At the start of this week, there were 51 subjects alive in total, so the risk of death in this week was 1/51. A one-sided level
{\displaystyle \alpha }
test will reject the null hypothesis if
Z
{\displaystyle Zz_{\alpha }}
where
z
{\displaystyle z_{\alpha }}
is the upper
{\displaystyle \alpha }
quantile of the standard normal distribution. Deviations from these assumptions matter most if they are satisfied differently in the groups being compared, for example if censoring is more likely in one group than another.
Here, \(\hat{S}(t)=\prod_{s \in \mathcal{D}: s \leq t} 1-\frac{d_{t,ctr}+d_{t,trt}}{n_{t,ctr}+n_{t,trt}}\)
is the pooled sample Kaplan-Meier estimator.
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Read related articleSee previous pollsCalculates a weighted log-rank test for the comparison of two groups. The first death was in week 6, when one patient in group 1 died.
The weighted logrank test statistic for a comparison of two groups is
$$z=\sum_{t \in \mathcal{D}} w(t) (d_{t,ctr}-e_{t,ctr}) / \sqrt{\sum_{t \in \mathcal{D}} w(t)^2 var(d_{t,ctr})}$$Under the the least favorable configuration in \(H_0\),
the test statistic is asymptotically standard normally distributed and large
values of \(z\) are in favor of the alternative. For example, the table shows survival times of 51 adult patients with recurrent malignant gliomas1 tabulated by type of tumour and indicating whether the patient had died or was still alive at analysisthat is, their survival time was censored.
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of one) would be a standard normal variate, and its p-value is two-sided. The second event occurred in week 10, when there were two deaths. We do not capture any email address. Let
1
,
{\displaystyle 1,\ldots ,J}
be the distinct times of observed events in either group.
Z
1
{\displaystyle Z_{1}}
and
Z
2
{\displaystyle Z_{2}}
are approximately bivariate normal with means
log
d
1
4
{\displaystyle \log {\lambda }\,{\sqrt {\frac {n\,d_{1}}{4}}}}
and
log
n
d
2
4
{\displaystyle \log {\lambda }\,{\sqrt {\frac {n\,d_{2}}{4}}}}
and correlation
d
1
d
2
{\displaystyle {\sqrt {\frac {d_{1}}{d_{2}}}}}
. .