# Interpretation AFT, Cox PH and discrete-time hazard model

I am struggling with the interpretation of the AFT model, Cox proportional hazard model and discrete-time hazard model.

My question is:

Can the coefficients in discrete-time hazard model also be interpreted (e.g. by using glm or glmer in R) in the way described below. That means, "Positive coefficients imply the survival time is lengthened; hence, the hazard rate is decreasing" and the other way around? Is there any way to show this mathematically?

What I read so far (e.g. http://monogan.myweb.uga.edu/teaching/pd/16duration2.pdf and How do I interpret Exp(B) in Cox regression? and Interpreting Cox regression):

AFT model

• In case of the AFT (Accelerated Failure Time) model a coefficient of .2 indicates a reduction of survival time by this factor, meaning that in this case the event is experienced five times faster.

• In a proportional hazard model:

1. Positive coefficients imply the hazard rate is increasing; hence, the survival time is shortened.
2. Negative coefficients imply the hazard rate is decreasing; hence, the survival time is lengthened.

Cox proportional hazard model

• In the Cox model a coefficient indicates an increase in the log hazard rate.
• In an accelerated failure time model:
1. Positive coefficients imply the survival time is lengthened; hence, the hazard rate is decreasing.
2. Negative coefficients imply the survival time is shortened; hence, the hazard rate is increasing

Discrete-time hazard model

In the discrete hazard model the regression coefficient reflects the log of the odds-ratio, hence the interpretation as a k-fold increase in risk.