# Flexible AFT models

Accelerated failure time (AFT) models are used widely in medical research, though to a much lesser extent than proportional hazards models. In an AFT model, the effect of covariates act to accelerate or decelerate the time to event of interest, i.e. shorten or extend the time to event. Commonly used parametric AFT models are limited in the underlying shapes that they can capture. In this project, we propose a general parametric AFT model, and in particular concentrate on using restricted cubic splines to model the baseline to provide substantial flexibility. We then extend the model to accommodate time-dependent acceleration factors. Delayed entry is also allowed, and hence, time-dependent covariates. We derive analytic score and Hessian elements for the proposal, providing an efficient implementation. We evaluate the proposed model through simulation, showing substantial improvements compared to all standard parametric AFT models. User friendly Stata software is provided, which can be downloaded by typing ssc install staft from within Stata.

This is a collaborative project with Professor Patrick Royston of the MRC CTU at UCL, and Associate Professor Mark Clements of Karolinska Institutet.