= Solution
Since the observed times are ordered, the final <risk set> is $R_m=\{m\}$. Its <Cox partial likelihood> factor is therefore
$$
\left(\frac{e^{\beta^Tz_m}}{e^{\beta^Tz_m}}\right)^{v_m}=1
$$
for either value of the last event indicator. Every earlier <risk set> and earlier event factor is unaffected by changing $v_m$. Thus \b[the entire <partial likelihood> as a function of $\beta$ is unchanged], not merely its value at one fitted coefficient. Its maximizing set, its <score function> and its <Observed Fisher information> are identical. In particular, any consistently chosen finite fitted $\widehat\beta$ is unchanged. The lone terminal event conveys no relative-hazard information because there is no other individual with whom to compare it.
Back to article page
