Interpreting time ratios in ATF models (streg)

[Sven Heim]

Hello,
I read a post from Robert Gutierrez on the interpretation of time ratios in accelerated failure time (AFT) models which really confused me.
http://www.stata.com/statalist/archi.../msg00698.html

Here, Roberto argues that a time ratio of 0.88 means in case of a dummy variable that the treated group dies at a 12% slower rate.
From my understanding time ratios (the tr option in streg) are exponentiated coefficients. Thus, the coefficient is -0.13 from ln(0.88). According to other examples this means that treated group dies at a 14% faster rate due to exp(-0.88)=0.14 as explained here for example:
http://data.princeton.edu/pop509/recid1.html

Or am I totally wrong?

Thanks,
Sven

[Steve Samuels]

Yes, you are totally wrong. You are mistaking -0.88 for a log ratio.
You've just done this calculation:
ratio= 0.88 log(ratio) = -0.13
So far so good.

But you now have recomputed a "real" ratio as the exponential of the negative of the original ratio (exp(-0.88). Neither of the examples in the Princeton link does that.

[Sven Heim]

Yes, you are totally wrong. You are mistaking -0.88 for a log ratio.
You've just done this calculation:
ratio= 0.88 log(ratio) = -0.13
So far so good.

But you now have recomputed a "real" ratio as the exponential of the negative of the original ratio (exp(-0.88). Neither of the examples in the Princeton link does that.

Sorry, my fault. It should be exp(-(-0.13)) which ist 1.14. But my question remains because I don't understand why the treated group dies slower in this case as Roberto says and not faster?
In the Princeton Link they interpret it differently from my understanding. There is also a negative original coefficient (-0.349) but their interpretation is that the treatment group dies faster and not slower.

E.g.
In the Princeton example they get [1-exp(-0.349) ]= 0.29 and they say, the treated have a 29% shorter life.
In the other example we would get [1-exp(-0.13)] =0.12. Roberto says, however, the treated group dies at a 12% slower rate. But shouldn't it be faster not slower?

Many thanks,
Sven

[Steve Samuels]

I see the disagreement now. The Princeton page is right and Bobby Gutierrez was incorrect (a rare occurrence!): a ratio <1 -> the beta coefficient (log ratio) will be negative. That will always mean that there is a decrease in time for Z = 1 compared to Z = 0, no matter how that decrease is characterized.