臺灣博碩士論文加值系統

在這篇文章，我們估計Cox比例危險模型中的參數$S_0(t)$與$ eta$，當資料是區間刪減數據。為了要運用這個模型，資料應該要是精確的或是右刪減資料，因此我們利用三種方法將區間刪減資料轉換成精確資料，並且利用 Nelson-Aalen 估計法來估計參數$S_0(t)$與$ eta$。而檢定統計量不是接近自由度1的卡方分配，而是相當接近自由度1的卡方分配乘上一個常數。

In this paper, we estimate the parameters $S_0(t)$ and $ eta$ in Cox proportional hazard model when data are all interval-censored. For the application of this model, data should be either exact or right-censored, therefore we
transform interval-censored data into exact data by three di®erent methods and then apply Nelson-Aalen estimate to obtain $S_0(t)$ and $ eta$. The test statistic
$hat{ eta}^2I(hat{ eta})$ is not approximately distributed as $chi^2_{(1)}$ but $chi^2_{(1)}$ times a
constant c.

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Turnbull''s algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3. Generate discrete interval-censored data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4. How to choose exact data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5. Parameter estimation of $ eta$ and $S_0(t)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.1. Estimation and test for the parameter $ eta$ . . . . . . . . . . . . . . . . . . . . . . . . 7
5.2. Estimation of $S_0(t)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6. Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
7. Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.1. A hemophilia study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.2. A breast cosmesis study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

[1] B. W. Turnbull (1974). Nonparametric estimation of a survivalship function with
doubly censored data. Journal of American Statistical Association, Vol. 69, No.
345, 169-173.
[2] Chin-san Lee (1999). An urn model in simulation of interval-censored failure time
data. Statistics & Probability Letters, Vol. 45, 131-139.
[3] Ching-fu Sen (2001). On the consistency of a simulation procedure amd the com-
struction of a nonparametric test for interval-censored data. Master of Science The-
sis, Department of Applied Mathematics, National Sun Yet-Sen University.
[4] D. M. Finkelstein (1985). A semiparametric model for regression analysis of interval-
censored failure time data. Biometrics, Vol. 41, 933-945.
[5] J. F. Lawless (1982). Statistical Models and Methods for Lifetime Data. Wiley:
New York.
[6] Ping-Chun Chang (2005). A study of statistical distribution of a nonparametric
test for interval censored data. Master of Science Thesis, Department of Applied
Mathematics, National Sun Yet-Sen University.
[7] V. De Gruttola and S. W. Lagakos (1989). Analysis of dounly-censored survival
data, with application to AIDS. Biometrics, Vol. 45, 1-11.