Accelerated Failure Time Model for Arbitrarily Censored Data With Smoothed Error Distribution

Abstract

This article develops a semiparametric procedure to estimate parameters of an accelerated failure time model. To express the density of the error distribution, we use the P-spline (B-splines with penalties) smoothing technique. To accommodate error densities with infinite support (and for other reasons) we replace the B-splines with their limits as the degree of the B-spline goes to infinity; namely, with normal densities. The spline coefficients as well as any number of regression parameters are quickly and accurately estimated via penalized maximum likelihood. The method directly provides predictive survival distributions for fixed values of covariates while allowing for left-, right-, and interval-censored data. The approach has been implemented as an R package and is applied here to the problem of predicting AIDS-free survival in the presence of interval censoring.

Predicting the time of conversion to MCI in the elderly

“…The smoothing accelerated failure time (AFT) procedure, using G-splines, 21 was selected. This method is a trade-off between parametric and semiparametric AFT models.…”

Bayesian Accelerated Failure Time Model With Multivariate Doubly Interval-Censored Data and Flexible Distributional Assumptions

“…The first research question outlined in the introduction was considered by Lesaffre, Komárek and Declerck (2005) who analyzed each tooth separately using the penalized AFT model of Komárek, Lesaffre and Hilton (2005). With the Bayesian MEAFT model of this paper, we analyze all teeth jointly and answer also the second research question.…”

“…The covariate x i,l was generated according to the extreme-value distribution of a minimum, with location equal to 8.5 and scale equal to 1, inspired more or less by the log 2 (1 + CD4 count) covariate in the AIDS dataset analyzed by Komárek, Lesaffre and Hilton (2005). The covariate z i,l (treatment vs. placebo) was binary, taking a value of 1 with probability 0.4.…”

Finite mixture models with fixed weights applied to growth data

“…An implementation of this approach can be found in the R package smoothSurv. Applications in survival analysis can be found in Komarek et al (2005). This model can be applied to positive continuous data, with the exponent of the response as dependent variable.…”

“…An extension of the approach could allow the weights to depend on the covariates, thereby allowing the shape of distribution to change with a factor. The PGMM as described by Komarek et al (2005) was applied to the Fourth Dutch Growth Study; it took 8 hrs (on a 2.33GHz 2GB RAM Intel duo core PC) to converge (results not presented). Due to the long estimation time in the case of constant weights, we did not extend the PGMM system to weights depending on covariates.…”