cif2.neyman {surv2sample}R Documentation

Two-Sample Neyman's Smooth Test for Cumulative Incidence Functions

Description

Compares cumulative incidence functions (CIF) for one failure cause in two samples of censored competing risks data using (possibly data-driven) Neyman's smooth test.

Usage

cif2.neyman(x, group, cause = 1, data.driven = FALSE,
            d = ifelse(data.driven, 5, 3), basis = "legendre",
            choltol = 1e-07)

## S3 method for class 'cif2.neyman':
summary(object, ...)

Arguments

x a "Survcomp" object, as returned by the Survcomp function.
group a vector indicating to which group each observation belongs. May contain values 1 and 2 only.
cause For which cause of failure should the CIFs be compared?
data.driven Should the test be data-driven?
d the number of basis functions for the test with fixed dimension, the maximum number of basis functions for the data-driven test.
basis the basis of functions. Possible values are "legendre" for Legendre polynomials and "cos" for cosines.
choltol a tolerance parameter for the Cholesky decomposition.
object an object of class "cif2.neyman", as returned by the function cif2.neyman.
... further parameters for printing.

Details

The test compares cumulative incidence functions F_1(t,k), F_2(t,k) for a particular failure cause k.

Neyman-type smooth tests are based on embedding the null hypothesis in a d-dimensional alternative. The embedding is here formulated in terms of subdistribution hazards derived from CIFs. The log-ratio of subdistribution hazards is expressed as a combination of d basis functions (Legendre polynomials or cosines) in transformed time, and their significance is tested by a score test. See Kraus (2007b) for details. The quadratic test statistic is asymptotically chi-square distributed with d degrees of freedom.

A data-driven choice of the number of basis functions is possible. The selection is based on a Schwarz-type criterion which is the maximiser of penalised score statistics for dimensions 1,...,d. For the p-value of the data-driven test a two-term approximation is used (see Kraus (2007a), eq. (12)), as the asymptotic chi-square with 1 d.f. is inaccurate.

If the test is data-driven, the summary method prints details on the selection procedure (statistics and penalised statistics for each dimension). This is equivalent to print(x, detail=TRUE, ...).

Value

cif2.neyman returns a list with class attributes "cif2.neyman" and "neyman.test". Its main components are:

stat the test statistic.
pval the p-value (based on the chi-square distribution for the fixed-dimension test and on the two-term approximation for the data-driven test).
stats, stats.penal statistics and penalised statistics for dimensions 1,...,d (only for data-driven tests).
S.dim the selected dimension (only for data-driven tests).

Most input parameters and some further components are included.

Author(s)

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

References

Kraus, D. (2007a) Data-driven smooth tests of the proportional hazards assumption. Lifetime Data Anal. 13, 1–16.

Kraus, D. (2007b) Smooth tests of equality of cumulative incidence functions in two samples. Research Report 2197, Institute of Information Theory and Automation, Prague. Available at http://www.davidkraus.net/surv2sample/.

See Also

cif and plot.cif for estimation and plotting of CIFs, cif2.ks, cif2.int and cif2.logrank for other two-sample tests.

Examples

## bone marrow transplant data
data(bmt1)

## compare CIFs for cause 1 (relapse)
## test with fixed dimension
cif2.neyman(Survcomp(bmt1$time, bmt1$event), bmt1$donor, cause = 1,
    data.driven = FALSE)
## data-driven test
print(a <- cif2.neyman(Survcomp(bmt1$time, bmt1$event), bmt1$donor,
    cause = 1, data.driven = TRUE))
## print details on the selection procedure
summary(a)

## compare CIFs for cause 2 (death in remission)
cif2.neyman(Survcomp(bmt1$time, bmt1$event), bmt1$donor, cause = 2)

[Package surv2sample version 0.1-2 Index]