Time-varying effects when analysing customer lifetime duration, application to the insurance market

The Cox model (Cox, 1972) is widely used in customer lifetime duration research, but it assumes that the regression coefficients are time invariant. In order to analyse the temporal covariate effects on the duration times, we propose to use an extended version of the Cox model where the parameters are allowed to vary over time. We apply this methodology to real insurance policy cancellation data and we conclude that the kind of contracts held by the customer and the concurrence of an external insurer in the cancellation influence the risk of the customer leaving the company, but the effect differs as time goes by.