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
. At time
, let
be a positive weight function, and
and
are the size of the risk set and the number of events in the jth stratum, respectively. Let
,
.
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)