Scalable likelihood-based estimation and variable selection for the Cox model with incomplete covariates
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929543608008704 |
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| author | Kwok, Ngok Sang Wong, Kin Yau |
| author_facet | Kwok, Ngok Sang Wong, Kin Yau |
| contents | Regression analysis with missing data is a long-standing and challenging problem, particularly when there are many missing variables with arbitrary missing patterns. Likelihood-based methods, although theoretically appealing, are often computationally inefficient or even infeasible when dealing with a large number of missing variables. In this paper, we consider the Cox regression model with incomplete covariates that are missing at random. We develop an expectation-maximization (EM) algorithm for nonparametric maximum likelihood estimation, employing a transformation technique in the E-step so that it involves only a one-dimensional integration. This innovation makes our methods scalable with respect to the dimension of the missing variables. In addition, for variable selection, we extend the proposed EM algorithm to accommodate a LASSO penalty in the likelihood. We demonstrate the feasibility and advantages of the proposed methods over existing methods by large-scale simulation studies and apply the proposed methods to a cancer genomic study. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_11482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalable likelihood-based estimation and variable selection for the Cox model with incomplete covariates Kwok, Ngok Sang Wong, Kin Yau Methodology Computation Regression analysis with missing data is a long-standing and challenging problem, particularly when there are many missing variables with arbitrary missing patterns. Likelihood-based methods, although theoretically appealing, are often computationally inefficient or even infeasible when dealing with a large number of missing variables. In this paper, we consider the Cox regression model with incomplete covariates that are missing at random. We develop an expectation-maximization (EM) algorithm for nonparametric maximum likelihood estimation, employing a transformation technique in the E-step so that it involves only a one-dimensional integration. This innovation makes our methods scalable with respect to the dimension of the missing variables. In addition, for variable selection, we extend the proposed EM algorithm to accommodate a LASSO penalty in the likelihood. We demonstrate the feasibility and advantages of the proposed methods over existing methods by large-scale simulation studies and apply the proposed methods to a cancer genomic study. |
| title | Scalable likelihood-based estimation and variable selection for the Cox model with incomplete covariates |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2410.11482 |