Efficient Estimation for Functional Accelerated Failure Time Model
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910322451808256 |
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| author | Liu, Changyu Su, Wen Liu, Kin-Yat Yin, Guosheng Zhao, Xingqiu |
| author_facet | Liu, Changyu Su, Wen Liu, Kin-Yat Yin, Guosheng Zhao, Xingqiu |
| contents | We propose a functional accelerated failure time model to characterize effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient estimation of model parameters, we develop a sieve maximum likelihood approach where parametric and nonparametric coefficients are bundled with an unknown baseline hazard function in the likelihood function. Not only do the bundled parameters cause immense numerical difficulties, but they also result in new challenges in theoretical development. By developing a general theoretical framework, we overcome the challenges arising from the bundled parameters and derive the convergence rate of the proposed estimator. Furthermore, we prove that the finite-dimensional estimator is $\sqrt{n}$-consistent, asymptotically normal and achieves the semiparametric information bound. The proposed inference procedures are evaluated by extensive simulation studies and illustrated with an application to the sequential organ failure assessment data from the Improving Care of Acute Lung Injury Patients study. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_05395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient Estimation for Functional Accelerated Failure Time Model Liu, Changyu Su, Wen Liu, Kin-Yat Yin, Guosheng Zhao, Xingqiu Methodology We propose a functional accelerated failure time model to characterize effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient estimation of model parameters, we develop a sieve maximum likelihood approach where parametric and nonparametric coefficients are bundled with an unknown baseline hazard function in the likelihood function. Not only do the bundled parameters cause immense numerical difficulties, but they also result in new challenges in theoretical development. By developing a general theoretical framework, we overcome the challenges arising from the bundled parameters and derive the convergence rate of the proposed estimator. Furthermore, we prove that the finite-dimensional estimator is $\sqrt{n}$-consistent, asymptotically normal and achieves the semiparametric information bound. The proposed inference procedures are evaluated by extensive simulation studies and illustrated with an application to the sequential organ failure assessment data from the Improving Care of Acute Lung Injury Patients study. |
| title | Efficient Estimation for Functional Accelerated Failure Time Model |
| topic | Methodology |
| url | https://arxiv.org/abs/2402.05395 |