Nonparametric maximum likelihood estimation for arbitrary truncation

The syntax is reminiscent of the Surv function, with additional vectors for left-truncation and right-truncation.

Usage

npsurv(
  time,
  time2 = NULL,
  event = NULL,
  type = c("right", "left", "interval", "interval2"),
  ltrunc = NULL,
  rtrunc = NULL,
  weights = NULL,
  arguments = NULL,
  ...
)

Arguments

time

excess time of the event of follow-up time, depending on the value of event

time2

ending excess time of the interval for interval censored data only.

event

status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE for death). For interval censored data, the status indicator is 0=right censored, 1=event at time, 2=left censored, 3=interval censored. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have experienced an event.

type

character string specifying the type of censoring. Possible values are "right", "left", "interval", "interval2".

ltrunc

lower truncation limit, default to NULL

rtrunc

upper truncation limit, default to NULL

weights

vector of weights, default to NULL for equiweighted

arguments

a named list specifying default arguments of the function that are common to all elife calls

...

additional arguments passed to the functions

Value

a list with components

• xval: unique ordered values of sets on which the distribution function is defined

• prob: estimated probability of failure on intervals

• convergence: logical; TRUE if the EM algorithm iterated until convergence

• niter: logical; number of iterations for the EM algorithm

• cdf: nonparametric maximum likelihood estimator of the distribution function

Note

Contrary to the Kaplan-Meier estimator, the mass is placed in the interval [max(time), Inf) so the resulting distribution function is not deficient.

See also

Surv

Examples

#' # Toy example with interval censoring and right censoring
# Two observations: A1: [1,3], A2: 4
# Probability of 0.5

test_simple2 <- npsurv(
  time = c(1,4),
  time2 = c(3,4),
  event = c(3,1),
  type = "interval"
)