A robust parameterisation for the analysis of survival data in the presence of covariates with extreme value observations

We propose a new parameterisation for standard survival models which allow for the effect of a covariate with extreme value observations. We show that the robust model can offer an improved fit to both the parametric exponential model and the Cox proportional hazards model. Furthermore, we demonstrate the application of this approach using data from a pancreatic cancer dataset. Under traditional survival models, covariates enter the model via: l=exp{bx} Whilst this allows for ease of interpretation, we show that that this can be a dangerous assumption in the presence of extreme value observations and can lead to misleading survival estimates. We propose two models which aim to counter this effect. For parametric models, the robust model is of the form: