A Landmark‐Turnbull Estimator for Non‐Markovian Illness‐Death Models With Interval‐Censored Observations

Handling interval‐censored data poses significant challenges, particularly in multi‐state models where transition times are uncertain and computational complexity is high. This study investigates the use of landmark‐based estimators tailored for interval‐censored settings, with a particular focus on three‐state illness–death models. We propose two estimators: the Landmark‐Turnbull (LMTB) estimator, which integrates the Turnbull method for nonparametric survival estimation, and the Interval Landmark (ILM) estimator, a simplified alternative that uses midpoint imputation within the landmarking framework. Both approaches allow the estimation of transition probabilities without imposing the Markov assumption, thereby offering greater flexibility and interpretability in realistic clinical settings. The performance of the proposed estimators is compared with the standard Interval Aalen–Johansen (IAJ) estimator. Simulation studies and an application to synthetic data inspired by colon cancer patient trajectories demonstrate that LMTB yields more accurate estimates for long‐term transitions, while ILM is preferable for short‐term predictions due to its lower variance and computational simplicity.