CSCI {csci}

Pointwise Confidence Intervals for Current Status Data

Description

Calculates several different methods for getting pointwise confidence intervals for current st

Usage

CSCI(C, D, times=NULL, type = c("VALID", "ABA", "LIKELIHOOD"), 
   conf.level = 0.95, control=controlCSCI())

Arguments

C

a vector of assessement times

D

a vector of indicators of event at or before the assessment time

times

a vector of times, t, to give the confidence interval for the event time distribution, F(t). If NULL then set to sort(unique(C)).

type

type of confidence interval, either "VALID", "ABA", or "LIKELIHOOD" (see details)

conf.level

confidence level for intervals (for type="LIKELIHOOD" only specific values are allowed, see note)

control

list with parameters for algorithms, see controlCSCI

Details

The function does three types of pointwise confidence intervals for the cumulative distribution function for the event time at the times specified by times. When type="VALID" the function gives a method that guarantees that the coverage will be at least nominal, but the confidence intervals are not ensured to be monotonic over the times of interest. When type="ABA" the function gives an approximate method that does not guarantee coverage, but has been shown by simulation to have good coverage for smoothly changing distributions, and it does ensure monotonicity (see Kim, et al, 2020). When type="LIKELIHOOD" the function gives an asymptotic likelihood ratio test-based confidence interval that does not guarantee coverage (Banerjee and Wellner, 2001).

Value

A list with 2 objects:

ciTable_all

data.frame with NPMLE and associated confidence intervals for all possible time values (not output for type='LIKELIHOOD')

ciTable_times

data.frame with NPMLE and assoicated confidence intervals for the values of 'times' argument

Note

Because the likelihood ratio test goes to a non-standard asymptotic distribution, we do not calculate quantiles from that distribution, but take them from Table 2 of Banerjee and Wellner (2001). Because of this, when type="LIKELIHOOD" then conf.level must be one of 0.25,0.50,0.75,0.80,0.85,0.90,0.95, or 0.99.

Author(s)

Sungwook Kim

References

Banerjee, M. and J. A. Wellner (2001). Likelihood ratio tests for monotone functions. Ann. Statist. 29 (6), 1699-1731.

Kim, S, Fay, MP, Proschan, MA (2020). Valid and Approximately Valid Confidence Intervals for Current Status Data. (see https://arxiv.org/abs/1805.06488).

Examples

data(hepABulg)
CSCI(C=hepABulg$age,D=hepABulg$testPos,type="VALID")