comparing time ratio and hazard ratio estimates in a survival model

[Michael Keller]

Hello,

I am replicating a paper in which the authors use a continuous time accelerated failure time model assuming a lognormal distribution [ streg varlist, dist(lognormal) ] and report the time ratio of their estimates. I would like to use a different survival model and see what happens, considering the data structure ( which seems discrete and not continuous to me ) I would like to use a discrete time proportional hazard model and see how the results change.
Now in an accelerated failure time model I estimate the effect of covariate on time ratios, i.e. a coefficient > 1, means that the event (dead) happens later in time, because of this covariate. In a hazard model I estimate the hazard ratio, which can be seen as the conditional incidence rate meaning that a coefficient > 1 means that the incidence rate increases and the event happens earlier in time.

My question: is there a way to estimate a coefficient for a accelerated failure time model which is comparable to the estimate of the proportional hazard model or is the only way to calculate for example the mean for both models and compare them. It would look nicer if i could use a table with two columns showing the difference with a similar interpretation.

[Steve Samuels]

Is there a way to estimate a coefficient for a accelerated failure time model which is comparable to the estimate of the proportional hazard model?

Not unless you choose a Weibull or Exponential accelerated model, as these are also proportional hazards model; but you would have to convert to the PH parameterization. Is a table of means the "only way" to compare these models? No-- you can compare quantiles, SDs. However if you want to select the "better" model, compare AIC and BIC, with estat ic. This assumes that you've validated the fit of both models.

For a rule of thumb for deciding on a discrete model vs a PH Cox model, see:
http://www.statalist.org/forums/foru...screte-setting. I think that the "should use discrete" criterion is probably good for parametric models too.

For some advice about not fitting a continous model when there are a small number of discrete categories, see: http://www.statalist.org/forums/foru...screte-setting

[Michael Keller]

Thank you Steve for the answer.
One follow up question: you mention that I should compare the AIC and BIC between the continuous and discrete model to see which fits better.
Is this also valid if my data are definitely discrete? My data are measured in years, I cannot say for which individual the event happens first or second and the average spell duration is about 7 years. I also measured the proportion of ties which is way above 0.25 (around 0.5).
Does the AIC and BIC still provide me with the information which model I should use??

[Steve Samuels]

Does the AIC and BIC still provide me with the information which model I should use??

No. I recommended this for comparison of two continuous models.

[Michael Keller]

okay, thanks