Sparse Estimation of Cox Proportional Hazards Models via Approximated Information Criteria

Abstract

Summary We propose a new sparse estimation method for Cox (1972) proportional hazards models by optimizing an approximated information criterion. The main idea involves approximation of the ℓ0 norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularisation by borrowing strength from both. It mimics the best subset selection using a penalised likelihood approach yet with no need of a tuning parameter. We further reformulate the problem with a reparameterisation step so that it reduces to one unconstrained nonconvex yet smooth programming problem, which can be solved efficiently as in computing the maximum partial likelihood estimator (MPLE). Furthermore, the reparameterisation tactic yields an additional advantage in terms of circumventing post-selection inference. The oracle property of the proposed method is established. Both simulated experiments and empirical examples are provided for assessment and illustration.

Analyzing Job Tenure Factors in Private and Public Companies in Albania by Using Cox Proportional Hazards Model

“…Su, Wijayasinghe, Fan, and Zhang [25] elaborated Minimizing Approximated Information Criteria (MIC) method to handle sparse estimation of Cox PH models. This model enjoys the advantages of best subset selection (BSS) algorithm and the regularization one.…”

coxphMIC: An R Package for Sparse Estimation of Cox Proportional Hazards Models via Approximated Information Criteria

“…In order for the user to be able to inspect the convergence and other detailed info of the optimization algorithms, we also output two objects opt.global and opt.local, which result from the global (SANN by default) and local optimization (BFGS by default) algorithms. The above results are presented as Table 4 in Su et al (2016). In this example, MIC started with MPLE given by the first column named beta0.…”

“…Beside the computational burden, both methods face the post-selection inference challenge. A new technique is developed by Su et al (2016) on the basis of Su (2015) for conducting sparse estimation of Cox PH models to help address the aforementioned deficiencies.…”

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In this paper, we describe an R package named coxphMIC, which implements the sparse estimation method for Cox proportional hazards models via approximated information criterion (Su et al, 2016). The developed methodology is named MIC which stands for "Minimizing approximated Information Criteria".

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A surrogate ℓ0 sparse Cox's regression with applications to sparse high‐dimensional massive sample size time‐to‐event data

“…Third, sHDMSS data presents a critical barrier to the application of existing sparse survival regression methods, since most current methods and standard software become inoperable for large data sets due to high computational costs and large memory requirements. Although many sparse survival regression methods are available, [3][4][5][6][7][8][9][10] to the best of our knowledge, only LASSO, Elastic Net 11 and ridge regression have been adapted to fit sHDMSS time-to-event data. In particular, Mittal et al 12 developed a tool, named CYCLOPS, for fitting LASSO and ridge Cox regression with sHDMSS time-to-event data by storing data in a sparse format, exploiting sparsity in the data and partial likelihood, and using multicore threading and vector processing, along with other high-performance computing techniques, which delivers > 10-fold speedup 12 over its competitors.…”