Multiple Imputation for Recurrent Events With Off‐Risk Periods

When observation of recurrent events ends before the planned follow‐up time, conclusions may depend on untestable assumptions about outcomes during the unobserved period. This is especially challenging for recurrent outcomes such as hospitalizations or infections, for which each event creates a temporary period during which a new event cannot occur and at‐risk time stops accruing. In such settings, multiple imputation must jointly determine future event counts and future at‐risk exposure. This paper proposes an off‐risk‐aware extension of controlled multiple imputation that simulates post‐dropout trajectories in calendar time while allowing exposure to accrue only during on‐risk intervals. Standard assumptions, including missing at random and jump‐to‐reference, are implemented by modifying only the post‐dropout rate assignment while leaving the exposure‐generation mechanism unchanged. In simulation, missing‐at‐random imputation closely matched direct likelihood, whereas jump‐to‐reference progressively attenuated the treatment effect toward the null as missingness increased. In the rhDNase illustration, missing‐at‐random imputation again yielded results very close to direct likelihood, while jump‐to‐reference produced only modest attenuation. The method provides a practical sensitivity‐analysis framework for trials in which recurrent events temporarily remove participants from risk, helping align missing‐data assumptions, outcome generation, and analysis on the at‐risk time scale.