= Paired log-rank reduction to a sign test
{title2=$U=(n_A-n_B)/2,\quad V=(n_A+n_B)/4$}
With one A and one B observation per stratum and no ties, the <stratified log-rank statistic> receives a nonzero contribution only when the earlier observation is a failure while both remain at risk. It is $+1/2$ if A fails first and $-1/2$ if B fails first. After the first observation, only one member remains and every further observed-minus-expected contribution is zero. Under an exchangeable null with <independent censoring>, conditional on being informative the two signs have equal probability, with mean zero and <variance> $1/4$. Thus standardization is the normal approximation to a <sign test> on informative pairs. Failure-time distances do not affect this statistic.
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