Flexible parametric accelerated failure time model

Accelerated Failure Time (AFT) models are viable alternatives to the Cox proportional hazard model, where failure times are explicitly modelled with respect to covariates. A major problem with parametric AFT models in practice is that statistical distribution used there often have a limited range of shapes, which may be inadequate to cope with real-life data. This paper presents an AFT model algorithm involving generalised lambda distributions (GLD) using maximum likelihood estimation, by extending and adapting existing work on GLD regression model and estimation, which would enhance the capabilities of AFT models owing to the rich shapes of GLDs. The proposed method is demonstrated to achieve parameter consistency and is very robust against outliers. A real-life example demonstrating the use of GLD AFT models compared to more established methods such as semi-parametric models of Buckley James regression, Accelerated Failure Time GEE model and Cox proportional hazard model is also given.