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A time-dependent proportional hazards survival model for credit risk analysis


  • J-K Im

    (Northwestern University, Evanston, IL, USA)

  • D W Apley

    (Northwestern University, Evanston, IL, USA)

  • C Qi

    (Consultant, Lake Forest, IL, USA)

  • X Shan

    (Consultant, Deerfield, IL, USA)


In the consumer credit industry, assessment of default risk is critically important for the financial health of both the lender and the borrower. Methods for predicting risk for an applicant using credit bureau and application data, typically based on logistic regression or survival analysis, are universally employed by credit card companies. Because of the manner in which the predictive models are fit using large historical sets of existing customer data that extend over many years, default trends, anomalies, and other temporal phenomena that result from dynamic economic conditions are not brought to light. We introduce a modification of the proportional hazards survival model that includes a time-dependency mechanism for capturing temporal phenomena, and we develop a maximum likelihood algorithm for fitting the model. Using a very large, real data set, we demonstrate that incorporating the time dependency can provide more accurate risk scoring, as well as important insight into dynamic market effects that can inform and enhance related decision making.

Suggested Citation

  • J-K Im & D W Apley & C Qi & X Shan, 2012. "A time-dependent proportional hazards survival model for credit risk analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(3), pages 306-321, March.
  • Handle: RePEc:pal:jorsoc:v:63:y:2012:i:3:p:306-321

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    References listed on IDEAS

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    Cited by:

    1. Azamat Abdymomunov & Sharon Blei & Bakhodir Ergashev, 2015. "Integrating Stress Scenarios into Risk Quantification Models," Journal of Financial Services Research, Springer;Western Finance Association, vol. 47(1), pages 57-79, February.
    2. Liu, Fan & Hua, Zhongsheng & Lim, Andrew, 2015. "Identifying future defaulters: A hierarchical Bayesian method," European Journal of Operational Research, Elsevier, vol. 241(1), pages 202-211.
    3. Aimée Backiel & Bart Baesens & Gerda Claeskens, 2016. "Predicting time-to-churn of prepaid mobile telephone customers using social network analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(9), pages 1135-1145, September.

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