surv2.ks {surv2sample}R Documentation

Two-Sample Kolmogorov–Smirnov, Cramer–von Mises and Anderson–Darling Test for Censored Data

Description

Performs the Kolmogorov–Smirnov, Cramer–von Mises and Anderson–Darling test to compare the distribution of survival times in two samples of censored data.

Usage

surv2.ks(x, group, process = "w", approx = "lwy", nsim = 2000,
         nsim.plot = 50)

Arguments

x a "Surv" object, as returned by the Surv function.
group a vector indicating to which group each observation belongs. May contain values 1 and 2 only.
process the type of the test process. Possible values are "w" for the difference of Nelson–Aalen estimates (asymptotically a Brownian motion, i.e., Wiener process), "b" for a transformation of this process (asymptotically a Brownian bridge).
approx the method of approximating the distribution of test statistics. Possible values are "lwy" or "mart" for the martingale-based simulation, "perm" for permutations, "boot" for the bootstrap.
nsim the number of simulations (martingale simulations, permutations or bootstrap samples).
nsim.plot the number of simulated paths of the test process to be returned (for possible plotting). Must be at most nsim.

Details

The function implements tests based on functionals of the logrank process U(t) (which is the process of logrank statistics computed from observations in (0,t), see Section 7.5 of Fleming and Harrington (1991)). This process (properly normalised) is asymptotically a Brownian motion in transformed time. If process is "w", the supremum (KS) and integral (CM, AD) test statistics are computed from this process. If process is "b", the tests are instead based on the process U(t)(1+v(t)/v(tau))^(-1), which is asymptotically a Brownian bridge in transformed time.

Value

A list with class attributes "surv2.int" and "lwy.test", with main components:

stat.ks the Kolmogorov–Smirnov statistic.
pval.ks the corresponding p-value.
pval.ks.asympt the asymptotic p-value.
stat.cm the Cramer–von Mises statistic.
pval.cm the corresponding p-value.
stat.ad the Anderson–Darling statistic.
pval.ad the corresponding p-value.
time sorted times.
test.process the test process.
test.process.sim simulated paths of the test process (a matrix with nsim.plot columns).

Some of input arguments are also contained in the output.

Author(s)

David Kraus (http://www.davidkraus.net/)

References

Andersen, P. K., Borgan, O., Gill, R. D. and Keiding, N. (1993) Statistical Models Based on Counting Processes. Springer, New York.

Fleming, T. R. and Harrington, D. P. (1991) Counting Processes and Survival Analysis. Wiley, New York.

See Also

See the plot method inherited from the class "lwy.test".

See also surv2.neyman, surv2.logrank, survdiff, survfit.

Examples

## gastric cancer data
data(gastric)

## print results
print(a <- surv2.ks(Surv(gastric$time, gastric$event),
    gastric$treatment))
## plot the test process and simulated paths
plot(a)

[Package surv2sample version 0.1-2 Index]