Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 5 / c / i / Solution

For each observed event $i$ with $v_i=1$, let $R_i=\{j:x_j\ge x_i\}$ be its risk set. The Cox partial likelihood isMaximize it to obtain $\hat{\beta }$, estimate its variance from the observed partial information, and test $H_0:\beta =0$ using a partial likelihood-ratio test, Wald test, or score test. A positive fitted coefficient means the group with $z=1$ has the larger hazard.