Semiparametric Survival Regression Analysis for the Generalized Gamma Distribution

• Activity Number: 32
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Sangbum Choi*+ and Xuelin Huang
• Companies: MD Anderson Cancer Center and MD Anderson Cancer Center
• Keywords: Nonparametric likelihood ; Transformation model ; Gamma distribution ; Survival analysis

Abstract

In many failure mechanisms, most subjects under study deteriorate physically over time, and thus a depreciation in health may precede failure. A latent stochastic process, called degradation process, may be assumed for modeling such depreciation whereby an event occurs when the process first crosses a threshold. A class of survival regression models can be constructed from the first-hitting-time of a latent accelerating degradation process, which turns out to be a transformation model in the literature. To characterize these models, we propose to use first-hittingtime models for the baseline distribution, specifically inverse-Gaussian, Birnbaum-Saunders and gamma distributions, among others. The proposed models have many desirable features, such as a wide variety of shapes of hazard rates, analytical tractability, good interpretability of the parameters, and, most of all, its motivation from a plausible stochastic setting for failure. We estimate the model parameters by the nonparametric maximum likelihood approach. The estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Simple and stable numerical algorithms are provided to calculate the par