長期追蹤調查資料的樣本相較於一次性觀察能貢獻較多資訊，但抽樣方法可能使這類資料有以下問題。首先，調查資料的抽樣可能有獨特的抽樣設計，所以不適合用簡單隨機抽樣所發展的統計方法來分析。另外，因抽樣條件和長期追蹤特徵，而可能無法蒐集到完整資料來代表母體，例如常見的右設限、或左截斷等特徵就是在描述資料的不完整性。當研究者欲建立不完整資料的迴歸模式時， Cox模式(Cox, 1972)是常用的方法之一。其中，左截斷在Cox模式中是可能被資料使用者忽略的資料特徵，若因為忽略了此特徵而沒用相對應的Cox模式，可能得到錯誤的統計推論。
本研究以透過「台灣地區中老年身心社會生活狀況長期追蹤調查資料」作為實證資料，並以討論台灣中老年人的存活因子為背景，其中令受訪者的壽命當作反應變數，而在這研究設計下，該資料同時具備左截斷右設限特徵和非簡單隨機抽樣設計。透過模擬分析和實證分析，本研究發現沒用左截斷Cox模式估計迴歸係數時，會發生影響統計推論的偏誤。而沒完整考慮抽樣設計的估計所產生的偏誤在模擬分析中明顯，但在實證分析中對統計推論影響不大。

Samples collected from longitudinal survey data contribute more information than from once observation. However, these samples have a few issues. First, subjects sampled in fashions of survey data may cause that they have different sampling probabilities within the group. As a result, they cannot be analyzed with statistical methods developed on the basis of simple random sampling. In addition, longitudinal survey is likely to lead to data incompleteness such as left-truncation and right-censorship. If users hope to build regression models with incomplete data, they can apply Cox model (Cox, 1972). In particular, left truncation is subject to be neglected in Cox model, and this would result in biased estimation of model coefficients through misjudging statistical analysis methods.
Discussing the elderly survival factors based on Survey of Taiwan Longitudinal Study on Aging (TLSA) may confront aforementioned two problems. Namely, the survey data of TLSA features both left-truncation-and-right-censorship and non-simple random sampling in search of survival factors. To see how the two data characteristics impact on Cox model coefficient estimates, the study adopts simulation and empirical analysis. Results from simulation shows that biased estimation in Cox model may occur when left truncation and the sampling design (stratified sampling) are neglected. In addition, empirical results also indicate that biased estimation in Cox model due to neglating left truncation may mislead the statistical inference.

Aalen, O. (1978). Nonparametric inference for a family of counting processes. The Annals of Statistics, 701-726.

Bender, R., Augustin, T., & Blettner, M. (2005). Generating survival times to simulate Cox proportional hazards models. Statistics in medicine, 24(11), 1713-1723.

Binder, D. A. (1992). Fitting Cox's proportional hazards models from survey data. Biometrika, 79(1), 139-147.

Carlin, B. P., & Hodges, J. S. (1999). Hierarchical proportional hazards regression models for highly stratified data. Biometrics, 55(4), 1162-1170.

Cox, D.R. & Snell, E.J. (1968). A general definition of residuals (with Discussion). J. Roy. Statist, Soc. B 30, 248-275.

Cox, D.R. (1972). Regression Models and Life Tables. Journal of the Royal Statistical Society, Series B34, 187-220.

Cox, D. R. (2007). Applied statistics: a review. The Annals of Applied Statistics, 1(1), 1-16.

Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 222, 309-368.

Heeringa, S. G., West, B. T., & Berglund, P. A. (2010). Applied survey data analysis: CRC Press.

Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American statistical association, 53(282), 457-481.

Kish, L. (1965). Survey sampling.

Klein, J., & Moeschberger, M. (2003). Survival analysis: statistical methods for censored and truncated data. Springer, New York.

Liao, H.-W. (1998). A simulation study of estimators in stratified proportional hazards models. In.

Lin, D. (2000). On fitting Cox's proportional hazards models to survey data. Biometrika, 87(1), 37-47.

Nelson, W. B. (2005). Applied life data analysis (Vol. 577): John Wiley & Sons.

Neyman, J. (1934). On the two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. Journal of the Royal Statistical Society, 97(4), 558-625.

Sterba, S. K. (2009). Alternative model-based and design-based frameworks for inference from samples to populations: From polarization to integration. Multivariate behavioral research, 44(6), 711-740.

侯佩君. (2011). 複雜抽樣調查的資料分析及實務應用—以 SAS, STATA 為例✽. 調查研究-方法與應用(25), 90-140.

孫傳凱. (2009). 婚姻與健康--台灣老人實證研究; Marriage and Health--the Emprical Study of the Elderly in Taiwan. 國立中央大學圖書館,

李宗派. (2007a). 老化概念 (Ⅰ): 生物科學之老化理論. 臺灣老人保健學刊, 3(2), 1-24.

李宗派. (2007b). 老化概念 (Ⅱ) 行為科學之老化理論與老化理論研究趨勢. 臺灣老人保健學刊, 3(2), 25-61.

林正祥, & 劉士嘉. (2012). 影響台灣不同世代老人存活相關因子探討. 臺灣公共衛生雜誌, 31(6), 597-611.

林正祥, & 林惠生. (2006). 台灣地區高齡人口存活之相關因素探討. 臺灣公共衛生雜誌, 25(5), 351-362.

林正祥, & 鄭維芬. (2011). 台灣地區老人教育程度差異對死亡率影響探討.

黃于庭. (2010). 台灣地區中老年身心社會生活狀況長期追蹤調查系列之存活分析. 成功大學統計學系學位論文, 1-85.