined to be the smallest dose level producing a clinically important response that can be declared statistically significantly more effective than the placebo response. In this thesis, we first consider the closed step-down testing procedures based on three types of weighted logrank statistics to identify the MED for right-censored survival data. When the survival data are accompany with covariates which are associated with patients’ physiology and conditions, the identified MED may be related to the covariates under study. In order to identify the covariates-dependent MED, we construct confidence intervals for the difference of two median survival times and difference of two restricted mean lifetimes under the stratified and unstratified Cox models, respectively, and then apply with the step-down closed testing scheme. In this thesis, we further conduct a Monte Carlo study to investigate the relative error rate, power and bias performances of the competing procedures under proportional hazards alternative and early hazards difference for small sample size. We also investigate the coverage probability and expected length of the confidence intervals stated above, and evaluate the efficiency of the application on MED identification. Finally, the use of those procedures is illustrated with a right-censored survival data.

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