This function estimates the sample MCF difference between two groups. Both the point estimates and the confidence intervals are computed (Lawless and Nadeau 1995). The twosample pseudoscore test proposed by Cook, Lawless, and Nadeau (1996) is also performed by default.
mcfDiff(mcf1, mcf2 = NULL, level = 0.95, ...) mcfDiff.test( mcf1, mcf2 = NULL, testVariance = c("robust", "Poisson", "none"), ... )
mcf1  A 

mcf2  An optional second 
level  A numeric value indicating the confidence level required. The default value is 0.95. 
...  Other arguments passed to 
testVariance  A character string specifying the method for computing
the variance estimate for the pseudoscore test statistic proposed by
Cook, Lawless, and Nadeau (1996). The applicable options include

The function mcfDiff
returns a mcfDiff
object (of S4 class)
that contains the following slots:
call
: Function call.
MCF
: Estimated Mean cumulative function Difference at each time
point.
origin
: Time origins of the two groups.
variance
: The method used for variance estimates.
logConfInt
: A logical value indicating whether normality is
assumed for log(MCF)
instead of MCF itself. For mcfDiff
object, it is always FALSE
.
level
: Confidence level specified.
test
: A mcfDiff.test
object for the hypothesis test
results.
The function mcfDiff.test
returns a mcfDiff.test
object (of S4
class) that contains the following slots:
.Data
: A numeric matrix (of two rows and five columns) for
hypothesis testing results.
testVariance
: A character string (or vector of length one)
indicating the method used for the variance estimates of the test statistic.
The function mcfDiff
estimates the twosample MCFs' difference and
internally calls function mcfDiff.test
to perform the pseudoscore
tests by default. A 
method is available as a simple wrapper for the
function mcfDiff
for comparing twosample MCFs from two
mcf.formula
objects. For instance, suppose mcf1
and
mcf2
are mcf.formula
objects, each of which represents the
sample MCF estimates for one group. The function call mcf1  mcf2
is
equivalent to mcfDiff(mcf1, mcf2)
.
The null hypothesis of the twosample pseudoscore test is that there is no
difference between the two sample MCFs, while the alternative hypothesis
suggests a difference. The test is based on a family of test statistics
proposed by Lawless and Nadeau (1995). The argument testVariance
specifies the method for computing the variance estimates of the test
statistics under different model assumption. See the document of argument
testVariance
for all applicable options. For the variance estimates
robust to departures from Poisson process assumption, both constant weight
and the linear weight function (with scaling) suggested in Cook, Lawless,
and Nadeau (1996) are implemented. The constant weight is powerful in cases
where the two MCFs are approximately proportional to each other. The linear
weight function is originally a(u) = t  u
, where u
represents
the time variable and t
is the first time point when the risk set of
either group becomes empty. It is further scaled by 1 / t
for test
statistics invariant to the unit of measurement of the time variable. The
linear weight function puts more emphasis on the difference at earily times
than later times and is more powerful for cases where the MCFs are no longer
proportional to each other, but not crossing. Also see Cook and Lawless
(2007, Section 3.7.5) for more details.
Lawless, J. F., & Nadeau, C. (1995). Some Simple Robust Methods for the Analysis of Recurrent Events. Technometrics, 37(2), 158168.
Cook, R. J., Lawless, J. F., & Nadeau, C. (1996). Robust Tests for Treatment Comparisons Based on Recurrent Event Responses. Biometrics, 52(2), 557571.
Cook, R. J., & Lawless, J. (2007). The Statistical Analysis of Recurrent Events. Springer Science & Business Media.
## See examples given for function mcf.