bigtcr-package {bigtcr} | R Documentation |
Bivariate Gap Time with Competing Risks
Description
This package implements the non-parametric estimator for the conditional cumulative incidence function and the non-parametric conditional bivariate cumulative incidence function for the bivariate gap times proposed in Huang et al. (2016).
Conditional Cumulative Incidence Functions
Denote by the time to a failure event of interest. Suppose the study
participants can potentially experience any of several, say
,
different types of failure events. Let
indicate
the failure event type.
The cumulative incidence function (CIF) for the th competing event is
defined as
Huang et al. (2016) proposed a non-parametric estimator for the conditional cumulative incidence function (CCIF)
where the constant is determined from the knowledge that survival times
could potentially be observed up to time
.
To compare the CCIF of different failure types , we consider the
following class of stochastic processes
where is a weight function. For a formal
test, we propose to use the supremum test statistic
an omnibus test that is consistent against any
alternatives under which for some
.
An approximate -value corresponding to the supremum test statistic is
obtained by applying the technique of permutation test.
Bivariate Gap Time Distribution With Competing Risks
For bivariate gap times (e.g. time to disease recurrence and the residual
lifetime after recurrence), let and
denote the two gap times so
that
gives the total survival time
. Note that, given the
first gap time
being uncensored, the observable region of the second
gap time
is restricted to
. Because the two gap times
and
are usually correlated, the second gap time
is subject to
induced informative censoring
. As a result, conventional statistical
methods can not be applied directly to estimate the marginal distribution
of
.
Huang et al. (2016) proposed non-parametric estimators for the cumulative
incidence function for the bivariate gap time
and the conditional bivariate cumulative incidence function
To compare the joint distribution functions and
of different failure types
, we consider the supremum test
based on the following class of
processes
where is a prespecified weight function.
The approximate -value can be obtained through simulation by applying
the technique of permutation tests.
Nonparametric Association Measure for the Bivariate Gap Time With Competing Risks
To evaluate the association between the bivariate gap times, Huang et al. (2016) proposed a modified Kendall's tau measure that was estimable with observed data
References
Huang CY, Wang C, Wang MC (2016). Nonparametric analysis of bivariate gap time with competing risks. Biometrics. 72(3):780-90. doi: 10.1111/biom.12494