= Solution
For each observed event $i$ with $v_i=1$, let $R_i=\{j:x_j\geq x_i\}$ be its <risk set>. The <Cox partial likelihood> is
$$
L_p(\beta)=\prod_{i:v_i=1}
\frac{e^{\beta z_i}}{\sum_{j\in R_i}e^{\beta z_j}}.
$$
Maximize it to obtain $\widehat\beta$, 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.
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