ictest {interval} | R Documentation |
The ictest
function performs several different tests for
interval censored data, and the wlr_trafo
function gives the
associated transformation to scores. The default tests use the permutation
form of the test (the method option tells whether it is asymptotic or exact), but the score test
form and multiple imputation form are supported.
The 3 different scores give three different tests
that generalize to interval censored data either the
Wilcoxon-Mann-Whitney test
(scores="wmw") or the logrank test (scores="logrank1" or
scores="logrank2") (see details).
The function calls the icfit
function, if an icfit object is not provided.
## Default S3 method: ictest(L, R, group, scores = c("logrank1","logrank2","wmw"), rho=NULL, alternative= c("two.sided", "less", "greater","two.sidedAbs"), icFIT=NULL, initfit=NULL, icontrol=icfitControl(), exact=NULL, method=NULL, methodRule=methodRuleIC1, mcontrol=mControl(), Lin=NULL, Rin=NULL,...) ## S3 method for class 'formula': ictest(formula, data, subset, na.action, ...) ## Default S3 method: wlr_trafo(x, R=NULL, scores = c("logrank1", "logrank2", "wmw"), icFIT = NULL, initfit = NULL, control=icfitControl(), Lin=NULL,Rin=NULL,...) ## S3 method for class 'Surv': wlr_trafo(x,...)
L |
numeric vector of left endpoints of censoring interval, if R is NULL then represents exact failure time |
R |
numeric vector of right endpoints of censoring interval |
x |
response, either a Surv object or a numeric vector representing the left endpoint. if latter and R is NULL then x is treated as exact |
group |
a vector denoting the group 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 "correlation" type test is performed. If there are only two groups, both methods give the same results. |
scores |
character vector defining the scores: "logrank1" (default), "logrank2", or "wmw" (see details) |
rho |
either 0 (gives scores="logrank1"), or 1 (gives scores="wmw") (see Note) |
alternative |
character giving alternative for two-sample and trend tests, K-sample should be two.sided |
icFIT |
a precalculated icfit object for increased computation speed. This should be the icfit from the pooled data. Normally initfit should be used instead (see Warning) |
initfit |
an object of class icfit or icsurv, used for the initial estimate (see Warning).
Ignored if icFIT is not null |
icontrol |
list of arguments for controling NPMLE algorithm in call to icfit (default icfitControl ) |
formula |
a formula with response a numeric vector (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 which indicates what should happen when the data contain NAs. Defaults to getOption("na.action") |
Surv |
a Surv object, see Surv |
exact |
a logical value, TRUE denotes exact test, ignored if method is not NULL |
method |
a character value, one of 'pclt','exact.network','exact.ce','exact.mc', 'scoretest', 'wsr.HLY', 'wsr.pclt', 'wsr.mc'. If NULL method chosen by methodRule. |
methodRule |
a function used to choose the method, default methodRuleIC1 . (see details in perm ) |
mcontrol |
list of arguments for controling algorithms of different methods (see mControl ) |
Lin |
logical vector, should L be included in the interval? (see details) |
Rin |
logical vector, should R be included in the interval? (see details) |
control |
list of arguments for controling NPMLE algorithm in call to icfit (default icfitControl ) |
... |
values passed to other functions |
The censoring in the default case (when Lin=Rin=NULL) assumes there are n (n=length(L)) failure times, and the ith one is in the interval between L[i] and R[i]. The default is not to include L[i] in the interval unless L[i]=R[i], and to include R[i] in the interval unless R[i]=Inf. When Lin and Rin are not NULL they describe whether to include L and R in the associated interval. If either Lin or Rin is length 1 then it is repeated n times, otherwise they should be logicals of length n.
The 3 different types of scores are compared in depth in Fay (1999). When scores='logrank1' this gives the most commonly used logrank scores for right censored data, and reduces to the scores of Sun (1996) for interval censored data. When scores='logrank2' this gives the scores associated with the grouped proportional hazards model of Finkelstein (1986). When scores='wmw' this gives the generalized Wilcoxon-Mann-Whitney scores.
For censored data 2 common likelihoods are the marginal likelihood of the ranks and the likelihood with nuisance parameters for the baseline survival. Here we use the latter likelihood (as in Finkelstein, 1986, Fay, 1996, and Sun, 1996).
Because of theoretical difficulties (discussed below), the default method is to
perform a permutation test on the scores. 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 (see perm
).
