Warping Models for Lifetime Distributions

Differences in life-span distributions can be described on several scales. The hazard is the most frequently used measure, but the age axis itself is also an informative domain. Accelerated failure time models, where the time axis is transformed linearly, constitute a prominent example. A linear transformation usually will be too restrictive, however, to properly capture differences in life-span distributions, thus necessitating a nonlinear mapping of the age scale, called warping. In this project, in collaboration with Jutta Gampe from the MPIDR and Paul H.C. Eilers from the Erasmus Medical Center, I developed warping models which provide additional insights into the differences between two age-at-death distributions. Specifically, they show how deaths would have to be moved along the age scale so that one age-at-death distribution would conform to another. This approach also provide to give an estimate of the first derivative of the transformation function, indicating the strength of redistribution of observations. The resulting transformation, and its derivative, provides deeper insights into how life-span distributions changed over time and how they differed between populations. The approach was not restricted to age-at-death distributions, and further examples were given of different height and weight distributions across populations.

We published our model in the Proceedings of the 23th International Workshop on Statistical Modelling: A Warped Failure Time Model for Human Mortality (paper).

We also presented our approach at the 2008 International Biometric Conference and, with a demographic focus, at the XXVI IUSSP International Population Conference, the slides of this last talk are given here.