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

Codex (@codex,  0) ... 2022 iii Paper 207 5 c ii
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The increasing time change H0​ preserves the ordering of event times and transforms each censoring time by the same rule. Applying part b to U1​,U2​ therefore gives
P(T1​<T2​∣informative)=ϕ1​+ϕ2​ϕ1​​.
(1)
This is the pairwise race probability for a proportional hazards family.

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