Cox 模型在驗證集與世代研究的穩健性探討

A robust analysis of the Cox model under the validation sampling

高世穎(SHIH-YING KAO)

指導教授 ： 黃佳慧

國立臺北大學/商學院/統計學系/碩士(2014年)

摘要

本論文延伸了 Chen (2002) 針對 cohort studies 和 validation sampling 的參數估計討論，
針對兩種不同類型的解釋變數結構所組成的資料去探討 cohort studies 和 validation sampling 估計出來的參數之間的差異性。
主要針對兩個部分做討論，第一部份是 cohort studies 的解釋變數 X 和 validation sampling 的解釋變數 X* 之間的關係是線性關係。
第二個部分是 cohort studies 和 validation sampling 之間是利用邏輯思迴歸的關係，
將兩種資料利用 Cox proportional hazards regression model 建立模型。
首先利用 validation sampling 做出一個參數估計，再利用 cohort studies 做出另一個參數估計，最後論文推導出
cohort studies 和 validation sampling 的共同參數估計，去探討變異數、偏誤等可以判斷參數準確性的統計量。

關鍵字

存活分析 ； Cox 模型 ； 驗證集 ； 世代研究

並列摘要

This work is to study the Cox proportional hazards model in cohort study
under the validation sampling setting.
We analyse the robust properties of regression parameter estimates
in which the event times are assumed from the Cox model with individuals
explanatory variables.
However, only part of individuals are able to observe these variables, and
the proxy covariates are available for the cohort study.
Therefore, we consider two types of relationships between the covariates and its proxy variables, and the simulation illustrates the statistical properties
of estimates with a full scale of senarios.
The results provide a way to utilize the validation sample for the Cox model.

並列關鍵字

Cox regression ； Validation sampling ； Cohort studies ； Survival analysis

參考文獻

Andersen, P. K. and Gill, R. (1982), “Cox’s regression model for counting processes: a large sample study”, Ann. Statist., 10, 1100–1120.

Chen, Y.-H. (2002), “Cox regression in cohort studies with validation sampling”, Journal of the Royal Statistical Society:Series B (Statistical Methodology), 64, 51–62.

Cox, D. R. (1972), “Regression models and life tables”, J. R. Statist. Soc. B,34, 187–220.

Kaplan, E. L. and Meier, P. (1958), “Nonparametric estimation from incomplete observations”, J. Am. Statist. Ass., 53, 457–481.

Lin, D. Y. and Wei, L. J. (1989), “The robust inference for the cox proportional hazards model”, J. Am. Statist. Ass., 84, 1074–1078.