= Solution
The <Log-rank test> compares observed failures in each group with the numbers expected under equal hazards, conditioning at every event time on the risk set and total failures. Its score sums $O_{1j}-Y_{1j}d_j/Y_j$ and is standardized by its null hypergeometric variance. It is most powerful for approximately <proportional hazards>. Strongly crossing survival curves can produce large positive and negative contributions that cancel, so very different distributions may yield a weak log-rank statistic.
Back to article page
