Log-Rank and Wilcoxon Algorithm
These tests are for comparison of two or more strata of survival data.
Suppose that we have data from stratum 0 and stratum 1. Denote the ordered observed failure times by
![$t_0<t_1<t_2<...<t_k$](/wiki/pub/Main/WfccmAlgorithmLogRankWilcoxon/latex4ad7765452f0addb569445ecd03aa302.png)
. At time
![$t_i$](/wiki/pub/Main/WfccmAlgorithmLogRankWilcoxon/latex47d079acbb969651377b0f213c82ced4.png)
, let
![$w(t_i)$](/wiki/pub/Main/WfccmAlgorithmLogRankWilcoxon/latex24403975228d77aa8d9e3f7c77afe649.png)
be a positive weight function, and
![$n_i{}_j$](/wiki/pub/Main/WfccmAlgorithmLogRankWilcoxon/latex0530f0bd3060c146427cd2717b701c0d.png)
and
![$d_i{}_j$](/wiki/pub/Main/WfccmAlgorithmLogRankWilcoxon/latex4f1970af0bdba0c7949ced930a84e30f.png)
are the size of the risk set and the number of events in the jth stratum, respectively. Let
![$n_i = n_i{}_0+n_i{}_1$](/wiki/pub/Main/WfccmAlgorithmLogRankWilcoxon/latex7ea393619e345d1806f12a4576f6fe36.png)
,
![$d_i = d_i{}_0+d_i{}_1$](/wiki/pub/Main/WfccmAlgorithmLogRankWilcoxon/latexfd65d78f7dae34b97b38ab5a3f84096e.png)
.
1. Log-Rank and Wilcoxon statistic :
-
is 1.0 for log-rank test
-
is
for wilcoxon test
2. covariance for Log-Rank and Wilcoxon statistic :
-
is 1.0 for log-rank test
-
is
for wilcoxon test
3. Computation of Chi-Square and prob-Chi-Square :
- Chi-Square =
- prob-Chi-Square comes from function of pchisq(Chi-Square, 1, false, false)