The increasing time change $H_0$ preserves the ordering of event times and transforms each censoring time by the same rule. Applying part b to $U_1,U_2$ therefore gives
$$
\mathbb P(T_1<T_2\mid\text{informative})
=\frac{\phi_1}{\phi_1+\phi_2}.
$$
This is the pairwise race probability for a <proportional hazards family>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 5 / c / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-207/5/c/ii/solution