本研究將根據右設限資料提出一個具平滑性質之存活風險率，而風險率模型所引進之參數將以最大概似估計法來估計。此估計程序可以提供一個存活風險率的平滑估計。我們根據牛頓法的原理，提出一個有效求取最大概似估計量的演算法。此估計方法的成功，於模擬試驗及對白血病患緩解時間的數據資料之分析結果將被說明。另外，我們的方法與尼爾生-艾倫方法的比較，和伯氏多項式階數之選取亦為本文討論的議題。 In this thesis, we study the maximum likelihood estimator for a survival hazard rate with right censored data, in which the hazard rate is specified by the Bernstein polynomial. Our estimation procedure can provide a smooth estimator of the survival hazard rate. We develop an efficient Newton-Raphson based algorithm for the computation of the maximum likelihood estimate. The success of this method is demonstrated in simulation studies and in the analysis of Leukemia remission-time data. In addition, the comparison with Nelson-Aalen method is presented and the selection of the degree for Bernstein polynomial is discussed.
