Cox survival models with partially crossed random effects: A Poisson modelling approach

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University of New Brunswick


In automobile insurance studies, the time to settlement data are often partially cross-classified by location and agent. Our research question of great interest is to link time to settlement with various covariates since the analysis information help develop procedures to detect fraud and process claims. An appropriate analysis of such data needs to account for location and agent effects. In this thesis, we incorporate partially crossed random effects into Cox survival models for such data and propose a Poisson modelling approach to model estimation. We predict the random effects using the orthodox best linear unbiased predictor method, and obtain consistent estimators for the regression parameters. This estimating method relies on only the first and second moments of the random effects, and is thus robust against distributional assumptions of random effects. The usefulness of our approach is demonstrated by simulation and application to the time to settlement data.