Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 35 / 7 / 8 / Solution

The observed death fraction isIn the independent two-exponential competing risks model, $\pi =\lambda /(\lambda +\gamma )$. Thus the observed fraction estimates the share of the combined rate attributable to death. Combining it with an estimate of $s=\lambda +\gamma$ yields $\hat{\lambda }=\hat{\pi }\hat{s}$ and $\hat{\gamma }=(1-\hat{\pi })\hat{s}$. This uses the event-type information that the death-only time analysis ignored.