ODSDesignIC {ICODS}

Outcome-Dependent Sampling with Interval-Censored Failure Time Data

Description

Provides an outcome-dependent sampling (ODS) design with interval-censored failure time data, where the observed sample is enriched by selectively including certain more informative failure subjects. The method is a sieve semiparametric maximum empirical likelihood approach for fitting the proportional hazards model to data from the interval- censoring ODS design.

Usage

ODSDesignIC(U, V, del1, del2, z, mVal, ind, a1, a2, 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.

z

matrix (nxp); covariates.

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.

ind

integer vector (n); indicating membership of the simple random sample (0), lower-tail supplemental sample (1), or upper-tail supplemental sample (2).

a1

numeric (1); lower cut-off point for selecting ODS sample (0 < a1 < a2 < tau).

a2

numeric (1); upper cut-off point for selecting ODS sample (0 < a1 < a2 < tau).

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 occurred 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 had 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 occurred 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 ODSDesign (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., Cai, J., and Zhou, H. (2018). Outcome-dependent sampling with interval-censored failure time data. Biometrics, 74(1): 58–67. <doi:10.1111/biom.12744>

Examples

data(odsData)

result <- ODSDesignIC(U = odsData$U, 
                      V = odsData$V,  
                      del1 = odsData$del1,  
                      del2 = odsData$del2, 
                      z = odsData$z, 
                      mVal = 1L, 
                      ind = odsData$ind, 
                      a1 = 0.43, 
                      a2 = 0.45, 
                      beta = NULL, 
                      maxit = 10L,
                      verbose = TRUE)

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