= Solution
Only sets 4, 5, 7 and 8 have an earlier failure with both members at risk. Sets 4 and 8 have B fail first and favor A, giving $6+3=9$ informative pairs. Sets 5 and 7 have A fail first and favor B, giving $18+9=27$. Both-censored pairs contribute zero; in sets 3 and 6 the earlier observation is censoring, so the later failure occurs with no remaining comparator and also contributes zero.
There are thus 36 informative independent strata. The <stratified log-rank statistic>, its null <variance>, and its standardized value are
$$
\boxed{U_A=(27-9)/2=9,\qquad V=36/4=9,\qquad Z=U_A/\sqrt V=3.}
$$
Equivalently the squared statistic is nine. The <normal approximation> gives a two-sided <p-value> $2[1-\Phi(3)]<0.0027$ using the stated bound. The exact conditional <sign test> instead gives $2\sum_{k=0}^{9}\binom{36}{k}2^{-36}\approx0.00393$; the slight difference is discreteness rather than a different direction of effect. \b[There is strong evidence favoring Method B], which is associated with the later failure in three quarters of the informative pairs, under the test assumptions.
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