Summing the observed-minus-expected contributions gives the unstandardized <log-rank statistic>
$$
T_0=\sum_{j=1}^m
\left\{u_j-
\frac{r_j^{(1)}}{r_j^{(0)}+r_j^{(1)}}
\right\}.
$$
Under the null it is centered at zero. A two-sided <Log-rank test> compares its magnitude with the square root of its null variance.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 4 / a / iv / Solution

The unstandardized log-rank statistic sums, over event times, the observed number of events in one group minus its conditional null expectation given the risk sets.


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