IDEAS home Printed from https://ideas.repec.org/a/wly/jnljps/v2025y2025i1n3808705.html

Relative Performance of Model Selection Criteria for Cox Proportional Hazards Regression Based on Kullback’s Symmetric Divergence

Author

Listed:
  • Clarisse Houénafa Dete
  • Bruno Enagnon Lokonon
  • Kossi Essona Gneyou
  • Marcel Senou
  • Romain Glèlè Kakaï

Abstract

The Cox proportional hazards model is one of the most used models to analyze time‐to‐event outcomes. The decision on the most suitable model for those data is an essential analysis point. For this purpose, different model selection criteria can be used under various assumptions. This study assesses the relative performance of new model selection criteria based on Kullback’s symmetric divergence in the Cox proportional hazards model. For this purpose, we compared the Kullback information criterion (KIC) and the corrected KIC(KICc) with other information criteria such as the Akaike information criterion (AIC), corrected AIC(AICc), and Bayesian information criterion (BIC) using a Monte Carlo experiment. Simulations were run using scenarios resulting from the combination of sample size (n = 30, 50, 100, 200, 300), censoring percentage (C = 5%, 10%, 15%, 20%, 25%, and 30%), and censoring distribution (uniform or exponential). The results revealed that the KIC family criteria favor models with more accurate predictive power, irrespective of sample size or censoring percentage. However, they tend to select more underfitted models, which means that the KIC family favors parsimonious models, regardless of sample size or censoring percentage. A larger sample size (n = 200, 300) improves the performance of these criteria in choosing the true model, irrespective of the censoring percentage. However, AIC and AICc outperform the KIC family criteria for relatively small to moderate sample sizes (n = 30, 50, 100) in true model (containing only the relevant covariates) selection. In addition, BIC tends to favor underfitted models over KIC family criteria. Variations in censoring percentage, sample size, and censoring distribution affect the performance of these criteria in identifying the true model. These findings suggest that we should prefer KIC or KICc for larger sample sizes and when prioritizing the predictive accuracy of the model. For smaller sample sizes, we should prefer AIC or AICc, and BIC in scenarios where model parsimony is critical. It is important to note that no model selection criterion is the best in all situations, as they performed differently under different circumstances.

Suggested Citation

  • Clarisse Houénafa Dete & Bruno Enagnon Lokonon & Kossi Essona Gneyou & Marcel Senou & Romain Glèlè Kakaï, 2025. "Relative Performance of Model Selection Criteria for Cox Proportional Hazards Regression Based on Kullback’s Symmetric Divergence," Journal of Probability and Statistics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljps:v:2025:y:2025:i:1:n:3808705
    DOI: 10.1155/jpas/3808705
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/jpas/3808705
    Download Restriction: no
    File URL: https://libkey.io/10.1155/jpas/3808705?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Joseph E. Cavanaugh, 2004. "Criteria for Linear Model Selection Based on Kullback's Symmetric Divergence," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(2), pages 257-274, June.
    2. Hojin Moon & Hyun‐Joo Kim & James J. Chen & Ralph L. Kodell, 2005. "Model Averaging Using the Kullback Information Criterion in Estimating Effective Doses for Microbial Infection and Illness," Risk Analysis, John Wiley & Sons, vol. 25(5), pages 1147-1159, October.
    3. Hua Liang & Hulin Wu & Guohua Zou, 2008. "A note on conditional aic for linear mixed-effects models," Biometrika, Biometrika Trust, vol. 95(3), pages 773-778.
    4. Chris T. Volinsky & Adrian E. Raftery, 2000. "Bayesian Information Criterion for Censored Survival Models," Biometrics, The International Biometric Society, vol. 56(1), pages 256-262, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Malloy, Elizabeth J. & Spiegelman, Donna & Eisen, Ellen A., 2009. "Comparing measures of model selection for penalized splines in Cox models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2605-2616, May.
    2. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    3. Miao Han & Liuquan Sun & Yutao Liu & Jun Zhu, 2018. "Joint analysis of recurrent event data with additive–multiplicative hazards model for the terminal event time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 523-547, July.
    4. Gonzalo García-Donato & María Eugenia Castellanos & Alicia Quirós, 2021. "Bayesian Variable Selection with Applications in Health Sciences," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
    5. Lee Kyu Ha & Chakraborty Sounak & Sun Jianguo, 2011. "Bayesian Variable Selection in Semiparametric Proportional Hazards Model for High Dimensional Survival Data," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-32, April.
    6. Mojtaba Ganjali & Taban Baghfalaki, 2018. "Application of Penalized Mixed Model in Identification of Genes in Yeast Cell-Cycle Gene Expression Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(2), pages 38-41, April.
    7. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    8. Braun, Julia & Sabanés Bové, Daniel & Held, Leonhard, 2014. "Choice of generalized linear mixed models using predictive crossvalidation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 190-202.
    9. Min Zhang & Marie Davidian, 2008. "“Smooth” Semiparametric Regression Analysis for Arbitrarily Censored Time-to-Event Data," Biometrics, The International Biometric Society, vol. 64(2), pages 567-576, June.
    10. Mirjana Glisovic‐Bensa & Walter W. Piegorsch & Edward J. Bedrick, 2024. "Bayesian benchmark dose risk assessment with mixed‐factor quantal data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(5), August.
    11. Yu, Dalei & Yau, Kelvin K.W., 2012. "Conditional Akaike information criterion for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 629-644.
    12. Liang, Hua & Zou, Guohua, 2008. "Improved AIC selection strategy for survival analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2538-2548, January.
    13. Marhuenda, Yolanda & Morales, Domingo & del Carmen Pardo, María, 2014. "Information criteria for Fay–Herriot model selection," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 268-280.
    14. Overholser, Rosanna & Xu, Ronghui, 2014. "Effective degrees of freedom and its application to conditional AIC for linear mixed-effects models with correlated error structures," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 160-170.
    15. Kruse, René-Marcel & Silbersdorff, Alexander & Säfken, Benjamin, 2022. "Model averaging for linear mixed models via augmented Lagrangian," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    16. Yiyun Shou & Michael Smithson, 2015. "Evaluating Predictors of Dispersion: A Comparison of Dominance Analysis and Bayesian Model Averaging," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 236-256, March.
    17. Ronghui Xu & Sudeshna Adak, 2002. "Survival Analysis with Time-Varying Regression Effects Using a Tree-Based Approach," Biometrics, The International Biometric Society, vol. 58(2), pages 305-315, June.
    18. Hafidi, Bezza, 2006. "A small-sample criterion based on Kullback's symmetric divergence for vector autoregressive modeling," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1647-1654, September.
    19. Ungerer, Christina & Reuther, Kevin & Baltes, Guido, 2021. "The lingering living dead phenomenon: Distorting venture survival studies?," Journal of Business Venturing Insights, Elsevier, vol. 16(C).
    20. Hojin Moon & Steven B. Kim & James J. Chen & Nysia I. George & Ralph L. Kodell, 2013. "Model Uncertainty and Model Averaging in the Estimation of Infectious Doses for Microbial Pathogens," Risk Analysis, John Wiley & Sons, vol. 33(2), pages 220-231, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljps:v:2025:y:2025:i:1:n:3808705. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/5139 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.