`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()`

.

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

- \(t_i\) for \(i=1, \dots, T\) are possible event times,
- \(n_{t_i}\) is the overall risk set size on the time \(t_i\) (\(n_{t_i} = n_{t_i}^A+n_{t_i}^B\)),
- \(n_{t_i}^A\) is the risk set size on the time \(t_i\) in group \(A\),
- \(n_{t_i}^B\) is the risk set size on the time \(t_i\) in group \(B\),
- \(o_{t_i}\) overall observed events in the time \(t_i\) (\(o_{t_i} = o_{t_i}^A+o_{t_i}^B\)),
- \(o_{t_i}^A\) observed events in the time \(t_i\) in group \(A\),
- \(o_{t_i}^B\) observed events in the time \(t_i\) in group \(B\),
- \(e_{t_i}\) number of overall expected events in the time \(t_i\) (\(e_{t_i} = e_{t_i}^A+e_{t_i}^B\)),
- \(e_{t_i}^A\) number of expected events in the time \(t_i\) in group \(A\),
- \(e_{t_i}^B\) number of expected events in the time \(t_i\) in group \(B\),
- \(w_{t_i}\) is a weight for the statistic,

also remember about few notes

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

thatâ€™s why we can substitute group \(A\) with \(B\) in \(U\) and receive same results.

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`

`n`

Gehan and Breslow proposed to use \(w_{t_i} = n_{t_i}\) (this is also called generalized Wilcoxon),`srqtN`

Tharone and Ware proposed to use \(w_{t_i} = \sqrt{n_{t_i}}\),`S1`

Peto-Petoâ€™s modified survival estimate \(w_{t_i} = S1({t_i}) = \prod_{i=1}^{T}(1-\frac{e_{t_i}}{n_{t_i}+1})\),`S2`

modified Peto-Peto (by Andersen) \(w_{t_i} = S2({t_i}) = \frac{S1({t_i})n_{t_i}}{n_{t_i}+1}\),`FH`

Fleming-Harrington \(w_{t_i} = S(t_i)^p(1 - S(t_i))^q\).

Watch out for

`FH`

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

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.

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

After preparing a functionality for this GitHubâ€™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.

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

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

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