cdfDT {SurvTrunc}

Distribution function estimation under double truncation

Description

This function computes the NPMLE of the event time distribution and truncation time distribution, when the event times are subject to double truncation.

Usage

cdfDT(
  y,
  l,
  r,
  error = 1e-06,
  n.iter = 10000,
  boot = FALSE,
  B.boot = 200,
  joint = FALSE,
  plot.cdf = FALSE,
  plot.joint = FALSE,
  display = TRUE
)

Arguments

y

vector of event times

l

vector of left truncation times

r

vector of right truncation times

error

prespecified error for convergence (default = 1e-6)

n.iter

maximum number of iterations

boot

Logical. Default=FALSE. If TRUE, the simple bootstrap method is applied to estimate the standard error and pointwise confidence intervals of the event time distribution

B.boot

Numeric value for number of bootstrap resamples. Default is 200.

joint

Logical. Default=FALSE. If TRUE, computes joint and marginal distributions of the truncation times

plot.cdf

Logical. Default is FALSE. If TRUE, the estimated cumulative distribution and survival functions of the event times are plotted. If boot=TRUE, confidence intervals are also plotted.

plot.joint

Logical. Default is FALSE. If TRUE, the estimated marginal distribution functions of the truncation times, and the joint distribution of the truncation times, are plotted. Note: Plot will only be displayed if both plot.joint=TRUE and joint=TRUE.

display

Logical. Default is TRUE. If FALSE, output will not be displayed upon execution of function.

Details

Estimates the distribution function of the survival time in the presence of left and right truncation. Also estimates the joint cumulative distribution function and marginal cumulative distribution functions of the left and right truncation times. The computation is performed using the algorithm introduced in Shen (2010). This is an iterative algorithm that converges to the NPMLE after a number of iterations. Note that the survival, left, and right truncation times must be the same length. If either of these vectors have missing observations, the entire observation will be excluded.

Value

time

Unique event times of the event time vector y

n.event

Number of events that occurred at each timepoint

F

Estimated cumulative distribution function of Y at each distinct value of y

Survival

Estimated survival function of Y at each distinct value of y (equal to 1-F)

sigma.F

Bootstrapped standard error of F at each distinct value of y (displayed if boot=TRUE)

CI.lower.F

Estimated lower limits of the Wald confidence intervals for F (displayed if boot=TRUE).

CI.upper.F

Estimated upper limits of the Wald confidence intervals for F (displayed if boot=TRUE).

P.K

Probability of the observed vector y falling within a random truncation interval [L,R]

Joint.LR

Estimated joint distribution function of (l,r)

Marginal.L

Estimated marginal cumulative distribution function of L at each observed l

Marginal.R

Estimated marginal cumulative distribution function of R at each observed r

n.iterations

Number of iterations needed for convergence

max.iter_reached

0 indicates convergence, 1 indicates that number of iterations exceeded n.iter

References

Shen P-S (2010). Nonparametric analysis of doubly truncated data. Ann Inst Stat Math 62(5):835-853

Examples

#AIDS data set:
out=cdfDT(AIDS$Induction.time,AIDS$L.time,AIDS$R.time,plot.cdf=TRUE)
out