Package 'icsp2'

Description

This is an internal implementation of right-censored logrank test for use within ic_logrank where many tests need to be performed efficiently for variance calculation.

Usage

cpp_logrank(time, event, group)

Arguments

Value

An object of class "cpp_logrank", a list with components:

observed

Numeric vector of observed events per group.

expected

Numeric vector of expected events per group.

variance

Numeric variance matrix

n_by_group

Numeric vector of sample sizes per group.

Examples

set.seed(1992)
time  <- rexp(100)
event <- sample(c(TRUE, FALSE), 100, replace = TRUE)
group <- sample(1:2, 100, replace = TRUE)
cpp_logrank(time, event, group)

Description

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

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.

Value

An object of class ic_logrank containing:

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)

Description

Control ic_sp2 fitting options

Usage

ic_sp_control(
  useGA = TRUE,
  maxIter = 10000,
  baseUpdates = 5,
  regStart = NULL,
  derivMethod = c(12, 1),
  updateCovars = TRUE
)

Arguments

Details

The constrained gradient step, controlled by useGA = TRUE, is a step that was added to improve the convergence in a special case. The option to turn it off is only in place to help demonstrate its utility.

regStart also for seeding of initial value of regression parameters. Intended for use in “warm start" for bootstrap samples and providing fixed regression parameters.

Description

Fit a semi-parametric model for interval-censored data

Usage

ic_sp2(
  formula,
  data,
  weights,
  subset,
  na.action,
  B = c(0, 1),
  control = ic_sp_control(...),
  model = c("ph", "po"),
  profile_ci = 0,
  ...
)

ic_sp_ph(
  formula,
  data,
  weights,
  subset,
  na.action,
  B = c(0, 1),
  control = ic_sp_control(...),
  model = c("ph", "po"),
  profile_ci = 0,
  ...
)

ic_sp_po(
  formula,
  data,
  weights,
  subset,
  na.action,
  B = c(0, 1),
  control = ic_sp_control(...),
  model = c("ph", "po"),
  profile_ci = 0,
  ...
)

Arguments

Value

A list containing the fitted model information, including coefficients, variance-covariance matrix, and other details.

Description

Data set contains interval censored survival time for time from onset of diabetes to to diabetic nephronpathy. Identical to the diabetes dataset found in the package glrt.

Usage

IR_diabetes

Format

An object of class data.frame with 731 rows and 3 columns.

Fields

left

left side of observation interval

right

right side of observation interval

gender

gender of subject

References

Borch-Johnsens, K, Andersen, P and Decker, T (1985). "The effect of proteinuria on relative mortality in Type I (insulin-dependent) diabetes mellitus." Diabetologia, 28, 590-596.

Examples

head(IR_diabetes)
 diabetes_fit <- ic_sp_po(
     Surv(left, right, type = 'interval2') ~ gender,
     data = IR_diabetes
     )

Description

Lines method for ic_sp2 objects

Usage

## S3 method for class 'ic_sp2'
lines(x, y, type = "s", strata, ...)

Arguments

Details

Due to the interval censoring, the survival curves are not unique, so two lines are drawn for each curve: one for the lower bound and one for the upper bound of the interval. A pair of lines is drawn for each stratum, if strata are present in the model. Therefore to unambiguously specify graphics parameters such as colour or line type, the user should specify them as a vector of length equal to the number of strata (for strata specific pars) or twice the number of strata (for line specific pars, e.g. strata 1 lower, strata 1 upper, strata 2 lower, strata 2 upper).

Description

RFM mice were sacrificed and examined for lung tumors. This resulted in current status interval censored data: if the tumor was present, this implied left censoring and if no tumor was present this implied right censoring. Mice were placed in two different groups: conventional environment or germ free environment.

Usage

miceData

Format

An object of class data.frame with 144 rows and 3 columns.

