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It is unclear to me when it is appropriate to fit an accelerated failure time (AFT) model rather than a proportional hazard (PH) model.

I've tried googling and it appears as though PH models are much more popular than AFT models and I haven't been able to find much material speaking regarding the use of one model type over the other.

I've attached an image of a section from Statistical Models and Methods for Lifetime Data that gives some guidelines for graphical methods but they don't seem feasible with a large number of covariates.

Would anyone be able to provide some intuition into when each model type is appropriate?

enter image description here

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