Phase-type frailty models: A flexible approach to modeling unobserved heterogeneity in survival analysis
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909556359036928 |
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| author | Yslas, Jorge |
| author_facet | Yslas, Jorge |
| contents | Frailty models are essential tools in survival analysis for addressing unobserved heterogeneity and random effects in the data. These models incorporate a random effect, the frailty, which is assumed to impact the hazard rate multiplicatively. In this paper, we introduce a novel class of frailty models in both univariate and multivariate settings, using phase-type distributions as the underlying frailty specification. We investigate the properties of these phase-type frailty models and develop expectation-maximization algorithms for their maximum-likelihood estimation. In particular, we show that the resulting model shares similarities with the Gamma frailty model, has closed-form expressions for its functionals, and can approximate any other frailty model. Through a series of simulated and real-life numerical examples, we demonstrate the effectiveness and versatility of the proposed models in addressing unobserved heterogeneity in survival analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_13142 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Phase-type frailty models: A flexible approach to modeling unobserved heterogeneity in survival analysis Yslas, Jorge Statistics Theory Probability Frailty models are essential tools in survival analysis for addressing unobserved heterogeneity and random effects in the data. These models incorporate a random effect, the frailty, which is assumed to impact the hazard rate multiplicatively. In this paper, we introduce a novel class of frailty models in both univariate and multivariate settings, using phase-type distributions as the underlying frailty specification. We investigate the properties of these phase-type frailty models and develop expectation-maximization algorithms for their maximum-likelihood estimation. In particular, we show that the resulting model shares similarities with the Gamma frailty model, has closed-form expressions for its functionals, and can approximate any other frailty model. Through a series of simulated and real-life numerical examples, we demonstrate the effectiveness and versatility of the proposed models in addressing unobserved heterogeneity in survival analysis. |
| title | Phase-type frailty models: A flexible approach to modeling unobserved heterogeneity in survival analysis |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2103.13142 |