<s>
The	O
logrank	B-General_Concept
test	I-General_Concept
,	O
or	O
log-rank	B-General_Concept
test	I-General_Concept
,	O
is	O
a	O
hypothesis	O
test	O
to	O
compare	O
the	O
survival	O
distributions	O
of	O
two	O
samples	O
.	O
</s>
<s>
It	O
is	O
a	O
nonparametric	B-General_Concept
test	I-General_Concept
and	O
appropriate	O
to	O
use	O
when	O
the	O
data	O
are	O
right	O
skewed	O
and	O
censored	O
(	O
technically	O
,	O
the	O
censoring	O
must	O
be	O
non-informative	O
)	O
.	O
</s>
<s>
The	O
test	O
is	O
sometimes	O
called	O
the	O
Mantel	B-General_Concept
–	I-General_Concept
Cox	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
logrank	B-General_Concept
test	I-General_Concept
can	O
also	O
be	O
viewed	O
as	O
a	O
time-stratified	O
Cochran	B-General_Concept
–	I-General_Concept
Mantel	I-General_Concept
–	I-General_Concept
Haenszel	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
test	O
was	O
first	O
proposed	O
by	O
Nathan	O
Mantel	O
and	O
was	O
named	O
the	O
logrank	B-General_Concept
test	I-General_Concept
by	O
Richard	O
and	O
Julian	O
Peto	O
.	O
</s>
<s>
The	O
logrank	B-General_Concept
test	I-General_Concept
statistic	O
compares	O
estimates	O
of	O
the	O
hazard	O
functions	O
of	O
the	O
two	O
groups	O
at	O
each	O
observed	O
event	O
time	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
the	O
two	O
groups	O
have	O
identical	O
hazard	O
functions	O
,	O
.	O
</s>
<s>
For	O
all	O
,	O
the	O
logrank	B-General_Concept
statistic	I-General_Concept
compares	O
to	O
its	O
expectation	O
under	O
.	O
</s>
<s>
If	O
the	O
two	O
groups	O
have	O
the	O
same	O
survival	O
function	O
,	O
the	O
logrank	B-General_Concept
statistic	I-General_Concept
is	O
approximately	O
standard	O
normal	O
.	O
</s>
<s>
A	O
one-sided	O
level	O
test	O
will	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
if	O
where	O
is	O
the	O
upper	O
quantile	O
of	O
the	O
standard	O
normal	O
distribution	O
.	O
</s>
<s>
If	O
the	O
hazard	O
ratio	O
is	O
,	O
there	O
are	O
total	O
subjects	O
,	O
is	O
the	O
probability	O
a	O
subject	O
in	O
either	O
group	O
will	O
eventually	O
have	O
an	O
event	O
(	O
so	O
that	O
is	O
the	O
expected	O
number	O
of	O
events	O
at	O
the	O
time	O
of	O
the	O
analysis	O
)	O
,	O
and	O
the	O
proportion	O
of	O
subjects	O
randomized	O
to	O
each	O
group	O
is	O
50%	O
,	O
then	O
the	O
logrank	B-General_Concept
statistic	I-General_Concept
is	O
approximately	O
normal	O
with	O
mean	O
and	O
variance	O
1	O
.	O
</s>
<s>
Suppose	O
and	O
are	O
the	O
logrank	B-General_Concept
statistics	I-General_Concept
at	O
two	O
different	O
time	O
points	O
in	O
the	O
same	O
study	O
(	O
earlier	O
)	O
.	O
</s>
<s>
The	O
logrank	B-General_Concept
statistic	I-General_Concept
can	O
be	O
derived	O
as	O
the	O
score	B-General_Concept
test	I-General_Concept
for	O
the	O
Cox	O
proportional	O
hazards	O
model	O
comparing	O
two	O
groups	O
.	O
</s>
<s>
It	O
is	O
therefore	O
asymptotically	O
equivalent	O
to	O
the	O
likelihood	B-General_Concept
ratio	I-General_Concept
test	I-General_Concept
statistic	I-General_Concept
based	O
from	O
that	O
model	O
.	O
</s>
<s>
The	O
logrank	B-General_Concept
statistic	I-General_Concept
is	O
asymptotically	O
equivalent	O
to	O
the	O
likelihood	B-General_Concept
ratio	I-General_Concept
test	I-General_Concept
statistic	I-General_Concept
for	O
any	O
family	O
of	O
distributions	O
with	O
proportional	O
hazard	O
alternative	O
.	O
</s>
<s>
If	O
is	O
the	O
logrank	B-General_Concept
statistic	I-General_Concept
,	O
is	O
the	O
number	O
of	O
events	O
observed	O
,	O
and	O
is	O
the	O
estimate	O
of	O
the	O
hazard	O
ratio	O
,	O
then	O
.	O
</s>
<s>
The	O
logrank	B-General_Concept
statistic	I-General_Concept
can	O
be	O
used	O
when	O
observations	O
are	O
censored	O
.	O
</s>
<s>
If	O
censored	O
observations	O
are	O
not	O
present	O
in	O
the	O
data	O
then	O
the	O
Wilcoxon	B-General_Concept
rank	I-General_Concept
sum	I-General_Concept
test	I-General_Concept
is	O
appropriate	O
.	O
</s>
<s>
The	O
logrank	B-General_Concept
statistic	I-General_Concept
gives	O
all	O
calculations	O
the	O
same	O
weight	O
,	O
regardless	O
of	O
the	O
time	O
at	O
which	O
an	O
event	O
occurs	O
.	O
</s>
<s>
The	O
Peto	O
logrank	B-General_Concept
test	I-General_Concept
statistic	O
gives	O
more	O
weight	O
to	O
earlier	O
events	O
when	O
there	O
are	O
a	O
large	O
number	O
of	O
observations	O
.	O
</s>
<s>
The	O
logrank	B-General_Concept
test	I-General_Concept
is	O
based	O
on	O
the	O
same	O
assumptions	O
as	O
the	O
Kaplan-Meier	O
survival	O
curve	O
—	O
namely	O
,	O
that	O
censoring	O
is	O
unrelated	O
to	O
prognosis	O
,	O
the	O
survival	O
probabilities	O
are	O
the	O
same	O
for	O
subjects	O
recruited	O
early	O
and	O
late	O
in	O
the	O
study	O
,	O
and	O
the	O
events	O
happened	O
at	O
the	O
times	O
specified	O
.	O
</s>
