Aintmap: Create A matrix and intmap In interval: Weighted Logrank Tests and NPMLE for Interval Censored Data

Description

The A matrix is an n by k matrix of zeros and ones, where each row represents one of n failure times, and each column represents a possible interval for the nonparametric maximum likelihood estimate (NPMLE). The function `Aintmap` creates an A matrix and associated intmap from left and right intervals (L and R) which may not may not include the boundary of the interval (using Lin or Rin). The matrix intmap denotes the intervals of the potential jumps in the distribution of the NPMLE, and its attribute LRin denotes whether to include each of the intervals or not. Called by `icfit`.

Usage

 `1` ```Aintmap(L,R,Lin=NULL,Rin=NULL) ```

Arguments

 `L` numeric vector of left endpoints of censoring interval `R` numeric vector of right endpoints of censoring interval `Lin` logical vector, should L be included in the interval? (see details) `Rin` logical vector, should R be included in the interval? (see details)

Details

The `Lin` and `Rin` specify whether or not to include the ends of the intervals. They may be length 1 (and apply to all n values) or length n. The function automatically only returns the innermost intervals (also called the Turnbull intervals [see Turnbull, 1976], or the regions of the maximal cliques [see Gentleman and Vandal, 2002]). The innermost intervals give the "primary reduction" of Aragon and Eberly (1992).

Value

A list with two objects:

 `A` an n by k matrix of 0 and 1s `intmap` the associated intmap

References

Aragon, J and Eberly, D (1992). On convergence of convex minorant algorithms for distribution estimation with interval-censored data. J. of Computational and Graphical Statistics. 1: 129-140.

Gentleman R, and Vandal, A (2002). Nonparametric estimation of the bivariate CDF for arbitrarily censored dtaa. Canadian J of Stat 30: 557-571.

Turnbull, B (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. JRSS-B, 38: 290-295.

Called from `icfit` and `ictest`
 `1` ```Aintmap(c(2,3,3,7),c(3,5,5,8),Lin=c(FALSE,TRUE,FALSE,FALSE),Rin=c(TRUE,FALSE,TRUE,FALSE)) ```