Log-Rank Test

Definition

The log-rank test is a test to compare the survival functions of two samples. The test uses the sequence of Mantel-Haenszel statistics of the $2\times 2$ tables at each uncensored event time.

Examples

$z$	$n$	$m_1$	$n_1$	$a$	$E(a)$	$a-E(a)$	$\mathrm{Var}(a)$
$3$	$10$	$1$	$5$	$1$	$0.50$	$0.50$	$0.250$
$5$	$9$	$1$	$4$	$1$	$0.44$	$0.56$	$0.247$
$7$	$8$	$1$	$3$	$1$	$0.38$	$0.62$	$0.234$
$12$	$6$	$1$	$1$	$0$	$0.17$	$-0.17$	$0.139$
$18$	$5$	$1$	$1$	$1$	$0.20$	$0.80$	$0.160$
$19$	$4$	$1$	$0$	$0$	$0$	$0$	$0$
$20$	$3$	$1$	$0$	$0$	$0$	$0$	$0$
The Mantel-Haenszel statistic of the data is calculated as
$MH=\frac{\sum _{i=1}^k[a_i-E(a_i)]}{\sqrt{\sum _{i=1}^k\mathrm{Var}(a_i)}}\approx \frac{2.31}{\sqrt{1.03}}\approx 2.26$
and the p-value is $0.12$