The role of discretization scales in causal inference with continuous-time treatment
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离散化时间尺度在连续时间处理因果推断中的作用
- 研究问题
- 当真实处理在连续时间变化，却按离散时间记录或分析时，时间尺度如何改变因果目标，并产生无法靠样本增大消除的偏差？
- 方法与思路
- 作者定义连续时间与离散化处理目标之间的识别偏差，在一类线性随机连续时间过程中分析 g-formula，并提出启发式敏感性度量。
- 材料陈述的贡献
- 摘要称识别偏差即使在无限条纵向轨迹下仍可存在，揭示重复测量有限时离散化的重要性，并建议报告相关敏感性指标。
- 阅读关注点
- 应核对连续与离散干预的对应关系、线性随机过程的具体条件，以及启发式度量能否反映目标差异及其适用范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实。摘要未给出偏差公式、消失条件或敏感性度量定义，不能外推至所有过程。
原文摘要
There are well-established methods for identifying the causal effect of a time-varying treatment applied at discrete time points. However, in the real world, many treatments are continuous or have a finer time scale than the one used for measurement or analysis. While researchers have investigated the discrepancies between estimates under varying discretization scales using simulations and empirical data, it is still unclear how the choice of discretization scale affects causal inference. To address this gap, we present a framework to understand how discretization scales impact the properties of causal inferences about the effect of a time-varying treatment. We introduce the concept of "identification bias", which is the difference between the causal estimand for a continuous-time treatment and the purported estimand of a discretized version of the treatment. We show that this bias can persist even with an infinite number of longitudinal treatment-outcome trajectories. We specifically examine the identification problem in a class of linear stochastic continuous-time data-generating processes and demonstrate the identification bias of the g-formula in this context. Our findings indicate that discretization bias can significantly impact empirical analysis, especially when there are limited repeated measurements. Therefore, we recommend that researchers carefully consider the choice of discretization scale and perform sensitivity analysis to address this bias. We also propose a simple and heuristic quantitative measure for sensitivity concerning discretization and suggest that researchers report this measure along with point and interval estimates in their work. By doing so, researchers can better understand and address the potential impact of discretization bias on causal inference.