 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-207/5/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

h_{i} (t) = h_{0} (t) e^{β z_{i}},

where

h_{0}

is an unspecified baseline hazard and

z_{i}

indicates treatment. With no tied events, the Cox partial likelihood is

L (β) = \prod_{i : v_{i} = 1} \frac{e ^{β z_{i}}}{\sum _{j \in R (x_{i})} e ^{β z_{j}}} .

Equality of the two hazard functions is

H_{0} : β = 0

, testable with a likelihood-ratio, score, or Wald test from this likelihood.

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