Nonparametric survival when each event time is only bracketed

Interval censoring only says the event happened somewhere in (L, R]. The likelihood cannot distinguish points inside an interval, so all mass sits on the innermost intervals and the NPMLE is a discrete distribution on those. The self-consistency equation is an EM run for a fixed number of sweeps, so the arms cannot stop apart.

Usage

Ssintc(L, R, event = NULL, n_iter = 200)

Arguments

L

Left endpoints; 0 for left-censored.

R

Right endpoints; Inf for right-censored.

event

Kept for interface compatibility.

n_iter

EM sweeps.

Value

List with estimate, p, surv, q, r, n, m.

Details

Formula: with alpha_ij = 1 when region j lies inside observation i, iterate p_j = (1/n) sum_i alpha_ij p_j / sum_k alpha_ik p_k.

References

Turnbull, B. W. (1976). JRSS B 38:290-295, equation (10).

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Ssintc(V, V)
#> $estimate
#> [1] 5
#> 
#> $p
#> [1] 0.1428571 0.1428571 0.1428571 0.1428571 0.1428571 0.1428571 0.1428571
#> 
#> $surv
#> [1] 0.8571429 0.7142857 0.5714286 0.4285714 0.2857143 0.1428571 0.0000000
#> 
#> $q
#> [1] 1 2 3 4 5 6 7
#> 
#> $r
#> [1] 2 3 4 5 6 7 8
#> 
#> $n
#> [1] 8
#> 
#> $m
#> [1] 7
#> 
#> $method
#> [1] "Turnbull NPMLE, interval censoring"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"