Parametric Landmark Estimation of the Transition Probabilities in Survival Data with Multiple Events

Multi-state models are a useful tool for analyzing survival data with multiple events. The transition probabilities play an important role in these models since they allow for long-term predictions of the process in a simple and summarized manner. Recent papers have used the idea of subsampling to estimate these quantities, providing estimators with superior performance in the case of strong violations of the Markov condition. Subsampling, also referred to as landmarking, leads to small sample sizes and usually heavily censored data, which leads to estimators with higher variability. Here, we use the flexibility of the generalized gamma distribution combined with the same idea of subsampling to obtain estimators free of the Markov condition with less variability. Simulation studies show the good small sample properties of the proposed estimators. The proposed methods are illustrated using real data.