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I am struggling to understand when I should consider using a Cox regression model versus using a Weibull AFT model to predict the end of life of mechanical components.

I have tried to apply the Cox regression model for my data and I noticed that it was not able to estimate time to failure for components that do not cross 50 percent survival probability whereas when I used the Weibull AFT model, I am able to get predictions for all the components. If I am dealing with failure of mechanical components, is it sufficient to decide to use Weibull AFT without the need to compare it against other models?

I am not a domain expert in reliability engineering or analysis and I might be going around in circles trying to justify why I would use a parametric model against a semi parametric one so I would appreciate any advice on how to decide given the kind of field and data I have. Thanks

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    $\begingroup$ Take a look at the links here: lifelines.readthedocs.io/en/latest/… $\endgroup$
    – Cam.Davidson.Pilon
    Commented Oct 13, 2019 at 15:55
  • $\begingroup$ thanks. I have tried to use the check_assumptions function to test if the variable follow the proportional hazards assumption and the results return was that the PH assumption is met. this was further confirmed by using the proportional_hazard_test function where all the non transfromed variables had a p-value > 0.05. However when I checked the assumptions using the log cumulative hazard plot, not all variables showed proportional hazards visually. How do I then justify which test is more reliable? $\endgroup$
    – Py_Mel
    Commented Oct 14, 2019 at 12:54
  • $\begingroup$ I just read from another source: r-bloggers.com/cox-model-assumptions that the plot log(-log(S(t))) vs. t or log(t) is only for categorical variables but in my case, i have for example temperature value at 3 levels. Will that also be considered as categorical but in the form of a number or continuous? $\endgroup$
    – Py_Mel
    Commented Oct 14, 2019 at 14:28
  • $\begingroup$ from performing the schoenfeld residuals test to check PH, the global p-value results in 0.054 for transformation of kaplan-meier, 0.056 for rank and 0.24 for identity. although the km and rank global p value are close to 0.05, is it safe to conclude that that assume proportional hazards? $\endgroup$
    – Py_Mel
    Commented Oct 14, 2019 at 15:00
  • $\begingroup$ Well, this can depend on your goal too. If you are only interested in prediction, than model fit isn't as important as out-of-sample prediction accuracy. Since you are having trouble predicting with CoxPH model, you may be forced to use a parametric model. Given that, you can compare Weibull vs LogNormal vs. ... $\endgroup$
    – Cam.Davidson.Pilon
    Commented Oct 14, 2019 at 17:13

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