In an AFT regression model, when the reponses are current status censored (observe yi either > ti or <= ti), we may still estimate the regression coefficients by the Buckley-James (extension from right censored case). We assume the inspection time ti have a larger support to cover the support of error epsilon, which is assumed iid.
CSbj(x, delta, Itime, maxiter = 99, error = 0.0001)It returns a list containing
The Buckley-James estimator of the regression coefficients.
Number of iterations done.
Locations of the jumps of final estimator of the error distribution.
Probabilities of the final estimator of the error distribution at jump locations. Mean of this error distribution is the intercept term est. of the regression model.
Design matrix N row p col.
Either 0 or 1. I[yi <= Itimei]. Length N. yi = beta xi + ei
The inspection times. Length N.
Default to 99. Control the iteration.
Default to 0.0001. Control the iteration.
Mai Zhou <maizhou@gmail.com>.
This function is an implementation of the Buckley-James estimator for the regression parameter beta in the AFT regression model when the observed responses are current status censored. Similar to the Binary Choice model in econometrics where all the inspection times are fixed at zero. I wrote an S-plus function for the binary choice model (name bibj). It is easily adapted to the current status situation, and this is the function. The AFT model we considered here has a intercept term. But we try to estimate the regression parameter beta, without intercept term. The estimator of intercept can be obtained as the mean of the iid error term after we got the estimator of the slope terms.
Depends on the functions monotone from package monotone
and lsfit from the basic stats package.
At this point, we do not have a good estimate for the variance for the Buckley-James estimators. Bootstrap is one method one can try.
Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC
Wang, W., and Zhou, M. (1995). Iterative least squares estimator of binary choice models: a semi-parametric approach. Tech. Report, University of Kentucky. https://www.ms.uky.edu/~mai/research/eco5wz.pdf
Buckley, J. J., and James, I. R. (1979). Linear regression with censored data. Biometrika 66, 429--436.
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)
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