Fields

l

left side of observation interval

u

right side of observation interval

grp

Group for mouse. Either "ce" (conventional environment) or "ge" (germ-free environment)

References

Hoel D. and Walburg, H.,(1972), Statistical analysis of survival experiments, \emph{The Annals of Statistics},
18, 1259-1294

Examples

head(miceData)
mice_ph_fit <- ic_sp_ph(Surv(l, u, type = 'interval2') ~ grp, data = miceData)

summary(mice_ph_fit)

Description

Print method for ic_sp2 objects

Usage

## S3 method for class 'ic_sp2'
print(x, ...)

Arguments

Description

Refit the model with fixed regression parameters

Usage

profile_fit(object, beta = object$coefficients)

Arguments

Value

Raw fitted model object with fixed regression parameters.

Description

Simulates interval censored data from a regression model with a Weibull baseline distribution. Used for demonstration

Usage

simIC_weib(
  n = 100,
  b1 = 0.5,
  b2 = -0.5,
  model = "ph",
  shape = 2,
  scale = 2,
  inspections = 2,
  inspectLength = 2.5,
  rndDigits = NULL,
  prob_cen = 1
)

Arguments

Details

Exact event times are simulated according to regression model: covariate x1 is distributed rnorm(n) and covariate x2 is distributed 1 - 2 * rbinom(n, 1, 0.5). Event times are then censored with a case II interval censoring mechanism with inspections different inspection times. Time between inspections is distributed as runif(min = 0, max = inspectLength). Note that the user should be careful in simulation studies not to simulate data where nearly all the data is right censored (or more over, all the data with x2 = 1 or -1) or this can result in degenerate solutions!

Author(s)

Clifford Anderson-Bergman

Examples

set.seed(1)
sim_data <- simIC_weib(n = 500, b1 = .3, b2 = -.3, model = 'ph',
                      shape = 2, scale = 2, inspections = 6,
                      inspectLength = 1)
#simulates data from a cox-ph with beta Weibull distribution.

ic_sp_ph(Surv(l, u, type = 'interval2') ~ x1 + x2, data = sim_data)
ic_sp_po(Surv(l, u, type = 'interval2') ~ x1 + x2, data = sim_data)

#'ph' fit looks better than 'po'; the difference between the transformed survival
#function looks more constant

Description

Profile Likelihood Covariance for Semi-Parametric Models

Usage

## S3 method for class 'ic_sp2'
vcov(object, type = "oim_curvature", fixed = 5, typical = 1, large = 2, ...)

Arguments

Details

The covariance matrix is calculated using the profile likelihood approach. (Murphey and Vand Der Vaart 2000). This method involves perturbing the regression parameters, updating the baseline hazard estimates using the profile_fit function with the perturbed parameters, and calculating the change in log-likelihood for each perturbation, which is then used to compute the covariance matrix. We borrowing the naming convention from the Stata stintcox manual https://www.stata.com/manuals/ststintcox.pdf.

Type "oim_curvature" (Boruvka and Cook 2015) uses the curvature of the log-likelihood function to determine the perturbation size for the profile likelihood calculations, as described in Boruvka and Cook (2014). The typical and large parameters are used to determine the scale of the perturbations.

Type "oim_fixed" (Zeng et al 2016) uses a fixed perturbation size based on the fixed parameter and the sample size n.

Type "opg_fixed" (Zeng et al 2017) uses a fixed perturbation size based on the fixed parameter and the sample size n, but uses the outer product of gradients instead of the observed information matrix for the covariance calculation.

For larged values of fixed the model fitting may fail to converge.

Value

Variance-covariance matrix of the regression parameters.

References

Murphy, S. A., & Van Der Vaart, A. W. (2000). On Profile Likelihood. Journal of the American Statistical Association, 95(450), 449–465. https://doi.org/10.1080/01621459.2000.10474219

Boruvka, A., and Cook, R. J. (2015), A Cox-Aalen Model for Interval-censored Data. Scand J Statist, 42, 414–426. doi: 10.1111/sjos.12113.

Donglin Zeng, Lu Mao, D. Y. Lin, Maximum likelihood estimation for semiparametric transformation models with interval-censored data, Biometrika, Volume 103, Issue 2, June 2016, Pages 253–271, https://doi.org/10.1093/biomet/asw013

Donglin Zeng, Fei Gao, D. Y. Lin, Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data, Biometrika, Volume 104, Issue 3, September 2017, Pages 505–525, https://doi.org/10.1093/biomet/asx029