On Estimating the Gamma Accelerated Failure-Time Models

Abstract

Publisher Summary It was suggested by Lawless and Yamaguchi that estimation of model parameters should involve two phases. First, the maximum likelihood estimates of parameters β and σ may be obtained for each fixed value of λ , using the Newton–Raphson algorithm. Then, the search for the value of λ that maximizes the log-likelihood function may be made. Yet, estimating the standard error of λ remains problematic. Of course, as pointed out by Peng et al., the variance of the shape parameter is of little use in practice. However, non-availability of the second partial of the log likelihood with respect to λ needed in the observed information matrix may cast doubt on the legitimacy of the standard errors of the estimates of the other model parameters. To describe the gamma-accelerated failure-time models, the chapter focuses on analyzing right-censored data from a clinical trial where the objective was to evaluate the efficacy of a single treatment or product with a control.