Sun's Log-Rank Test for Interval-Censored Data

Usage

ic_logrank(
  formula,
  data,
  subset,
  na.action,
  B = c(0, 1),
  n_samples = 1000,
  type = c("sas", "hly"),
  ...
)

Arguments

formula: A formula with Surv(l, u, type = 'interval2') response and a single grouping variable on the right-hand side. May also contain strata() terms for stratified analysis.
data: A data frame containing the variables in the formula.
subset: Optional expression indicating which subset of rows to use.
na.action: Function to handle missing values.
B: A vector of length 2 giving bounds for observation times. Default is c(0, 1).
n_samples: The number of "imputation" samples for the variance calculation. Default is 1000.
type: The method for calculating the test statistic and variance. Options are "sas" (default) or "hly".
...: Additional arguments (currently unused).

Value

An object of class ic_logrank containing:

logrank: The log-rank statistics "observed - expected" for all groups and strata
logrank_overall: The log-rank statistics "observed - expected" for all groups
statistic: The overall chi-squared test statistic based on imputation
df: Degrees of freedom
p.value: P-value from chi-squared distribution
var: Variance-covariance matrix
groups: Group levels being compared
n: Sample sizes per group
method: Description of test method
data.name: Name of the data
call: The matched call

Details

Performs Sun's (1996) non-parametric log-rank test for comparing survival distributions across groups with interval-censored data. This test compares group-specific NPMLE survival curves without assuming proportional hazards.

The test statistic is \(Q = U(0)' I(0)^{-1} U(0)\), which follows a chi-squared distribution with k-1 degrees of freedom under the null hypothesis, where k is the number of groups.

The default test type is "sas", which uses Sun's test statistic combined with variance estimated based on the Huang, Lee and Yu (2008) procedure sampling exact observation times from the Turnbull intervals.

Alternatively, the "hly" type calculates the test statistic and variance using the multiple imputation approach of Huang, Lee and Yu (2008) directly.

Stratified tests are constructed by calculating the \(U\) and \(V\) matrices for each stratum separately and then summing the stratum-specific matrices to give a global test statistic \(\sum\bar{U}' (\sum\hat{V})^{-1} \sum\bar{U}\). This is the procedure described in the SAS documentation for PROC ICLIFETEST.

References

Sun, J. (1996). A non-parametric test for interval-censored failure time data with application to AIDS studies. Statistics in Medicine, 15(13), 1387-1395.

Huang, J., Lee, C., and Yu, Q. (2008). A Generalized Log-Rank Test for Interval-Censored Failure Time Data via Multiple Imputation. Statistics in Medicine 27:3217–3226. http://dx.doi.org/10.1002/sim.3211

SAS Institute Inc. (2026). SAS/STAT® 26.03 User's Guide: The ICLIFETEST Procedure. https://documentation.sas.com/doc/en/statug/latest/statug_iclifetest_details01.htm Accessed 14 April 2026.

Examples

# Simple two-group comparison
data(miceData)
ic_logrank(Surv(l, u, type = "interval2") ~ grp, data = miceData)
#> 
#> Sun's log-rank test for interval-censored data 
#> ============================================== 
#> 
#> Call:
#> ic_logrank(formula = Surv(l, u, type = "interval2") ~ grp, data = miceData)
#> 
#> Sample sizes by group:
#> Group
#> ce ge 
#> 96 48 
#> 
#> Log-rank Statistics:
#>       ce       ge 
#> -3.40709  3.40709 
#> 
#>   Chi-squared statistic: Q = 0.9351
#>   Degrees of freedom:    df = 1
#>   P-value:               p = 0.3335
#> 
#> Variance-covariance matrix:
#>          ce       ge
#> ce  12.4135 -12.4135
#> ge -12.4135  12.4135
#> 
#> Calculated with  1000  samples