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How can I determine whether to use proportional hazard (PH) or accelerate failure time (AFT) survival models in order to analyze my data?

Are there any established guidelines or common practices that researchers follow to make this decision?

I know that the PH model assumes that the impact of a covariate is to multiply the hazard by a constant factor, while the AFT model assumes that the effect of a covariate is to accelerate or decelerate the progression of a disease by a constant factor. But it is not clear to me which one of the models would be best for my data, or how to make an objective decision on this.

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  • $\begingroup$ There are some technical differences, but they're similar models. In my experience, picking PH or AFT mostly depends on which framework you'd rather interpret your results in. $\endgroup$
    – Eli
    Jul 10, 2023 at 18:58

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It's mostly an issue of what describes your data best.

If you have a categorical predictor in your model that you are trying to model (e.g., 1 or more treaments versus contol) and a well balanced set of other covariates, you can get an idea of which is better by doing some simple plots. If you plot survival versus the log of time for the groups and the survival curves in that scale are reasonably evenly spaced in the horizontal (log-time) direction, then that's consistent with an AFT model's acceleration of time. If you plot the log of the cumulative hazard versus time for the groups and the curves are reasonably evenly spaced in the vertical (log-cumulative-hazard) direction, then that's consistent with proportional hazards (PH).

Things are trickier to plot if you are modeling continuous covariates, but the basic principles are the same. For example, you can fit a Cox semi-parametric PH survival model to the data and use scaled Schoenfeld residuals to evaluate whether the association of the predictor with outcome is relatively constant over time. Several chapters of Frank Harrell's Regression Modeling Strategies discuss survival modeling, with examples of the types of diagnostic plots that you can use to evaluate how well either an AFT or a PH model work.

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