coin (version 0.4-2)

SurvTest: Independent Two- and K-Sample Tests for Censored Data

Description

Testing the equality of survival distributions in two or more independent groups.

Usage

## S3 method for class 'formula':
surv_test(formula, data, subset = NULL,  
    weights = NULL, \dots)
## S3 method for class 'IndependenceProblem':
surv_test(object, 
    alternative = c("two.sided", "less", "greater"),
    distribution = c("asymptotic", "approximate", "exact"), 
    ties.method = c("logrank", "HL"), ...)

Arguments

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 obse

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.

alternative

a character, the alternative hypothesis must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

distribution

a character, the null distribution of the test statistic can be computed exactly or can be approximated by its asymptotic distribution (asympt) or via Monte-Carlo resampling (approx). Alternatively,

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.

Value

• 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.

Details

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 $$a_i = \delta_i - \sum_{j: X_j \le X_i} \delta_j / (n - |{k: X_k < X_j}|)$$ 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 $$a_i = \delta_i - \sum_{j: X_j \le X_i} \delta_j / (n - |{k: X_k \le X_j}| + 1)$$ 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.

References

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.

Examples

### asymptotic tests for carcinoma data
data(ocarcinoma, package = "coin")
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())