SurvTest {coin} | R Documentation |
Testing the equality of survival distributions in two or more independent groups.
## S3 method for class 'formula': surv_test(formula, data, subset = NULL, weights = NULL, ...) ## S3 method for class 'IndependenceProblem': surv_test(object, ties.method = c("logrank", "HL"), ...)
formula |
a formula of the form Surv(time, event) ~ x | block where
time is a positive numeric variable denoting the survival time and
event is a logical being TRUE when the event of interest
was observed and FALSE in case of censoring. x is a factor
with two or more levels giving the corresponding groups. block is an
optional factor for stratification. |
data |
an optional data frame containing the variables in the model formula. |
subset |
an optional vector specifying a subset of observations to be used. |
weights |
an optional formula of the form ~ w defining
integer valued weights for the observations. |
object |
an object of class IndependenceProblem . |
ties.method |
a character specifying the way ties are handled in the definition of the logrank scores, see below. |
... |
further arguments to be passed to or from methods. |
The null hypothesis of the equality of the distribution of the survival
functions in the groups induced by x
is tested.
The test implemented here is based on the classical logrank test,
reformulated as a linear rank test. There are several ways of dealing with
ties. Here, two methods are implemented. The first one (ties.method = "logrank"
)
is described in Callaert (2003) for the uncensored case and leads, in
the presence of censored observations, to coefficients
a_i = delta_i - sum_{j: X_j <= X_i} delta_j / (n - |{k: X_k < X_j}|)
for a linear rank statistic T = sum_{i = 1}^ n a_i U_i (in two-sample situations where U_i = 0 or U_i = 1 denotes the groups). The second method is described in Hothorn & Lausen (2003) where the coefficients
a_i = delta_i - sum_{j: X_j <= X_i} delta_j / (n - |{k: X_k <= X_j}| + 1)
are suggested.
Note, however, that the test statistics will differ from the results
of survdiff
since the conditional variance
is not identical to the variance estimate used by the classical logrank
test.
An object inheriting from class IndependenceTest-class
with
methods show
, statistic
, expectation
,
covariance
and pvalue
. The null distribution
can be inspected by pperm
, dperm
,
qperm
and support
methods.
Herman Callaert (2003), Comparing Statistical Software Packages: The Case of the Logrank Test in StatXact. The American Statistician 57, 214–217.
Torsten Hothorn & Berthold Lausen (2003), On the Exact Distribution of Maximally Selected Rank Statistics. Computational Statistics & Data Analysis 43, 121–137.
### asymptotic tests for carcinoma data surv_test(Surv(time, event) ~ stadium, data = ocarcinoma) survdiff(Surv(time, event) ~ stadium, data = ocarcinoma) ### example data given in Callaert (2003) exdata <- data.frame(time = c(1, 1, 5, 6, 6, 6, 6, 2, 2, 2, 3, 4, 4, 5, 5), event = rep(TRUE, 15), group = factor(c(rep(0, 7), rep(1, 8)))) ### p = 0.0523 survdiff(Surv(time, event) ~ group, data = exdata) ### p = 0.0505 surv_test(Surv(time, event) ~ group, data = exdata, distribution = exact())