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A Spline-Based Framework for the Flexible Modelling of Continuously Observed Multistate Survival Processes

Eletti, A., Marra, G. & Radice, R. ORCID: 0000-0002-6316-3961 (2023). A Spline-Based Framework for the Flexible Modelling of Continuously Observed Multistate Survival Processes. Statistical Modelling: An International Journal, 23(5-6), pp. 495-509. doi: 10.1177/1471082x231176120


Multistate modelling is becoming increasingly popular due to the availability of richer longitudinal health data. When the times at which the events characterising disease progression are known, the modelling of the multistate process is greatly simplified as it can be broken down in a number of traditional survival models. We propose to flexibly model them through the existing general link-based additive framework implemented in the R package GJRM. The associated transition probabilities can then be obtained through a simulation-based approach implemented in the R package mstate, which is appealing due to its generality. The integration between the two is seamless and efficient since we model a transformation of the survival function, rather than the hazard function, as is commonly found. This is achieved through the use of shape constrained P-splines which elegantly embed the monotonicity required for the survival functions within the construction of the survival functions themselves. The proposed framework allows for the inclusion of virtually any type of covariate effects, including time-dependent ones, while imposing no restriction on the multistate process assumed. We exemplify the usage of this framework through a case study on breast cancer patients.

Publication Type: Article
Additional Information: © 2023 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 License ( which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access page (
Publisher Keywords: additive predictor; multistate process; shape constrained P-splines; survival analysis; transition probabilities
Subjects: H Social Sciences > HA Statistics
Departments: Bayes Business School > Actuarial Science & Insurance
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