A warped failure time model for human mortality

Carlo G. Camarda, Max Planck Institute for Demographic Research
Paul H.C. Eilers, Utrecht University

Traditionally, mortality dynamics are studied by direct investigation of the hazard. A different approach would be to ask how the age-axis would need to be transformed so that one age-at-death distribution would conform to another. In the simplest case the transformation is linear, leading to plain accelerated failure time model. In this paper we present an extension of such model and call it Warped Failure Time (WaFT) model. Starting from a specific target distribution, the model allows estimation of the warping function of the age-axis that can map one distribution onto the other. The only assumption we make about the warping function is the smoothness. Parametric and non-parametric estimates from actual data can be used as target distributions. To estimate the warping function we use a penalized Poisson likelihood approach. Actual applications are presented and the resulting warping functions are easy to analyse and allow alternative interpretations of mortality development.