Graphical representation of survival curves in the presence of time-dependent categorical covariates with application to liver transplantation

Graphical representation of survival curves is often used to illustrate associations between exposures and time-to-event outcomes. However, when exposures are time-dependent, calculation of survival probabilities is not straightforward. Our aim was to develop a method to estimate time-dependent survival probabilities and represent them graphically. Cox models with time-dependent indicators to represent state changes were fitted, and survival probabilities were plotted using pre-specified times of state changes. Time-varying hazard ratios for the state change were also explored. The method was applied to data from the Adult-to-Adult Living Donor Liver Transplantation Cohort Study (A2ALL). Survival curves showing a ‘split’ at a pre-specified time <i>t</i> allow for the qualitative comparison of survival probabilities between patients with similar baseline covariates who do and do not experience a state change at time <i>t</i>. Time since state change interactions can be visually represented to reflect changing hazard ratios over time. A2ALL study results showed differences in survival probabilities among those who did not receive a transplant, received a living donor transplant, and received a deceased donor transplant. These graphical representations of survival curves with time-dependent indicators improve upon previous methods and allow for clinically meaningful interpretation.

生存曲线的可视化呈现常被用于阐明暴露因素与事件发生时间结局之间的关联。然而，当暴露因素为时变变量时，生存概率的计算并非易事。本研究旨在开发一种可估算时变生存概率并以可视化方式呈现的方法。本研究采用包含表征状态转变的时变指示变量的Cox模型（Cox Model）进行拟合，并基于预先设定的状态转变时间绘制生存概率曲线；同时还对状态转变对应的时变风险比开展了探索分析。本研究将该方法应用于成人活体肝移植队列研究（Adult-to-Adult Living Donor Liver Transplantation Cohort Study, A2ALL）的数据集。在预先设定的时间点t处呈现“分叉”特征的生存曲线，可用于定性比较基线协变量相似、且在时间t发生或未发生状态转变的患者群体间的生存概率差异。状态转变后时间的交互效应可通过可视化方式呈现，以反映风险比随时间的动态变化。A2ALL队列的研究结果显示，未接受肝移植、接受活体供肝移植以及接受尸体供肝移植的患者群体间生存概率存在显著差异。这类基于时变指示变量的生存曲线可视化方法相较于既往研究方法有所改进，且能够提供具有临床意义的解读价值。