 Accelerated failure time model

An accelerated failure time model changes the time scale of a common event-time distribution. In a log-location-scale representation, $T_z=e^{\mu (z)}{e}^{\sigma X}$ with common $X$ and positive scale $\sigma$. An additive change in $\mu (z)$ multiplies all time quantiles by the same factor. A larger time multiplier indicates longer survival, whereas a larger hazard multiplier in a proportional hazards model indicates faster failure.

The Accelerated Failure Time (AFT) model is a type of survival analysis model used to analyze time-to-event data. Unlike the more commonly used Cox proportional hazards model, which focuses on the hazard function (the instantaneous risk of an event occurring), the AFT model directly models the time until an event occurs, often called the "failure time.