競爭風險資料在首次觸及時間模型的探討

The Discussion of First-Hitting-Time Models with Competing Risks Data

林恒君(Heng-Jun Lin)

指導教授 ： 陳蔓樺

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2023年)

https://doi.org/10.6846/TKU.2023.00106

摘要

隨著現今醫學發展的進步，存活分析被廣泛地應用於醫學領域中。而在進行醫學研究時，並非所有蒐集到的樣本皆為完整的資料，當僅能觀察到樣本部分的訊息，則稱為設限資料。另外，在進行存活分析時，競爭風險的存在是一個重要的問題。由於受試者在追蹤期間可能經歷許多不同的事件，因此有些受試者可能會經歷競爭事件，導致我們在研究期間內無法觀察到感興趣事件的發生。當資料存在競爭風險時，若是使用了忽略競爭風險之傳統方法來進行分析，可能會造成很大的偏誤。
本篇考慮在競爭風險情況下，將維納過程之首次觸及時間模型擴展於各類設限資料，其資料包含確切時間、左設限、區間設限，以及右設限資料。當時間資料服從逆高斯分配時，則適用此模型。在建立模型之概似方程式後，將計算出最大概似估計量，並利用費雪訊息矩陣求得估計參數值的標準誤。

關鍵字

設限資料 ； 競爭風險 ； 維納過程 ； 首次觸及時間模型 ； 費雪訊息矩陣

並列摘要

With the development of modern medicine, survival analysis is widely used in the medical field. When conducting medical research, not all collected samples are complete data. When part of the sample information can be observed, it is called censored data. Additionally, the presence of competing risks is an important issue when performing survival analyses. Because subjects may occur many different events during the follow-up period, some subjects may occur competing events, preventing us from observing the occurrence of the event of interest during the study period. The traditional method ignoring competing risks exists, which may cause huge bias.
This paper considers the extension of the first touch time model of the Wiener process to various restricted data in the case of competing risks. Its data includes exact time, left limit, interval limit, and right limit data. This model is suggested when the time data follow the inverse Gaussian distribution. After establishing the approximate equation of the model, the maximum likelihood estimator will be calculated, and the standard error of the estimated parameter value will be obtained by using the Fisher information matrix.

並列關鍵字

Censored data ； Competing risk ； Wiener process ； First-hitting-time model ； Fisher information matrix

參考文獻

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