Synthetic control (SC) methods have gained rapid popularity in economics recently, where they have been applied in the context of inferring the effects of treatments on standard continuous outcomes assuming linear input-output relations. In medical applications, conversely, survival outcomes are often of primary interest, a setup in which both commonly assumed data-generating processes (DGPs) and target parameters are different. In this paper, we therefore investigate whether and when SCs could serve as an alternative to matching methods in survival analyses. We find that, because SCs rely on a linearity assumption, they will generally be biased for the true expected survival time in commonly assumed survival DGPs -- even when taking into account the possibility of linearity on another scale as in accelerated failure time models. Additionally, we find that, because SC units follow distributions with lower variance than real control units, summaries of their distributions, such as survival curves, will be biased for the parameters of interest in many survival analyses. Nonetheless, we also highlight that using SCs can still improve upon matching whenever the biases described above are outweighed by extrapolation biases exhibited by imperfect matches, and investigate the use of regularization to trade off the shortcomings of both approaches.

翻译：合成控制方法近年来在经济学领域迅速普及，被用于推断标准连续型结果变量上的处理效应，且假设输入与输出之间呈线性关系。然而在医学应用中，生存结局通常是主要关注指标，其常见的数据生成过程与目标参数均与标准设定不同。本文旨在探究合成控制法能否以及在何种条件下可替代生存分析中的匹配方法。研究发现：由于合成控制法依赖线性假设，在常见的生存数据生成过程中，即使考虑采用加速失效时间模型等其他尺度上的线性化处理，其对真实期望生存时间的估计仍普遍存在偏倚。此外，合成控制单位分布的方差低于真实对照组，导致其分布汇总指标（如生存曲线）在多数生存分析中对目标参数存在偏倚。尽管如此，本文也指出，当上述偏倚小于不完美匹配所导致的外推偏倚时，合成控制法仍可改善匹配效果，并探讨了利用正则化方法在两种方法的缺陷之间进行权衡的策略。