CaseCohortIC {ICODS}

Case-Cohort Studies with Interval-Censored Failure Time Data

Description

Provides a sieve semiparametric likelihood approach under the proportional hazards model for analyzing data from a case-cohort design with failure times subject to interval-censoring. The likelihood function is constructed using inverse probability weighting, and the sieves are built with Bernstein polynomials. A weighted bootstrap procedure is implemented for variance estimation.

Usage

CaseCohortIC(U, V, del1, del2, xi, z, sp, mVal, B, beta = NULL,
  maxit = 10L, verbose = TRUE, ...)

Arguments

U

numeric vector (n); examination time. See Details for further information.

V

numeric vector (n); examination time. See Details for further information.

del1

integer vector (n); indicator of a left-censored observation I(T<=U). See Details for further information.

del2

integer vector (n); indicator of an interval-censored observation I(U<T<=V). See Details for further information.

xi

integer vector (n); indicating membership of the case-cohort sample.

z

matrix (nxp); covariates.

sp

numeric (1); sampling probability 0 < sp < 1.

mVal

integer vector (m); one or more options for the degree of the Bernstein polynomials. If more than one option provided, the value resulting in the lowest AIC is selected. The results returned are for only that m-value.

B

integer (1); number of bootstrap samples used to calculate the variance estimate.

beta

numeric vector (p); initial values for beta. If NULL, initial guess set to 0.5 for each of the p parameters.

maxit

integer(1); maximum number of calls to optimization method.

verbose

logical; TRUE generates progress screen prints.

...

optional inputs to "control" of function optim().

Details

The implementation uses stats::optim() to minimize the likelihood. The hard-coded method is "BFGS". Users are able to make changes to the 'control' input of optim() by passing named inputs through the ellipses. If a call to optim() returns convergence = 1, i.e., optim() reached its internal maximum number of iterations before convergence was attained, the software automatically repeats the call to optim() with input variable par set to the last parameter values. This procedure is repeated at most maxit times.

Input parameters U, V, del1, and del2 are defined as follows. Suppose there are K follow-up examinations at times TE = (T1, T2, ..., TK), and the failure time is denoted as TF. For left-censored data, the failure occurs prior to the first follow-up examination (TF < T1); therefore, define U = T1, V = tau, and (del1,del2)=(1,0). For right-censored data, the failure has not yet occurred at the last follow-up examination (TF > TK); therefore, define U = 0, V = TK, and (del1,del2)=(0,0). For interval-censored data, the failure occurs between two follow-up examinations, e.g. T2 < TF < T3; therefore, define U and V to be the two consecutive follow-up examination times bracketing the failure time TF and (del1,del2)=(0,1).

Value

an object of class CaseCohort (inheriting from ICODS) containing

optim

a list of the results returned by optim().

beta

the estimated beta parameters.

se

the standard error of the estimated beta parameters.

pValue

the p-value of the estimated beta parameters.

m

the selected degree of the Bernstein polynomials.

AIC

the AIC value for the selected degree of the Bernstein polynomials.

References

Zhou, Q., Zhou, H., and Cai, J. (2017). Case-cohort studies with interval-censored failure time data. Biometrika, 104(1): 17–29. <doi:10.1093/biomet/asw067>

Examples

data(ccData)

result <- CaseCohortIC(U = ccData$U, 
                       V = ccData$V,  
                       del1 = ccData$del1,  
                       del2 = ccData$del2, 
                       xi = ccData$xi,
                       z = ccData$z, 
                       sp = 0.2, 
                       mVal = 1L,
                       B = 10L, 
                       beta = NULL, 
                       maxit = 10L,
                       verbose = TRUE)

print(result)
mVal(result)
estimate(result)
optimObj(result)
minAIC(result)
summary(result)