Article
A New Parametric Accelerated Failure Time Model for Semi-Competing Risk Data
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Authors
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Antoniya Dineva
- Universität Bielefeld, Medizinische Fakultät OWL, Biostatistik und Medizinische Biometrie, Bielefeld, Germany
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Oliver Kuß
- Deutsches Diabetes-Zentrum (DDZ), Leibniz-Zentrum für Diabetes-Forschung an der Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
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Annika Hoyer
- Universität Bielefeld, Medizinische Fakultät OWL, Biostatistik und Medizinische Biometrie, Bielefeld, Germany
| Published: | September 15, 2023 |
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Outline
Text
In cohort studies, the occurrence of a specific disease is often of main interest. For proper modeling, death as a competing risk should be accounted for. Especially, the “semi-competing” character of the data has to be acknowledged: Disease occurrence (the non-terminal event) can be observed before death (the terminal event), but not vice versa. Hence, the terminal event might censor the non-terminal event, but remains observable if the non-terminal event occurs first [1]. The underlying setting can be described by an illness-death-model incorporating transitions between the three states “healthy”, “diseased” and “dead”. In recent publications, fitting a Cox frailty model for each transition is suggested [2], [3], [4]. An appealing alternative that hasn’t gained a lot of attention yet is fitting an accelerated failure time model (AFT) instead.
This work focuses on filling up this gap by developing a new method specified by accelerated failure time (AFT) models for each of the three transitions. The major advantage of this model is its intuitive and straightforward interpretation based on the survival instead of the hazard function, facilitating communication of results.
We propose a parametric approach by assuming a Weibull distribution for the event times for each transition. This leads to three Weibull distributions, modelling the time until disease onset, the time until death of disease-free subjects, and the time until death after disease onset. To adjust for intra-individual correlations between time to disease occurrence and time to death, we add random effects to the linear predictor that connect the Weibull distributions leading finally to a trivariate model. We estimate parameters by maximum likelihood, additionally considering interval censoring of the non-terminal event times. Furthermore, left truncation is incorporated to account for the delayed entry into the study cohort.
The model is illustrated using data from a large German cohort study, focusing on the occurrence of diabetes as a non-terminal event. Our model leads to plausible results, indicating that people with diabetes die earlier compared to people without diabetes.
The authors declare that they have no competing interests.
The authors declare that an ethics committee vote is not required.
References
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- Fine JP, Jiang H, Chappell R. On semi-competing risks data. Biometrika. 2001;88(4):907-919.
- 2.
- Lee C, Gilsanz P, Haneuse S. Fitting a shared frailty illness-death model to left-truncated semi-competing risks data to examine the impact of education level on incident dementia. BMC Med Res Methodol. 2021;21(1):18.
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- Xu J, Kalbfleisch JD, Tai B. Statistical analysis of illness-death processes and semicompeting risks data. Biometrics. 2010;66(3):716-25.
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- Gorfine M, et al. Marginalized frailty-based illness-death model: application to the UK-Biobank survival data. Journal of the American Statistical Association. 2021;116(535):1155-1167.
