On maximum likelihood estimation of competing risks using the cause-specific semi-parametric Cox model with time-varying covariates – An application to credit risk

Mark Thackham and Jun Ma

Journal of the Operational Research Society, 2022, vol. 73, issue 1, 5-14

Abstract: Credit-granting institutions need to estimate the probability of loan default, which represents the chance a customer fails to make repayments as promised. Critically this estimation is intertwined with the competing risk a customer fully repays their loan while also having key predictive drivers with values that change over time. A conventional model in this setting is a competing risks Cox Model with time-varying covariates. However partial likelihood estimation of this model has two shortcomings: (1) the baseline hazard is not estimated, so calculating probabilities requires a further estimation step; and (2) a covariance matrix for both regression coefficients and the baseline hazard is not produced. This paper caters for these shortcomings by devising a maximum likelihood technique to jointly estimate regression coefficients and the cause-specific baseline hazards using constrained optimisation to ensure the latter’s non-negativity. We show via simulation our technique produces regression coefficients estimates with lower bias in small samples with heavy censoring. When applied to a real-world credit risk dataset consisting of home loan data our Maximum Likelihood approach produces a smoother estimate of the cause-specific baseline hazards for default and redemption than those obtained using the Partial Likelihood and Breslow approach. This provides better clarity of the shape of these functions through both a less volatile central estimate as well as quantifying the error of this central estimate. We implement our method in R.

Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1080/01605682.2020.1800418 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:tjorxx:v:73:y:2022:i:1:p:5-14

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/tjor20

DOI: 10.1080/01605682.2020.1800418

Access Statistics for this article

Journal of the Operational Research Society is currently edited by Tom Archibald

More articles in Journal of the Operational Research Society from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().