CAUSAL INFERENCE FOR SURVIVAL OUTCOMES WITH MULTIPLE CAUSES

Causal inference is widely used in modern statistical research. By introducing causal inference methods to survival analysis, we are able to obtain the causal relationship between variables. In this thesis, we introduce the background, history and basic concepts of causal inference and survival analysis, respectively. In traditional causal inference, randomized controlled trial is the golden standard to claim causality. For observational data, four assumptions need to be made to get causal relationships. The most important one is the conditional exchangeability assumption, which requires that there is no unobserved confounder. It is a very strong assumption and is untestable. The deconfounder algorithm enables us to perform causal inference on observational data based on a weaker assumption - assuming there is no unobserved single-cause confounder. The algorithm first captures the joint distribution of the observed causes with a latent variable model, and then infer the value of the latent variable for each individual. The inferred latent variable would be used as a substitute for unobserved confounders in subsequent models to perform causal inferences. In this thesis, we propose the multi-cause Cox regression model which connects the deconfounder algorithm and traditional Cox model. While the regression coefficients in traditional Cox model only describe the statistical association between covariates and hazard rate, the regression coefficients in our multi-cause Cox regression model more closely represent the causal relationship. The performance of the proposed model is demonstrated by studies on a simulated dataset as well as a real dataset. Compared with the traditional Cox model, we find that the prediction accuracy by using the multi-cause Cox regression model is higher. This indicates that the multi-cause Cox regression model is able to reduce the negative impact of unobserved multi-cause confounders and capture the causal relationships more accurately in survival data.

在现代统计研究中，因果推断的分析方法被广泛应用。在分析生存数据的过程 中通过引入因果推断的分析方法可以得到变量间的因果关系。在本文中，我们分别 介绍了因果推断和生存分析的背景，历史和基本概念。在传统因果推断中，随机对 照实验是获得因果关系的金标准，而对于观测数据，需要基于四个假设才能通过对 数据的直接分析得到因果关系，其中一个重要的假设是条件可交换性，即假设不存 在未被观测到的混淆因子，此假设很强并且无法检验其合理性。使用 deconfounder 算法使得我们能够基于较弱的假设 (不存在未被观测到的单原因混淆因子)，对观 测数据进行分析得到因果关系。此算法是利用潜变量模型捕捉所观测到的因子间 的联合分布，然后使用该潜变量模型为每个个体推断潜变量的值，再将推断得到 的潜变量作为未观测混淆因子的替代加入到后续模型中，得到因果关系。具体而 言，在本文中我们提出了结合 deconfounder 算法与 Cox 模型的多原因 Cox 回归模 型，对比传统 Cox 模型中回归系数仅描述协变量与生存风险在统计上的相关关系， 此模型得到的回归系数则更接近协变量与生存风险的因果关系。最后，我们分别 在模拟数据和真实数据中运用该模型，并与传统 Cox 模型的结果进行对比，发现 多原因 Cox 回归模型的预测精度较高，这说明我们提出的模型能够降低未观测到 的多原因混淆因子带来的负面影响，更准确地捕捉生存数据中蕴含的因果关系。

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