Abstract
We present a hierarchical frailty model based on distributions derived from non-negative Lévy processes. The model may be applied to data with several levels of dependence, such as family data or other general clusters, and is an alternative to additive frailty models. We present several parametric examples of the model, and properties such as expected values, variance and covariance. The model is applied to a case-cohort sample of age at onset for melanoma from the Swedish Multi-Generation Register, organized in nuclear families of parents and one or two children. We compare the genetic component of the total frailty variance to the common environmental term, and estimate the effect of birth cohort and gender.
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Acknowledgements
We are grateful to Professor Yudi Pawitan at Karolinska Institutet in Stockholm, Sweden, for getting access to the melanoma data and discussions on the paper. We also wish to thank the associate editor and the referee for valuable comments. Marion Haugen was supported by Statistics for Innovation (sfi)2, project number 460739.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Moger, T.A., Haugen, M., Yip, B.H.K. et al. A hierarchical frailty model applied to two-generation melanoma data. Lifetime Data Anal 17, 445–460 (2011). https://doi.org/10.1007/s10985-010-9188-3
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DOI: https://doi.org/10.1007/s10985-010-9188-3