On the choice of timescale for other cause mortality in a competing risk setting using flexible parametric survival models

In competing risks settings where the events are death due to cancer and death due to other causes, it is common practice to use time since diagnosis as the timescale for all competing events. However, attained age has been proposed as a more natural choice of timescale for modeling other cause mortality. We examine the choice of using time since diagnosis versus attained age as the timescale when modeling other cause mortality, assuming that the hazard rate is a function of attained age, and how this choice can influence the cumulative incidence functions (CIF$CIF$s) derived using flexible parametric survival models. An initial analysis on the colon cancer data from the population-based Swedish Cancer Register indicates such an influence. A simulation study is conducted in order to assess the impact of the choice of timescale for other cause mortality on the bias of the estimated CIFs$CIFs$ and how different factors may influence the bias. We also use regression standardization methods in order to obtain marginal CIF$CIF$ estimates. Using time since diagnosis as the timescale for all competing events leads to a low degree of bias in CIF$CIF$ for cancer mortality (CIF1$CIF_{1}$) under all approaches. It also leads to a low degree of bias in CIF$CIF$ for other cause mortality (CIF2$CIF_{2}$), provided that the effect of age at diagnosis is included in the model with sufficient flexibility, with higher bias under scenarios where a covariate has a time-varying effect on the hazard rate for other cause mortality on the attained age scale.