library(knitr) opts_chunk$set( comment = "", fig.width = 12, message = FALSE, warning = FALSE, tidy.opts = list( keep.blank.line = TRUE, width.cutoff = 150 ), options(width = 150), eval = TRUE )
library("survminer")
This vignette covers changes between versions 0.2.4 and 0.2.5 for specifiyng weights in the log-rank comparisons done in
ggsurvplot()
.
As it is stated in the literature, the Log-rank test for comparing survival (estimates of survival curves) in 2 groups ($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
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.
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-Peto'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 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.
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)
ggsurvplot(fit, data = lung, pval = TRUE, pval.method = TRUE, log.rank.weights = "sqrtN", pval.method.coord = c(3, 0.1), pval.method.size = 4)
ggsurvplot(fit, data = lung, pval = TRUE, pval.method = TRUE, log.rank.weights = "S1", pval.method.coord = c(5, 0.1), pval.method.size = 3)
ggsurvplot(fit, data = lung, pval = TRUE, pval.method = TRUE, log.rank.weights = "S2", pval.method.coord = c(5, 0.1), pval.method.size = 3)
ggsurvplot(fit, data = lung, pval = TRUE, pval.method = TRUE, log.rank.weights = "FH_p=1_q=1", pval.method.coord = c(5, 0.1), pval.method.size = 4)
Gehan A. A Generalized Wilcoxon Test for Comparing Arbitrarily Singly-Censored Samples. Biometrika 1965 Jun. 52(1/2):203-23.
Tarone RE, Ware J 1977 On Distribution-Free Tests for Equality of Survival Distributions. Biometrika;64(1):156-60.
Peto R, Peto J 1972 Asymptotically Efficient Rank Invariant Test Procedures. J Royal Statistical Society 135(2):186-207.
Fleming TR, Harrington DP, O'Sullivan M 1987 Supremum Versions of the Log-Rank and Generalized Wilcoxon Statistics. J American Statistical Association 82(397):312-20.
Billingsly P 1999 Convergence of Probability Measures. New York: John Wiley & Sons.
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