Penalized full likelihood approach to variable selection for Cox’s regression model under nested case–control sampling

Lifetime Data Analysis volume 26, pages292–314(2020)Cite this article

Abstract

Assuming Cox’s regression model, we consider penalized full likelihood approach to conduct variable selection under nested case–control (NCC) sampling. Penalized non-parametric maximum likelihood estimates (PNPMLEs) are characterized by self-consistency equations derived from score functions. A cross-validation method based on profile likelihood is used to choose the tuning parameter within a family of penalty functions. Simulation studies indicate that the numerical performance of (P)NPMLE is better than weighted partial likelihood in estimating the log-relative risk and in identifying the covariates and the model, under NCC sampling. LASSO performs best when cohort size is small; SCAD performs best when cohort size is large and may eventually perform as well as the oracle estimator. Using the SCAD penalty, we establish the consistency, asymptotic normality, and oracle properties of the PNPMLE, as well as the sparsity property of the penalty. We also propose a consistent estimate of the asymptotic variance using observed profile likelihood. Our method is illustrated to analyze the diagnosis of liver cancer among those in a type 2 diabetic mellitus dataset who were treated with thiazolidinediones in Taiwan.

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Acknowledgements

Funding was provided by Ministry of Science and Technology, Taiwan (Grant No. MOST-105-2319-B400-002). We are very grateful to the AE and referees, whose valuable comments and suggestions led to significant improvement of this paper.

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Affiliations

  1. Division of Biostatistics and Bioinformatics, Institute of Population Health Science, National Health Research Institutes, 35, Keyan Rd., Zhunan Town, Miaoli County, 35053, Taiwan

    Jie-Huei Wang, I-Shou Chang & Chao Agnes Hsiung

  2. Institute of Statistical Science, Academia Sinica, 128, Academia Rd., Section 2, Nankang, Taipei, 11529, Taiwan

    Jie-Huei Wang & Chun-Hao Pan

  3. National Institute of Cancer Research, National Health Research Institutes, 35, Keyan Rd., Zhunan Town, Miaoli County, 35053, Taiwan

    I-Shou Chang

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  1. Jie-Huei Wang
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  2. Chun-Hao Pan
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  3. I-Shou Chang
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  4. Chao Agnes Hsiung
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Correspondence to I-Shou Chang.

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Wang, J., Pan, C., Chang, I. et al. Penalized full likelihood approach to variable selection for Cox’s regression model under nested case–control sampling. Lifetime Data Anal 26, 292–314 (2020). https://doi.org/10.1007/s10985-019-09475-z

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Keywords

  • Nested case–control sampling
  • Oracle property
  • PNPMLE
  • SCAD