Accelerated Failure-Time Models › Advantages

The main advantage of an AFT model is interpretability on the time scale. Exponentiating a coefficient gives a time ratio: the factor by which the event time is multiplied when a covariate increases by one unit, holding the other covariates and the individual error term fixed. A time ratio of 1.25 means that the model predicts events about 25 percent later. For a question phrased in time units, this factor describes changes in event-time quantiles directly; a hazard ratio instead describes an instantaneous-rate contrast.

The parametric AFT models studied here provide a full event-time likelihood. That means we can estimate survival curves, event-time quantiles, means when they exist, and prediction intervals directly from the fitted model. We can also compare non-nested distributions with information criteria such as AIC or BIC, provided the models are fitted to the same observations and use the same censoring convention.

The censored likelihood is another practical strength. An observed event contributes its density, while a censored observation contributes its survival probability. This is the same likelihood principle we used in Maximum Likelihood Estimation, now adapted to incomplete event times. AFT models can therefore be fitted to right-censored data without discarding censored subjects or imputing their event times.

Finally, AFT models are useful when the proportional hazards assumption is questionable. A log-normal or log-logistic AFT model can represent non-monotone hazards, where risk rises and later falls. The Weibull AFT model is more restrictive, but it has a direct connection to Cox regression, which helps us translate between time ratios and hazard ratios when that connection is justified.