February 11, 2026
The authors in this article have presented a stepwise guidance on how to extend the simple time-to-first event model to complex multistate methodology, where multiple events are incorporated. They considered non- and semiparametric methods and show how they are related. Special attention is given to the prerequisites of the models, for example, the Markov property,
They state that this work aims to give step-by-step guidance for the applied researcher on how standard time-to-first event analysis can be extended to multiple time-to-event analysis, giving special attention to the underlying model assumptions.
They extended competing risks to multistate models. They began with the smallest three-state model, the illness–death model, and then extended it to a progressive model. They estimated the transition hazard in a Markov multistate model. They state the Markov assumption means that the transition hazard does not depend on previous states, the number of previous states, nor on previous event times like the entry time into the current state. The dependence on (the number of) previous states or the entry time into the current state can be tested, for example, by including the number of previous states in a regression model as a covariate. For semiparametric treatment estimation, one can use the model by Prentice–Williams–Peterson (PWP), which is an extension of the AG model by additionally stratifying according to the number of previous events (e.g., hospitalizations). In the illness–death model, we are also interested in the transition probabilities. Here, any transition probability depends on all transition hazards.
They ran simulations with Markovian illness-death models and non-Markovian illness-death models, where both of these had random censoring. Finally they ran both a Markovian and non-Markovian illness-death model with state-dependent censoring, even though this type of censoring tries to destroy the statistical i.i.d. assumption of the multistate process. A simulation study showed the importance of considering model assumptions. A real data example was used for illustration.
If, in a randomized trial, the decision is to consider a recurrent endpoint as primary, they considered an analysis based on partly conditional transition rates as a natural choice. However, more research is needed on how event-driven censoring may potentially impact such an analysis. The multistate approach used in the present paper is quite generic.
Written by,
Usha Govindarajulu
Keywords: time-to-event, recurrent events, Andersen-Gill, PWP, semi-parametric, competing risks
References:
Schmeller S, Erdmann A, Beyersmann J, Angermann C, and Ozga A-K (2026) “The Challenge of Time-to-Event Analysis for Multiple Events: A Guided Tour From Time-to-First-Event to Recurrent Time-to-Event Analysis” Biometrical Journal. https://doi.org/10.1002/bimj.70107
https://onlinelibrary.wiley.com/cms/asset/811ade68-6fa4-4b6d-96cb-2584e92b8074/bimj70107-fig-0001-m.jpg