efron.petrosian {DTDA} | R Documentation |
This function computes the NPMLE of a lifetime distribution function observed under one-sided (right or left) and two-sided (double) truncation. It provides bootstrap pointwise confidence limits too.
efron.petrosian(X, U = NA, V = NA, wt = NA, error = NA, nmaxit = NA, boot = TRUE, B = NA, alpha = NA, display.F = FALSE, display.S = FALSE)
X |
Numeric vector with the times of ultimate interest. |
U |
Numeric vector with the left truncation times. If there are no truncation times from the left, put U =NA . |
V |
Numeric vector with the right truncation times. If there are no truncation times from the left, put V =NA . |
wt |
Numeric vector of non-negative initial solution, with the same length as X . Default value is set to 1/n, being n the length of X . |
error |
Numeric value. Maximum distance among the densities computed in two successive steps. If this is missing, it is set to 10% of 1/n. |
nmaxit |
Numeric value. Maximum number of iterations. If this is missing, it is set to nmaxit =100 . |
boot |
Logical. If TRUE (default), the simple bootstrap method is applied to lifetime distribution estimation. Pointwise confidence bands are provided. |
B |
Numeric value. Number of bootstrap resamples . The default NA is equivalent to B =500 . |
alpha |
Numeric value. (1-alpha ) is the nominal coverage for the pointwise confidence intervals. |
display.F |
Logical. Default is FALSE. If TRUE, the estimated cumulative distribution function associated to X , (F) is plotted. |
display.S |
Logical. Default is FALSE. If TRUE, the estimated survival function associated to X , (S) is plotted. |
The NPMLE of the lifetime is computed by the first algorithm proposed in Efron and Petrosian (1999). This is an alternative algorithm which converges to the NMPLE after a number of iterations. If the second (respectively third) argument is missing, computation of the Lynden-Bell estimator for right-truncated (respectively left-truncated) data is obtained. Note that individuals with NAs in the three first arguments will be automatically excluded.
A list containing the following values:
time |
The timepoint on the curve. |
n.event |
The number of events that ocurred at time t . |
events |
The total number of events. |
density |
The estimated density values. |
cumulative.df |
The estimated cumulative distribution values. |
truncation.probs |
The probabilities of truncation values, in each region. |
S0 |
error reached in the algorithm. |
Survival |
The estimated survival values. |
n.iterations |
The number of iterations used by this algorithm. |
B |
Number of bootstrap resamples computed. |
alpha |
The nominal level used to construct the confidence intervals. |
upper.df |
The estimated upper limits of the confidence intervals for F. |
lower.df |
The estimated lower limits of the confidence intervals for F. |
upper.Sob |
The estimated upper limits of the confidence intervals for S. |
lower.Sob |
The estimated lower limits of the confidence intervals for S. |
Carla Moreira, Jacobo de Uña-Álvarez and Rosa Crujeiras
Efron, B. and Petrosian, V.(1999) Nonparametric methods for doubly truncated data. Journal of the American Statistical Association 94, 824-834.
Lynden-Bell, D. (1971) A method of allowing for known observational selection in small samples applied to 3CR quasars. Monograph National Royal Astronomical Society 155, 95-118.
## Generating data which are doubly truncated n<-25 X<-runif(n,0,1) U<-runif(n,0,0.5) V<-runif(n,0.5,1) for (i in 1:n){ while (X[i]<U[i]|X[i]>V[i]){ U[i]<-runif(1,0,0.5) X[i]<-runif(1,0,1) V[i]<-runif(1,0.5,1) } } efron.petrosian(X=X,U=U,V=V,display.F=TRUE,display.S=TRUE) ## Generating data which are left truncated n<-25 X<-runif(n,0,1) U<-runif(n,0,0.5) for (i in 1:n){ while (X[i]<U[i]){ U[i]<-runif(1,0,0.5) X[i]<-runif(1,0,1) } } efron.petrosian(X=X,U=U,V=NA) ## Generating data which are right truncated n<-25 X<-runif(n,0,1) V<-runif(n,0.5,1) for (i in 1:n){ while (X[i]>V[i]){ V[i]<-runif(1,0.5,1) X[i]<-runif(1,0,1) } } efron.petrosian(X=X,U=NA,V=V,display.F=TRUE)