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

J. K. Im, D. W. Apley*, C. Qi, X. Shan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)306-321
Number of pages16
JournalJournal of the Operational Research Society
Issue number3
StatePublished - Mar 2012


  • data analysis: estimating survival models
  • failure models: survival analysis for credit risk modelling
  • risk: predicting consumer credit risk

ASJC Scopus subject areas

  • Modeling and Simulation
  • Strategy and Management
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research


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