# Re: st: "time ratios" and "hazard ratios"

 From sjsamuels@gmail.com To statalist@hsphsun2.harvard.edu Subject Re: st: "time ratios" and "hazard ratios" