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Summing the observed-minus-expected contributions gives the unstandardized log-rank statisticUnder the null it is centered at zero. A two-sided Log-rank test compares its magnitude with the square root of its null variance.

Construct the two countries' period-specific risk sets with the same left truncation and right censoring rules, then compare their event counts by a Log-rank test. This is a nonparametric comparison because it does not specify the shape of either country's hazard function.

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.