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WfccmAlgorithmLogRankWilcoxon
(13 Sep 2005,
ColeBeck
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---+ 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 %$t_0<t_1<t_2<...<t_k$%. At time %$t_i$%, let %$w(t_i)$% be a positive weight function, and %$n_i{}_j$% and %$d_i{}_j$% are the size of the risk set and the number of events in the jth stratum, respectively. Let %$n_i = n_i{}_0+n_i{}_1$%, %$d_i = d_i{}_0+d_i{}_1$%. ---++++ 1. Log-Rank and Wilcoxon statistic : %$E = \sum w(t_i) (d_i{}_0 - \frac{n_i{}_0 d_i}{n_i})$% * %$w(t_i)$% is *1.0* for log-rank test * %$w(t_i)$% is %$n_i$% for wilcoxon test ---++++ 2. covariance for Log-Rank and Wilcoxon statistic : %$V = \sum w(t_i) (d_i \frac{n_i{}_0 n_i{}_1 (n_i-d_i)}{n_i^2 (n_i-1)})$% * %$w(t_i)$% is *1.0* for log-rank test * %$w(t_i)$% is %$n_i$% for wilcoxon test ---++++ 3. Computation of Chi-Square and prob-Chi-Square : * Chi-Square = %$\frac{E^2}{V}$% * prob-Chi-Square comes from function of *pchisq(Chi-Square, 1, false, false)*
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Topic revision: r5 - 13 Sep 2005,
ColeBeck
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