Partitioning Time in Target Trial Emulation

In target trial emulation, the treatment strategies that patients follow are inferred from the treatments they actually receive in routine care. However, in most settings, the outcome may preclude the observation of planned treatment, giving rise to immortal time bias through misclassification of treatment strategy, while markers of treatment response may influence subsequent treatment decisions, giving rise to time-varying confounding. A key step toward unbiased treatment effect estimation is to partition follow-up into sufficiently short time intervals to unfold the feedback relationships involving treatment and represent the resulting causal relations with a directed acyclic graph. In this study, we present the possible within-interval causal orderings induced by this partitioning, discuss their causal implications, and assess their plausibility across clinical settings. For each causal ordering, we derive the corresponding g-formula. Using ancestral multi-world networks and simulations, we show that the standard cloning-censoring-weighting estimator is invalid when treatment affects the outcome within a time interval, and we propose a modified version of the method that restores its validity in this setting. Finally, we analyze the consequences of choosing time intervals that are either excessively wide or excessively narrow, thereby formally establishing the need for time partitioning and providing practical guidance for selecting an appropriate partition based on the clinical setting.