Efficient Estimation for the Accelerated Failure Time Model

• Published in: Journal of the American Statistical Association Vol. 102; no. 480; pp. 1387 - 1396
• Main Authors: Zeng, Donglin, Lin, D. Y
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.12.2007; American Statistical Association; Taylor & Francis Ltd
• Subjects: Algorithms; Analytical estimating; Applications; Approximation; Asymptotic methods; Censored data; Censoring; Censorship; Data analysis; Estimators; Exact sciences and technology; General topics; Inference; Kernel functions; Kernel smoothing; Least squares; Linear inference, regression; Linear models; Linear regression; Mathematical functions; Mathematics; Maximum likelihood method; Medical sciences; Nonparametric inference; Probability; Probability and statistics; Profile likelihood; Regression analysis; Sciences and techniques of general use; Semiparametric efficiency; Statistical analysis; Statistical methods; Statistics; Survival; Survival data; Theory and Methods; Time series; Biometrics; Error estimation; Censoring; Non parametric method; Non parametric estimation; Covariate; Statistical simulation; Asymptotic convergence; Epidemiology; Medical science; Estimator efficiency; Covariance; Consistent estimator; Smooth function; Distribution function; Clinical trial; Likelihood function; Survival data; Censored data; Maximization; Approximate method; Linear regression; Semiparametric efficiency; Statistical estimation; Covariance matrix; Semiparametric method; Search algorithm; Kernel method; Statistical method; Kernels; Statistical regression; Kernel function; Profile likelihood; Asymptotic normality; Failure time; Asymptotic approximation; Maximum likelihood; Application; Kernel smoothing
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214507000001085

The accelerated failure time model provides a natural formulation of the effects of covariates on potentially censored response variable. The existing semiparametric estimators are computationally intractable and statistically inefficient. In this article we propose an approximate nonparametric maximum likelihood method for the accelerated failure time model with possibly time-dependent covariates. We estimate the regression parameters by maximizing a kernel-smoothed profile likelihood function. The maximization can be achieved through conventional gradient-based search algorithms. The resulting estimators are consistent and asymptotically normal. The limiting covariance matrix attains the semiparametric efficiency bound and can be consistently estimated. We also provide a consistent estimator for the error distribution. Extensive simulation studies demonstrate that the asymptotic approximations are accurate in practical situations and the new estimators are considerably more efficient than the existing ones. Illustrations with clinical and epidemiologic studies are provided.