What does 'y' stands for in the AFT model?

[shi-ang]

Hi,

Thank you for the excellent package!

As I'm learning about the AFT model, I have some naive questions about your implementation of AFT, and hopefully you can help me with those.

(a) In the AFT fitters (for example, Weibull AFT), the survival/cumulative hazard functions depend on both x and y. In my understanding, x represents the features, but then what does y represent?

(b) The way I learned about the Weibull AFT is from Page 398 of this textbook (link), which leads to a proportional hazard representation for the hazard function (Eq. 12.2.11). And the representation in your implementation (Weibull AFT) obviously differs from the one in the textbook. Is my understanding correct? And what causes the difference?

Thank you a lot!

Best,
Shi-ang