在醫學研究中，最廣泛比較的是兩組治療下存活機率的差異，在實際狀況下，兩組治療的風險比例是會隨著時間而變化，例如，對於冠狀動脈患者在手術治療和藥物治療下兩種治療效果的差異，在治療前期，手術治療的死亡風險較高，但在後期治療效果反而是藥物治療的死亡風險高。在這樣的情況下，在比較存活機率的檢定中，對數等級檢定(log-rank test)有較弱的檢定力。一種替代方案是考慮兩組之間的限制平均壽命，其可以基於非參數或半參數方法估計。在本文中，對於混合區間設限資料，我們考慮兩種方法來構建兩組治療限制平均壽命差異的信賴區間。第一種方法基於兩組治療限制平均壽命的估計差異，這兩組治療限制平均壽命的估計是使用Turnbull 的非參數最大概似估計(NPMLE)獲得的。第二種方法基於偽觀察值法，此方法依賴於”leave-one-out” jackknife 的方法，限制平均壽命的估計也是使用Turnbull 的NPMLE。在模擬結果中發現第一種方法表現良好，第二種方法表現保守，因為三明治法的變異數估計高估了真實的變異數。在實際HIV 資料分析中會說明兩種方法的應用。 Comparing the difference between two groups of treatment is widely used in medical research. In practice, the risk ratio of the two groups of treatment can change with time. For example, for the comparison between the effect of surgical treatment and drug treatment in coronary patients, the mortality rate of surgical treatment is higher than drug treatment in the early stage while the outcome can be reversed in the late stage. In this situation, it is well known that log rank test has low power of detecting the survival difference between the two treatments. One alternative is to consider the restricted mean survival time (rmst) between the two groups, which can be estimated based on nonparametric or semiparametric approach. In this article, for mixed interval censored data, we consider two approaches to constructing confidence intervals for the difference of rmst between two treatment groups. The first approach is based on the estimated difference of two rmsts, which are obtained using Turnbull’s nonparametric maximum likelihood estimator (NPMLE). The second approach is based on pseudo-observation scheme, which also relies on delete-one jackknife pseudo-observation of Turnbull’s NPMLE. Simulation results indicate that the first approach performs well while the second approach gives conservative intervals since sandwich variance estimators overestimate the true variances. Both methods are applied to HIV data for illustration.
