library("survminer")

This vignette covers changes between versions 0.2.4 and 0.2.5 for specifiyng weights in the log-rank comparisons done in ggsurvplot().

Log-rank statistic for 2 groups

As it is stated in the literature, the Log-rank test for comparing survival (estimates of survival curves) in 2 groups (\(A\) and \(B\)) is based on the below statistic

\[LR = \frac{U^2}{V} \sim \chi(1),\]

where \[U = \sum_{i=1}^{T}w_{t_i}(o_{t_i}^A-e_{t_i}^A), \ \ \ \ \ \ \ \ V = Var(U) = \sum_{i=1}^{T}(w_{t_i}^2\frac{n_{t_i}^An_{t_i}^Bd_i(n_{t_i}-o_{t_i})}{n_{t_i}^2(n_{t_i}-1)})\] and

also remember about few notes

\[e_{t_i}^A = n_{t_i}^A \frac{o_{t_i}}{n_{t_i}}, \ \ \ \ \ \ \ \ \ \ e_{t_i}^B = n_{t_i}^B \frac{o_{t_i}}{n_{t_i}},\] \[e_{t_i}^A + e_{t_i}^B = o_{t_i}^A + o_{t_i}^B\]

that’s why we can substitute group \(A\) with \(B\) in \(U\) and receive same results.

Weighted Log-rank extensions

Regular Log-rank comparison uses \(w_{t_i} = 1\) but many modifications to that approach have been proposed. The most popular modifications, called weighted Log-rank tests, are available in ?survMisc::comp

Watch out for FH as I submitted an info on survMisc repository where I think their mathematical notation is misleading for Fleming-Harrington.

Why are they useful?

The regular Log-rank test is sensitive to detect differences in late survival times, where Gehan-Breslow and Tharone-Ware propositions might be used if one is interested in early differences in survival times. Peto-Peto modifications are also useful in early differences and are more robust (than Tharone-Whare or Gehan-Breslow) for situations where many observations are censored. The most flexible is Fleming-Harrington method for weights, where high p indicates detecting early differences and high q indicates detecting differences in late survival times. But there is always an issue on how to detect p and q.

Remember that test selection should be performed at the research design level! Not after looking in the dataset.

Plots

library("survival")
data("lung")
fit <- survfit(Surv(time, status) ~ sex, data = lung)

After preparing a functionality for this GitHub’s issue Other tests than log-rank for testing survival curves and Log-rank test for trend we are now able to compute p-values for various Log-rank test in survminer package. Let as see below examples on executing all possible tests.

Log-rank (survdiff)

ggsurvplot(fit, data = lung, pval = TRUE, pval.method = TRUE)

Log-rank (comp)

ggsurvplot(fit, data = lung, pval = TRUE, pval.method = TRUE,
           log.rank.weights = "1")

Gehan-Breslow (generalized Wilcoxon)

ggsurvplot(fit, data = lung, pval = TRUE, pval.method = TRUE,
           log.rank.weights = "n", pval.method.coord = c(5, 0.1),
           pval.method.size = 3)