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This page explains the difference in the types of weight in log rank test in survival analysis.

We use, as a test statistic,

$$ Z_W = \frac{\sum_{k=1}^D W(t_k) \left( dN_1 (t_k) - Y_1(t_k) dN(t_k)/Y(t_k) \right)}{\left[ \sum_{k=1}^D W(t_k)^2 Y_1(t_k) \frac{dN(t_k)}{Y(t_k)} \frac{Y(t_k) - dN(t_k)}{Y(t_k)} \frac{Y_0(t_k)}{Y(t_k) - 1} \right]^{1/2}} $$

where $t_k$ : is the times of the event, $Y_i(\cdot)$ : number at risk at specific time for group $i=0,1$,$D$ : number of events, $dN_i(\cdot)$ : number of events at specific time of group $i$, and $W(\cdot)$ : any predictable process which serves as a "weight".

The above page explains that Gehan's weight, where $W(t) = Y(t)$ is used if one is interested in early differences in survival times. It's understandable, since early times have larger $Y(t)$. But I don't understand why Peto-Peto is usefule for situations where many observations are censored.

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