Cox's proportional hazards (CPH) model is quite likely the most popular modeling technique in survival analysis. While the CPH model is able to represent a relationship between a collection of risks and their common effect, Bayesian networks have become an attractive alternative with an increased modeling power and far broader applications. Our paper focuses on a Bayesian network interpretation of the CPH model (BN-Cox). We provide a method of encoding knowledge from existing CPH models in the process of knowledge engineering for Bayesian networks. This is important because in practice we often have CPH models available in the literature and no access to the original data from which they have been derived. We compare the accuracy of the resulting BN-Cox model to the original CPH model, Kaplan-Meier estimate, and Bayesian networks learned from data, including Naive Bayes, Tree Augmented Naive Bayes, Noisy-Max, and parameter learning by means of the EM algorithm. BN-Cox model came out as the most accurate of all BN approaches and very close to the original CPH model. We study two approaches for simplifying the BN-Cox model for the sake of representational and computational efficiency: (1) parent divorcing and (2) removing less important risk factors. We show that removing less important risk factors leads to smaller loss of accuracy.

中文翻译：

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Cox 比例风险模型的贝叶斯网络解释

Cox 的比例风险 (CPH) 模型很可能是生存分析中最流行的建模技术。虽然 CPH 模型能够表示风险集合与其共同影响之间的关系，但贝叶斯网络已成为一种有吸引力的替代方案，具有增强的建模能力和更广泛的应用。我们的论文侧重于 CPH 模型 (BN-Cox) 的贝叶斯网络解释。我们在贝叶斯网络的知识工程过程中提供了一种从现有 CPH 模型中编码知识的方法。这很重要，因为在实践中，我们经常在文献中提供 CPH 模型，但无法访问从中导出它们的原始数据。我们将生成的 BN-Cox 模型与原始 CPH 模型、Kaplan-Meier 估计的准确性进行比较，以及从数据中学习的贝叶斯网络，包括朴素贝叶斯、树增强朴素贝叶斯、Noisy-Max，以及通过EM算法进行参数学习。BN-Cox 模型是所有 BN 方法中最准确的，并且非常接近原始 CPH 模型。为了代表性和计算效率，我们研究了两种简化 BN-Cox 模型的方法：（1）父母离婚和（2）去除不太重要的风险因素。我们表明，去除不太重要的风险因素会导致精度损失较小。为了代表性和计算效率，我们研究了两种简化 BN-Cox 模型的方法：（1）父母离婚和（2）去除不太重要的风险因素。我们表明，去除不太重要的风险因素会导致精度损失较小。为了代表性和计算效率，我们研究了两种简化 BN-Cox 模型的方法：（1）父母离婚和（2）去除不太重要的风险因素。我们表明，去除不太重要的风险因素会导致精度损失较小。