STAND (version 2.0)

ictest: Performs Tests for Interval Censored Data

Description

This function performs several different tests for interval censored data. It has 3 different models that generalize either the Wilcoxon rank sum test (model = "PO") or the logrank test (model = "GPH" or model = "Sun"). Each model may be one of 2 types, either an asymptotic permutation test or a score test.

The censoring is such that if the ith observation fails at $x$, we only observe that $L[i] < x \le R[i]$. Data may be entered with "exact" values, i.e., $L[i] = x = R[i]$. In that case the $L[i]$ is changed internally to $L*[i]$ which is the next lower of any of the observed endpoints (unless $R[i] = 0$ then an error results).

The function requires a previously calculated survival curve (see icfit).

Usage

ictest(L, R, S, group, model, type = "permutation", fuzz , output.scores)

Arguments

L

a vector of left endpoints of the interval. We assume each $L[i] \ge 0$.

R

a vector of right endpoints of the interval. Exact values may be entered as L[i] == R[i] they are changed internally.

S

a vector of survival values calculated from all the data (i.e., ignoring group membership) (see time below), typically output from icfit.

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.

model

a character vector with three possible values describing the model: model = "GPH" (default) gives the grouped proportional hazards model. This generalizes a logrank test. model = "Sun" gives a Logistic model. This generalizes another form of the logrank test. model = "PO" gives a proportional odds model. This generalizes the Wilcoxon rank sum test. (see details).

type

a character vector with two possible values, "permutation" or "score" (see details)

fuzz

a small numeric value. Because we need to determine places in the survival curve where there are no changes, and the machine may have rounding error, we use this. (Default = 1e-12)

output.scores

a logical value. output.scores = TRUE outputs the scores in the output list. Default is output.scores = FALSE

Value

Returns a list with the following elements:

scores

only returned if output.scores = T. 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).

chisq.value

Chi-square value of the test

df

Degrees of freedom for the chi-square test.

pvalue

p-value from the chi-square value.

test

a character vector of length one, either "2-sample","correlation" or "k-sample" where k in the number of unique group values.

model

same as model input, either "GPH","Sun" or "PO"

type

same as type input, either "permutation" or "score"

Details

The 3 models are compared in depth in Fay (1999). For censored data two common likelihoods are the marginal likelihood or 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). It is difficult to create proper 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. One way around this is to perform a permutation test on the scores (Fay, 1996). A second way around (the boundary problem at least) it is to redefine the interval points so that no boundary problems exist (see Fay, 1996). These are the two methods used here.

We present two generalizations of the logrank test. The method of Sun (1996) is more difficult to calculate and has no theoretical advantages of which I am aware. The grouped proportional hazards model of Finkelstein (1996) is recommended. Note that when icfit and ictest are used on right-censored data, because 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 S code for the corrections.

References

Fay, M. P. (1996), "Rank Invariant Tests for Interval Censored Data Under the Grouped Continuous Model," Biometrics, 52: 811-822.

Fay, M. P. (1999), "Comparing Several Score Tests for Interval Censored Data," Statistics in Medicine, 18: 273-285.

Finkelstein, D. M. (1986), "A Proportional Hazards Model for Interval Censored Failure Time Data," Biometrics, 42: 845-854.

Sun, J. (1996), "A Non-parametric Test for Interval Censored Failure Time Data With Applications to AIDS Studies," Statistics in Medicine, 15: 1387-1395.

See Also

icfit,icplot

Examples

## Perform a logrank-type test using the observed information variance.
## need data set for this example
#   out<-icfit(left,right)
#  ictest(left,right,out$surv,group,out$time,model = "GPH",type = "score")
#
## Perform a Wilcoxon rank sum-type test using asymptotic permutation variance.
#
# ictest(left,right,out$surv,group,out$time, model = "PO",type = "permutation")