The Cox Hazard Model for Claims Data

By Samuel Berestizhevsky, Tanya Kolosova

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Claim management requires applying statistical techniques in the analysis and interpretation of the claims data. The central piece of claim management is claims modeling and predic-tion. Two strategies are commonly used by insurers to analyze claims: the two-part approach that decomposes claims cost into frequency and severity components, and the pure premium approach that uses the Tweedie distribution.In this paper, we evaluate an additional approach: time-to-event modeling. We provide a general framework to look into the process of modeling and prediction of claims using the Cox hazard model. The Cox hazard model is a standard tool in survival analysis for studying the dependence of a hazard rate on covariates and time. Although the Cox hazard model is very popular in statistics, in practice, data to be analyzed often fails to hold assumptions underlying the Cox model. We use a Bayesian approach to survival analysis to deal with violations of assumptions of the Cox hazard model.This paper is a case study intended to indicate a possible application of the Cox hazard model to workers’ compensation insurance, particularly the occurrence of claims while dealing with violations of the assumptions of this model.

Keywords Claims modeling, claims prediction, insurance analytics, risk assessment, Cox model assumptions validation, time-to-event analysis, Cox hazard model, Bayesian approach, SAS


Berestizhevsky, Samuel, and Tanya Kolosova, "The Cox Hazard Model for Claims Data," Variance 13:2, 2021, pp. 265-278.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.