長度偏差和區間設限資料分析是生存分析的一個重要課題，許多方法已被開發用來處理這種複雜的資料結構。然而現有的方法側重於低維資料，並假定協變數是精確測量的，而在應用中經常會收集到受測量誤差影響的高維數據。在本
篇論文中，我們提出了一種有效的推論方法來處理加速失效時間模型下協變數存在測量誤差的高維長度偏差和區間設限的生存資料。我們採用 SIMEX 方法來修正測量誤差的影響，並提出提升演算法來進行變數選擇和估計。所提出的方法能夠處理協變數的維度大於樣本量的情況，並能適應不同的協變數分佈。

Analysis of length-biased and interval-censored data is an important topic in survival analysis, and many methods have been developed to address this complex data structure. However, existing methods focus on low-dimensional data and assume the covariates to be precisely measured, while high-dimensional data subject to measurement error are frequently collected in applications. In this thesis, we explore a valid inference method for handling high-dimensional length-biased and interval-censored survival data with measurement error in covariates under the accelerated failure time model. We primarily employ the SIMEX method to correct for measurement error effects and propose the boosting procedure to do variable selection and estimation. The proposed method is able to handle the case that the dimension of covariates is larger than the sample size and enjoys appealing features that the distributions of the covariates are left unspecified.

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