Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 207 / 2 / d / Solution

Let $A_i(s)$ be age in years at follow-up time $s$ and let $G_i\in \{0,1\}$ indicate the genetic risk factor. An age-dependent log-linear transition intensity model isHere $e^{{\theta }_0}$ is the onset baseline hazard for a 50-year-old without the factor; $e^{{\theta }_G}$ is the genetic hazard ratio, and $e^{{\theta }_A}$ is the hazard ratio per additional year of age. A smooth function of age could replace the linear age term if a constant age hazard ratio were unsuitable.

Under the stated constant multiplicative hazard ratios, the requested extrapolation is therefore the baseline rate times both multipliers: