Description Usage Arguments Details Value Author(s) References See Also Examples
The FHtestrcc
function performs a test for right-censored data based on counting processes. It uses the G-ρ,λ family of statistics for testing the differences of two or more survival curves.
1 2 3 4 |
L |
Numeric vector of the left endpoints of the censoring intervals (exact and right-censored 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 right-censored 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 two-sample and trend tests: |
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. |
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 follow-up 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.
information |
Full description of the test. |
data.name |
Description of data variables. |
n |
Number of observations in each group. |
obs |
The weighted observed number of events in each group. |
exp |
The weighted expected number of events in each group. |
statistic |
Either the chi-square or Z statistic. |
var |
The variance matrix of the test. |
alt.phrase |
Phrase used to describe the alternative hypothesis. |
pvalue |
p-value associated with the alternative hypothesis. |
call |
The matched call. |
R. Oller and K. Langohr
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.
Oller, R. and Langohr, K. (2017). FHtest: An R Package for the Comparison of Survival Curves with Censored Data. Journal of Statistical Software 81, 1–25.
FHtestrcp
1 2 3 4 5 6 7 8 9 10 11 | ## Two-sample tests
FHtestrcc(Surv(futime, fustat) ~ rx, data = ovarian)
FHtestrcc(Surv(futime, fustat) ~ rx, data = ovarian, rho = 1)
## Trend test
library(KMsurv)
data(bmt)
FHtestrcc(Surv(t2, d3) ~ group, data = bmt, rho = 1, alternative = "decreasing")
## K-sample test
FHtestrcc(Surv(t2, d3) ~ as.character(group), data = bmt, rho = 1, lambda = 1)
|
Loading required package: interval
Loading required package: survival
Loading required package: perm
Loading required package: Icens
Loading required package: MLEcens
Loading required package: KMsurv
Two-sample test for right-censored data
Parameters: rho=0, lambda=0
Distribution: counting process approach
Data: Surv(futime, fustat) by rx
N Observed Expected O-E (O-E)^2/E (O-E)^2/V
rx=1 13 7 5.23 1.77 0.596 1.06
rx=2 13 5 6.77 -1.77 0.461 1.06
Statistic Z= -1, p-value= 0.303
Alternative hypothesis: survival functions not equal
Two-sample test for right-censored data
Parameters: rho=1, lambda=0
Distribution: counting process approach
Data: Surv(futime, fustat) by rx
N Observed Expected O-E (O-E)^2/E (O-E)^2/V
rx=1 13 5.89 4.12 1.77 0.761 1.68
rx=2 13 3.50 5.27 -1.77 0.595 1.68
Statistic Z= -1.3, p-value= 0.194
Alternative hypothesis: survival functions not equal
Trend FH test for right-censored data
Parameters: rho=1, lambda=0
Distribution: counting process approach
Data: Surv(t2, d3) by group
N Observed Expected O-E
group=1 38 16.6 15.7 0.935
group=2 54 15.8 27.1 -11.223
group=3 45 25.7 15.4 10.288
Statistic Z= 1.9, p-value= 0.0272
Alternative hypothesis: decreasing survival functions (higher group implies earlier event times)
K-sample test for right-censored data
Parameters: rho=1, lambda=1
Distribution: counting process approach
Data: Surv(t2, d3) by as.character(group)
N Observed Expected O-E (O-E)^2/E (O-E)^2/V
as.character(group)=1 38 4.55 3.79 0.769 0.156 1.02
as.character(group)=2 54 4.87 7.50 -2.633 0.924 8.99
as.character(group)=3 45 5.41 3.54 1.864 0.981 6.28
Chisq= 9.9 on 2 degrees of freedom, p-value= 0.00697
Alternative hypothesis: survival functions not equal
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