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arXiv · 2410.11482

Scalable likelihood-based estimation and variable selection for the Cox model with incomplete covariates

Ngok Sang Kwok·Kin Yau Wong
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Abstract

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.

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Ngok Sang Kwok, Kin Yau Wong. 2024-10-15. Scalable likelihood-based estimation and variable selection for the Cox model with incomplete covariates. https://arxiv.org/abs/2410.11482

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