We compare two multi-state modelling frameworks that can be used to represent dates of events following hospital admission for people infected during an epidemic. The methods are applied to data from people admitted to hospital with COVID-19, to estimate the probability of admission to intensive care unit, the probability of death in hospital for patients before and after intensive care unit admission, the lengths of stay in hospital, and how all these vary with age and gender. One modelling framework is based on defining transition-specific hazard functions for competing risks. A less commonly used framework defines partially-latent subpopulations who will experience each subsequent event, and uses a mixture model to estimate the probability that an individual will experience each event, and the distribution of the time to the event given that it occurs. We compare the advantages and disadvantages of these two frameworks, in the context of the COVID-19 example. The issues include the interpretation of the model parameters, the computational efficiency of estimating the quantities of interest, implementation in software and assessing goodness of fit. In the example, we find that some groups appear to be at very low risk of some events, in particular intensive care unit admission, and these are best represented by using ‘cure-rate’ models to define transition-specific hazards. We provide general-purpose software to implement all the models we describe in the flexsurv R package, which allows arbitrarily flexible distributions to be used to represent the cause-specific hazards or times to events.
Bibliographical noteFunding Information: This work was supported by the Medical Research Council programmes MRC_MC_UU_00002/11, MRC_MC_UU_00002/10 and MRC_MC_UU_00002/2. We are grateful to the Joint Modelling Cell and Epidemiology Cell at Public Health England for providing and discussing the CHESS data.
The authors received no financial support for the research, authorship and/or publication of this article.
Open Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) 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 (https://us.sagepub.com/en-us/nam/open-access-at-sage).
Publisher Copyright: © The Author(s) 2022.
Citation: Jackson CH, Tom BD, Kirwan PD, et al. A comparison of two frameworks for multi-state modelling, applied to outcomes after hospital admissions with COVID-19. Statistical Methods in Medical Research. 2022;31(9):1656-1674. doi:10.1177/09622802221106720
- Competing risks
- cause-specific hazard
- cumulative incidence