Comparing proportional hazards and accelerated failure time models: an application in influenza

The proportional hazards (PH) model is routinely employed for the analysis of time-to-event data in medical research when it is required to assess the effect of an intervention in the presence of covariates. The assumption of PH required for the PH approach may not hold, especially in circumstances where the effect of the intervention is to delay or accelerate the onset of an event rather than to reduce or increase the overall proportion of subjects who observe the event through time. If the assumption of PH is violated, the results from a PH model will be difficult to generalize to situations where the length of follow-up is different to that used in the analysis. It is also difficult to translate the results into the effect upon the expected median duration of illness for a patient in a clinical setting. The accelerated failure time (AFT) approach is an alternative strategy for the analysis of time-to-event data and can be suitable even when hazards are not proportional and this family of models contains a certain form of PH as a special case. The framework can allow for different forms of the hazard function and may provide a closer description of the data in certain circumstances. In addition, the results of the AFT model may be easier to interpret and more relevant to clinicians, as they can be directly translated into expected reduction or prolongation of the median time to event, unlike the hazard ratio. We recommend that consideration is given to an AFT modelling approach in the analysis of time-to-event data in medical research.