FHtestrcp: The Fleming-Harrington test for right-censored data based on...

In FHtest: Tests for Right and Interval-Censored Survival Data Based on the Fleming-Harrington Class

Description

The FHtestrcp function performs a test for right-censored data based on a permutation distribution. It uses the G-ρ,λ family of statistics for testing the differences of two or more survival curves.

Usage

## Default S3 method:
FHtestrcp(L, R, group, rho = 0, lambda = 0, alternative, method = NULL,
          methodRule = methodRuleIC1, exact = NULL, permcontrol = permControl(), ...)
## S3 method for class 'formula'
FHtestrcp(formula, data, subset, na.action, ...)

Arguments

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 group is a factor or character, then a k-sample test is performed, where k is the number of unique values of group. If group is numeric, then a trend ("correlation" type) test is performed. If there are only two groups, both methods give the same results.
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: "different", "increasing" or "decreasing" survival functions. For the k-sample case, "different" should be chosen.
method	A character value, one of "pclt", "exact.network", "exact.ce", "exact.mc". If no value is specified, function methodRule chooses the value.
methodRule	A function used to choose the method. Default value is methodRuleIC1 (see details in perm).
exact	A logical value, where TRUE denotes exact test. Ignored if method is not NULL.
permcontrol	List of arguments for controlling permutation tests. Default value is permControl.
formula	A formula with a numeric vector as response (which assumes no censoring) or Surv object. The right side of the formula is the group variable. No strata() is allowed.
data	Data frame for variables in formula.
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 NAs. Default value is set to getOption("na.action").
...	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 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.

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 p-values (the last two are only available for the two-sample 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 two-sided methods for calculating p-values (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 L and R, containing the rank scores (see Kalbfleisch and Prentice, 2003).
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.
p.conf.int	Confidence interval of p-value. For method = "exact.mc" only.
call	The matched call.

Author(s)

R. Oller and K. Langohr

References

Abd-Elfattah, E. F. and Butler, R. W. (2007). The weighted log-rank class of permutation tests: P-values 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.

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.

See Also

FHtestrcc

Examples

## Two-sample 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)

## K-sample test
FHtestrcp(Surv(t2, d3) ~ as.character(group), data = bmt, rho = 1, lambda = 1)

Example output

Loading required package: interval
Loading required package: survival
Loading required package: perm
Loading required package: Icens
Loading required package: MLEcens
Depends on Icens package available on bioconductor. 
To install use for example:
install.packages('BiocManager')
BiocManager::install('Icens')
Loading required package: KMsurv

	Two-sample test for right-censored data

Parameters: rho=0, lambda=0
Distribution: permutation approach (asymptotic approximation using central limit theorem)

Data: Surv(futime, fustat) by rx

      N   O-E
rx=1 13  1.77
rx=2 13 -1.77

Statistic Z= -1, p-value= 0.303
Alternative hypothesis: survival functions not equal


	Two-sample test for right-censored data

Parameters: rho=0, lambda=0
Distribution: permutation approach (exact method using a network algorithm)

Data: Surv(futime, fustat) by rx

      N   O-E
rx=1 13  1.77
rx=2 13 -1.77

Statistic= -1, p-value= 0.297
Alternative hypothesis: survival functions not equal


	Two-sample test for right-censored data

Parameters: rho=1, lambda=0
Distribution: permutation approach (asymptotic approximation using central limit theorem)

Data: Surv(futime, fustat) by rx

      N   O-E
rx=1 13  1.77
rx=2 13 -1.77

Statistic Z= -1.3, p-value= 0.196
Alternative hypothesis: survival functions not equal


	Trend FH test for right-censored data

Parameters: rho=1, lambda=0
Distribution: permutation approach (asymptotic approximation using central limit theorem)

Data: Surv(t2, d3) by group

         N     O-E
group=1 38   0.935
group=2 54 -11.223
group=3 45  10.288

Statistic Z= 1.8, p-value= 0.0333
Alternative hypothesis: decreasing survival functions (higher group implies earlier event times)


	Trend FH test for right-censored data

Parameters: rho=1, lambda=0
Distribution: permutation approach (exact method using Monte Carlo with 999 replications)

Data: Surv(t2, d3) by group

         N     O-E
group=1 38   0.935
group=2 54 -11.223
group=3 45  10.288

Statistic= 1.8, p-value= 0.029
99 percent confidence interval on p-value:  0.0163 0.0444 
Alternative hypothesis: decreasing survival functions (higher group implies earlier event times)


	K-sample test for right-censored data

Parameters: rho=1, lambda=1
Distribution: permutation approach (asymptotic approximation using central limit theorem)

Data: Surv(t2, d3) by as.character(group)

                       N    O-E
as.character(group)=1 38  0.769
as.character(group)=2 54 -2.633
as.character(group)=3 45  1.864

Chisq= 9.8 on 2 degrees of freedom, p-value= 0.00755
Alternative hypothesis: survival functions not equal

FHtest documentation built on Oct. 23, 2020, 5:21 p.m.