Log-rank test

The log-rank test compares observed and null-expected event counts across groups at each event time, conditional on the current risk sets. It is especially sensitive to proportional-hazards alternatives.

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.

A log-rank weight multiplies a group difference in estimated hazard increments. The ordinary log-rank test uses the harmonic-mean risk-set weight $r_0{r}_1/(r_0+r_1)$.