cif2.neyman {surv2sample} | R Documentation |
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.
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, ...)
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. |
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, ...)
.
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.
David Kraus (http://www.davidkraus.net/)
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/.
cif
and plot.cif
for estimation and
plotting of CIFs, cif2.ks
, cif2.int
and
cif2.logrank
for other two-sample tests.
## 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)