時變係數比例風險模型之貝氏推論

Bayesian Inference of the Time-Varying Coefficient Proportional Hazards Model

鄭麗雪(Li-Hsueh Cheng)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/博士(2020年)

https://doi.org/10.6840/cycu202000061

摘要

本文提出了時變係數比例風險模型的貝氏估計，且探討了不同的設限資
料，包括右設限資料，case I 區間設限資料和 case II 區間設限資料。在模型中，我們的事前分佈是建立在時變係數的分段常數和基線累積風險的伯氏多項式上，而且也建立了事後模型的 Kullback-Leibler divergence 型式的一致性。我們藉由模擬計算對該方法進行了評價。此外，透過區間設限的血友病資料分析給出該方法的例證。

關鍵字

時變係數 ； 設限存活資料 ； 伯氏多項式 ； 比例風險模型

並列摘要

In this thesis, we propose a Bayesian estimation of the time-varying coefficient proportional hazards model with various censored survival data, including right
censored, case I interval-censored, and case II interval-censored data. In the model, we consider a piecewise constant prior for the time-varying coefficient and a Bernstein polynomial based prior for the cumulative aseline hazard. The Kullback-Leibler divergence type consistency of the posterior model is established and the performance of the proposed method is evaluated via simulations. In ddition, the illustration of the proposed method is given by an interval-censored hemophilia data analysis.

並列關鍵字

Time-varying Coefficient ； Censored Survival Data ； Bernstein polynomial ； Proportional hazards model

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