The FlemingHarrington test for rightcensored data based on permutations
Description
The FHtestrcp
function performs a test for rightcensored data based on a permutation distribution. It uses the Gρ,λ family of statistics for testing the differences of two or more survival curves.
Usage
1 2 3 4 5 
Arguments
L 
Numeric vector of the left endpoints of the censoring intervals (exact and rightcensored data are represented as intervals of [a,a] and (a, infinity) respectively). 
R 
Numeric vector of the right endpoints of the censoring intervals (exact and rightcensored data are represented as intervals of [a,a] and (a, infinity) respectively). 
group 
A vector denoting the group variable for which the test is desired. If 
rho 
A scalar parameter that controls the type of test (see details). 
lambda 
A scalar parameter that controls the type of test (see details). 
alternative 
Character giving the type of alternative hypothesis for twosample and trend tests: 
method 
A character value, one of 
methodRule 
A function used to choose the method. Default value is 
exact 
A logical value, where 
permcontrol 
List of arguments for controlling permutation tests. Default value is 
formula 
A formula with a numeric vector as response (which assumes no censoring) or 
data 
Data frame for variables in 
subset 
An optional vector specifying a subset of observations to be used. 
na.action 
A function that indicates what should happen if the data contain 
... 
Additional arguments. 
Details
The appropriate selection of the parameters rho
and lambda
gives emphasis to early, middle or late hazard differences. For instance, in a given clinical trial, if one would like to assess whether the effect of a treatment or therapy on the survival is stronger at the earlier phases of the therapy, we should choose lambda= 0
, with increasing values of rho
emphasizing stronger early differences. If there were a clinical reason to believe that the effect of the therapy would be more pronounced towards the middle or the end of the followup period, it would make sense to choose rho = lambda > 0
or rho = 0
respectively, with increasing values of lambda
emphasizing stronger middle or late differences. The choice of the weights has to be made prior to the examination of the data and taking into account that they should provide the greatest statistical power, which in turns depends on how it is believed the null is violated.
Many standard statistical tests may be put into the form of the permutation test (see Graubard and Korn, 1987). There is a choice of four different methods to calculate the pvalues (the last two are only available for the twosample test): (1) pclt
: using permutational central limit theorem (see, e.g., Sen, 1985). (2) exact.mc
: exact method using Monte Carlo. (3) exact.network
: exact method using a network algorithm (see, e.g., Agresti, Mehta, and Patel, 1990). Currently, the network method does not implement many of the time saving suggestions such as clubbing. (4) exact.ce
: exact method using complete enumeration. This is good for very small sample sizes and when doing simulations, since the complete enumeration matrix need only be calculated once for the simulation.
There are several ways to perform the permutation test, and the function methodRuleIC1
chooses which of these ways will be used. The choice is basically between using a permutational central limit theorem (method="pclt"
) or using an exact method. There are several algorithms for the exact method. Note that there are two exact twosided methods for calculating pvalues (see permControl
and the tsmethod
option).
Value
information 
Full description of the test. 
data.name 
Description of data variables. 
n 
Number of observations in each group. 
diff 
The weighted observed minus expected number of events in each group. 
scores 
Vector with the same length as 
statistic 
Either the chisquare or Z statistic. 
var 
The variance matrix of the test. 
alt.phrase 
Phrase used to describe the alternative hypothesis. 
pvalue 
pvalue associated with the alternative hypothesis. 
p.conf.int 
Confidence interval of pvalue. For 
call 
The matched call. 
Author(s)
R. Oller and K. Langohr
References
AbdElfattah, E. F. and Butler, R. W. (2007). The weighted logrank class of permutation tests: Pvalues and confidence intervals using saddlepoint methods. Biometrika 94, 543–551.
Fleming, T. R. and Harrington, D. P. (2005). Counting Processes and Survival Analysis New York: Wiley.
Harrington, D. P. and Fleming, T. R. (1982). A class of rank test procedures for censored survival data. Biometrika 69, 553–566.
Kalbfleisch, J. D. and Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data. New York: Wiley, 2nd Edition.
Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. New York: Wiley, 2nd Edition.
See Also
FHtestrcc
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13  ## Twosample tests
FHtestrcp(Surv(futime, fustat)~rx, data=ovarian)
FHtestrcp(Surv(futime, fustat)~rx, data=ovarian, method="exact.network")
FHtestrcp(Surv(futime, fustat)~rx, data=ovarian, rho=1)
## Trend tests
library(KMsurv)
data(bmt)
FHtestrcp(Surv(t2, d3)~group, data=bmt, rho=1, alternative="decreasing")
FHtestrcp(Surv(t2, d3)~group, data=bmt, rho=1, alternative="decreasing", exact=TRUE)
## Ksample test
FHtestrcp(Surv(t2, d3)~as.character(group), data=bmt, rho=1, lambda=1)

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