Product Limit Estimate for Interval Censored Data
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).
pleicf(dd,nondet=TRUE,mine=1e-06,maxc=10000,eps=1e-14)
dd: n by 2 matrix or data frame (see note below)nondet: if TRUE, dd is left censored datamine: 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.This function is a driver function for icfit
that uses an EM-algorithm applied to interval censored data (see Turnbull, 1976).
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.
Data frame with columns - a: value of jth uncensored value (ordered)
ple: PLE of F(x) at a
surv: , i.e the "survival" or "exceedance" function
prob: prob[X = x] from icfit
n: sample size
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.
E. L. Frome
icfit, plend, plekm
# 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$par[1]));GSD<-round(exp(tmp$par[2]),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