You are here: Vanderbilt Biostatistics Wiki>Main Web>Projects>MicroArrayMassSpec>GeneralWfccmDesign>WfccmClassDescriptions>WfccmAlgorithmLogRankWilcoxon (revision 2)EditAttach

Log-Rank and Wilcoxon Algorithm

Suppose that the number of groups is 2. 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 let $n_i_j$ and $d_i_j$ be the size of the risk set and the number of events in the jth sample, respectively. Let $n_i = \sum n_i_j, d_i = \sum d_i_j$.

Log-Rank and Wilcoxon statistic :

$e_i = \sum w(t_i)(d_i_j-\frac{n_i_j d_i}{n_i})$
  • $w(t_i)$ is 1.0 for log-rank test
  • $w(t_i)$ is $n_i$ for wilcoxon test

covariance for Log-Rank and Wilcoxon statistic :

$e_i = \sum w(t_i)(d_i_j-\frac{n_i_j d_i}{n_i})$
  • $w(t_i)$ is 1.0 for log-rank test
  • $w(t_i)$ is $n_i$ for wilcoxon test

Computation of $s_0$ :

  1. Compute the 100 quantiles of the $s_i$ values, denoted by $q_0<q_1<q_2<...<q_1_0_0$.
  2. For $\alpha \in$ (0, .01, .02, ... 1.0)
    1. Let $d_i^{\alpha} = r_i/(s_i+s^{\alpha})$, where $s^{\alpha}$ be the $\alpha$ percentile of the $s_i$ values.
    2. Compute $v_j = mad(d_i^{\alpha} | s_i \in [q_j, q_j_+_1))$, j = 1, 2, ... 100, where _mad_ is the median absolute deviation from the median, multiplied with 1.4826.
    3. Compute cv($\alpha$) = $\frac{stdev(v_j)}{mean(v_j)}$.
  3. Choose $\hat \alpha$ = argmin[cv($\alpha$)].
  4. Finally compute $\hat s_0$ = $s^{\hat \alpha}$. $s_0$ is henceforth fixed at the value $\hat s_0$.
Edit | Attach | Print version | History: r5 | r4 < r3 < r2 < r1 | Backlinks | View wiki text | Edit WikiText | More topic actions...
Topic revision: r2 - 22 Oct 2004, HaojieWu
 

This site is powered by FoswikiCopyright © 2013-2022 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding Vanderbilt Biostatistics Wiki? Send feedback