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.