Rank-based inference for the accelerated failure time model

Abstract

A broad class of rank-based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations. The corresponding estimators can be obtained via linear programming, and are shown to be consistent and asymptotically normal. The limiting covariance matrices can be estimated by a resampling technique, which does not involve nonparametric density estimation or numerical derivatives. The new estimators represent consistent roots of the non-monotone estimating equations based on the familiar weighted log-rank statistics. Simulation studies demonstrate that the proposed methods perform well in practical settings. Two real examples are provided.

Determination of Predictors Associated With HIV/AIDS Patients on ART Using Accelerated Failure Time Model for Interval Censored Survival Data

“…AFTM is a linear regression model in which the response variable is logarithm or a known monotone transformation of a failure time (Kalbfleish and Prentice, 1980). AFTM has been extensively studied by Buckely and James (1979;Koul et al, 1981;Robins and Tsiatis, 1992;Jin et al, 2003;Kwong and Hutton, 2003;Orbe et al, 2002). Kay and Kinnersley (2002), suggested that AFTM is an alternative choice, when the proportional hazard assumptions does not hold.…”

On the accelerated failure time model for current status and interval censored data

“…The simple interpretation of the AFT model makes it a useful alternative to the popular proportional hazards model. The AFT model has been studied extensively in the literature for analyzing right censored data (Buckley and James, 1979;Tsiatis, 1990;Wei, Lin and Ying, 1990;Jin, Lin, Ying and Wei, 2003). Inference for the AFT model with current status or general interval censored data is more difficult since the NPMLE is not directly applicable.…”

On the Plackett Distribution with Bivariate Censored Data

“…To estimate the regression coefficients, we will utilize the procedure of Jin et al (2003). The regression parameters are estimated by the following algorithm; we illustrate the algorithm for (9):…”

“…In Jin et al (2003), they derived the consistency and asymptotic normality ofα. The variance of the limiting distribution of n 1/2 (α−α) is difficult to estimate directly, since it involves the derivative of the density of the error term 1 .…”