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

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- Solution iv

Solution

Summing the observed-minus-expected contributions gives the unstandardized log-rank statistic

T_{0} = \sum_{j = 1}^{m} {u_{j} - \frac{r _{j}^{(1)}}{r _{j}^{(0)} + r _{j}^{(1)}}} .

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.

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