# pleicf: Product Limit Estimate for Interval Censored Data In STAND: Statistical Analysis of Non-Detects

## Description

Compute Product Limit Estimate (PLE) of F(x) for interval censored data (i.e., the nonparametric maximum likelihood estimate that generalizes the Kaplan-Meier estimate to interval censored data).

## Usage

 `1` ```pleicf(dd,nondet=TRUE,mine=1e-06,maxc=10000,eps=1e-14) ```

## Arguments

 `dd` n by 2 matrix or data frame (see note below) `nondet` if `TRUE`, `dd` is left censored data `mine` minimum error for convergence in icfit. Default = 1e-06. `maxc` maximum number of iterations. Default is 10000. `eps` adjustment factor described by Ng. Default is 1e-14.

## Details

This function is a driver function for `icfit` that uses an EM-algorithm applied to interval censored data (see Turnbull, 1976).

## Value

Data frame with columns

 `a` value of jth uncensored value (ordered) `ple` PLE of F(x) at a `surv` 1 - F(), i.e the "survival" or "exceedance" function `prob` prob[X = x] from `icfit` `n` sample size

## Note

If `nondet` is `TRUE` column 1 of dd is the data value and column 2 is 1 if a detect and 0 otherwise. If `nondet` is `FALSE` `dd` contains the left and right endpoints required by `icfit`.

E. L. Frome

## References

Fay, M. P. (1999), "Comparing Several Score Tests for Interval Censored Data," Statistics in Medicine,18:273-85. (Corr: 1999, Vol 19, p.2681).

Ng, M. P. (2002), "A Modification of Peto's Nonparametric Estimation of Survival Curves for Interval-Censored Data," Biometrics, 58, 439-442.

Turnbull, B. W. (1976), "The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data," Journal of the Royal Statistical Society, Series B (Methodological), 38(3), 290-295.

`icfit`, `plend`, `plekm`
 ```1 2 3 4 5 6``` ```# PLE for interval censored filmbadge data data(filmbadge) ple.fb<-pleicf(filmbadge[,1:2],FALSE) # PLE for input to qq.lnorm tmp <- qq.lnorm(ple.fb) ; GM<-round(exp(tmp\$par));GSD<-round(exp(tmp\$par),2) tp<-paste("Lognormal Q-Q plot for Filmbadge Data GM= ",GM,"GSD= ",GSD) title(tp) # title for q-q plot with graphical parameter estimates ```