A parametric model for old age mortality in mediation analysis

This paper is addressing the modelling of old age mortality and its
dependence of factors earlier in life. We argue for alternatives
to the widely used proportional hazards (PH) model, especially Cox
regression. There are several reasons for this. First, it is well known
that old age mortality very often is well described by the Gompertz
distribution. Second, accelerated failure time (AFT) models can be
expressed as linear models, which is important when interest lies in the analysis of mediating effects in the analysis of the impact of early-life factors on old-age mortality. Third, the results of an AFT model fit is easier and more intuitive to interpret in tems of years lost or gained,
compared to the PH model fit which reports relative risks. Fourth, contrary to "common knowledge", the family of Gompertz distributions is both a collection of PH families and a collection of AFT families, which we demonstrate in the paper. For instance, Kleinbaum and Klein (2005), in their text book on survival analysis, writes: "The Gompertz model is a parametric PH model but not an AFT model". This mistake is reiterated by other authors.