結合機器學習的特徵點比例風險模式的半競爭風險資料動態預測

Abstract

在長期追蹤研究中，利用電子健康紀錄 (electronic health record) 準確預測慢性病患者的預後是一項重要的精準醫學議題。在慢性病的長期病程中，首次的復發事件 (recurrent event) 為影響病患存活的重要生物標誌 (biomarker)。而在存活資料中若包含生物標誌事件（如，首次復發）資訊，以及可能的預後因子，此種資料結構即為半競爭風險資料 (semi-competing risks data)。特徵點比例風險模式可在不同的特徵時間點 (landmark times) 納入隨時間變動的共變數資訊，常使用來進行動態存活預測。本研究利用所有不同特徵時間點下半競爭風險資料之子集合組成為堆疊競爭風險資料集，進行動態存活預測。在每個特徵時間點之子集合中，病患可被分為是否發生標誌事件兩組，且只有發生標誌事件的病患才會有標誌事件時間做為預測因子。隨機存活森林是一種常用於預測的機器學習方法，但卻無法直接用於堆疊半競爭風險資料集。因此，我們將結合機器學習方法與特徵點比例風險模式，發展針對堆疊半競爭風險資料集之資料結構之三階段模式建構方法，以進行動態存活預測。於第一階段，我們使用隨機存活森林篩選重要變數。第二階段則基於第一階段被篩選出的重要變數，使用單棵存活樹得到分類資訊，並且以存活樹所得連續型變數的切點作為平滑曲線 (splines) 的節點 (knots)，使得第三階段建構之特徵點比例風險模式能更具彈性。因此於第三階段，我們結合在每個特徵時間點的標誌事件狀態以及第二階段得到的分群資訊建構特徵點比例風險模式，以符合資料結構之動態存活預測。在模擬部分，我們考慮由兩種不同的時間相依比例風險模式以及雙變數對數常態模式生成資料之標誌事件時間和存活時間，並且以 AUC、C-index 和 Brier分數評估本研究所提出的各個特徵點比例風險模式以及隨機存活森林之動態存活預測。有限模擬之結果顯示我們所提出之三階段動態預測方法有良好的表現，特別是在雙變數對數常態模式情境況下，整體動態預測表現尤佳。

It is an important issue of precision medicine to accurately predict the prognosis of patients with chronic diseases in longitudinal follow-up studies using electronic health records. In the long-term course of a chronic disease, the first recurrent event is a key biomarker affecting the patient’s survival. The survival data including the information of the first recurrent events as the biomarker events and potential prognostic factors are referred to as semi-competing risks data. For the dynamic survival prediction, landmark proportional hazards modeling approach is often used to include the information of time-varying covariates at different landmark times. In this study, we consider the stacked semi-competing risks data across different landmark times. In such data set, patients at each landmark time are categorized into two groups, with and without the biomarker event, and the time to biomarker event can be used as a predictor only for the patient with biomarker event. Random survival forest is a popular machine learning method for prediction but cannot be directly used for the stacked semi-competing risks data. We integrate the machine learning tools and landmark proportional hazards modeling approach to develop a three-stage model construction method for dynamic survival prediction based on semi-competing data. In the first stage, we use the random survival forest to select important covariates. In the second stage, a classification tree is adopted to obtain the classification information based the selected covariates in the first stage. The cut points for continuous covariates in the second stage will be used as the knots of splines in these covariates so that their flexible trends are incorporated into the landmark models in the third stage. The third stage is to construct the landmark proportional hazards models by combining the status of biomarker event at each landmark time and the grouping information in the second stage for dynamic survival prediction to be consistent with the data structure. In simulation study, we consider that the times to biomarker event and death are generated from two different time-dependent proportional hazards models and one bivariate log-normal model. The AUC, C-index and Brier score are used to evaluate the performance of dynamic survival prediction based on the landmark proportional hazards models from the proposed methods and random survival forest. The limited simulation results show that the proposed three-stage dynamic prediction method performs well, especially in the bivariate log-normal model scenario.