Another method is to perform a standard score test (method="scoretest"). It is difficult to prove the asymptotic validity of the standard score tests for this likelihood because the number of nuisance parameters typically grows with the sample size and often many of the parameters are equal at the nonparametric MLE, i.e., they are on the boundary of the parameter space (Fay, 1996). Specifically, when the score test is performed then an adjustment is made so that the nuisance parameters are defined based on the data and do not approach the boundary of the parameter space (see Fay, 1996). Theoretically, the score test should perform well when there are many individuals but few observation times, and its advantage in this situation is that it retains validity even when the censoring mechanism may depend on the treatment.
Another method is to use multiple imputation, or within subject resampling (method="wsr.HLY") (Huang, Lee, and Yu, 2008). This method samples interval censored observations from the nonparametric distribution, then performs the usual Martingale-based variance. A different possibility is to use a permutational central limit theorem variance for each wsr (method="wsr.pclt") or use Monte Carlo replications to get an possibly exact method from each within subject resampling (method="wsr.mc").
Note that when icfit and ictest are used on right censored data, because of the method of estimating variance is different, even Sun's method does not produce exactly the standard logrank test results.
There are some typos in Appendix II of Fay (1999), see the correction.
The function wlr_trafo
returns only the numeric vector of scores, while
ictest
returns an object of class `ictest', which is a list with the following values.
scores |
This is a vector the same length as L and R, containing the scores used in the permutation test. |
U |
The efficient score vector. When group is a factor or character vector then each element of U has the interpretation as the weighted sum of "observed" minus "expected" deaths for the group element defined by the label of U. Thus negative values indicate better than average survival (see Fay, 1999). |
N |
number of observations in each group |
method |
full description of the test |
data.name |
description of data variables |
algorithm |
algorithm used in permutation calculation. For example, `pclt', 'exact.mc', 'exact.network' |
statistic |
either the chi-square or Z statistic, or NULL for exact methods |
parameter |
degrees of freedom for chi-square statistic |
alternative |
alternative hypothesis |
alt.phrase |
phrase used to describe the alternative hypothesis |
p.value |
p value associated with alternative |
p.values |
vector of p-values under different alternatives |
p.conf.int |
confidence interval on p.value, for algorithm='exact.mc' only |
nmc |
number of Monte Carlo replications, for algorithm='exact.mc' only |
nwsr |
number of within subject resamplings, for WSR methods only |
np |
number of permutation replications within each WSR, for method='wsr.mc' only |
Because the input of icfit
is only for saving computational time,
no checks are made to determine if the icfit
is in fact the correct one. Thus you will get
wrong answers with no warnings if you input the wrong icfit
object. The safer way to save
computational time is to input the precalculated icfit
object into initfit
. When this
is done, you will get either the correct answer or a warning even when you input a bad guess for the
initfit.
The rho
argument gives the scores which match the scores from the
survdiff
function, so that when rho=0 then scores="logrank1",
and when rho=1 then scores="wmw". These scores will exactly match those used in survdiff,
but the function survdiff
uses an asymptotic method
based on the score test to calculate p-values, while ictest
uses
permutation methods to calculate
the p-values, so that the p-values will not match exactly.
Michael P. Fay
Fay, MP (1996). "Rank invariant tests for interval censored data under the grouped continuous model". Biometrics, 52: 811-822.
Fay, MP (1999). "Comparing Several Score Tests for Interval Censored Data." Statistics in Medicine, 18: 273-285 (Correction: 1999, 18: 2681).
Finkelstein, DM (1986). "A proportional hazards model for interval censored failure time data" Biometrics, 42: 845-854.
Huang, J, Lee, C, Yu, Q (2008). "A generalized log-rank test for interval-censored failure time data via multiple imputation" Statistics in Medicine, 27: 3217-3226.
Sun, J (1996). "A non-parametric test for interval censored failure time data with applications to AIDS studies". Statistics in Medicine, 15: 1387-1395.
## perform a logrank-type test using the permutation form of the test data(bcos) testresult<-ictest(Surv(left,right,type="interval2")~treatment, scores="logrank1",data=bcos) testresult ## perform a Wilcoxon rank sum-type test ## using asymptotic permutation variance left<-bcos$left right<-bcos$right trt<-bcos$treatment ## save time by using previous fit ictest(left,right,trt, initfit=testresult$fit, method="pclt",scores="wmw")