Maximum Likelihood Estimation Using Spline Smoothing for the Accelerated Failure Time Model

• Activity Number: 371
• Type: Contributed
• Date/Time: Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Ying Ding*+ and Bin Nan
• Companies: University of Michigan and University of Michigan
• Keywords: Efficient estimator ; Accelerated failure time model ; Cubic B-spline ; Censored survival data

Abstract

It is well known that the partial likelihood estimator in the Cox model is semiparametric efficient. However, developing an efficient estimator in the linear model for censored survival data is not completely satisfactory. Ritov and Wellner (1988) derived the semiparametric efficient score functions for the slope parameters, which involve the derivative of the density or the hazard function of the error term. Estimating the derivative of a density or a hazard function, though not impossible, is not attractive to most statisticians. We propose a different approach to the estimating equation methods, i.e. the rank-based and least-squares methods, by directly maximizing the log likelihood function in which the log hazard function of the error term is approximated by cubic B-splines. Efficiency, asymptotic properties and numerical implementation of this method are investigated.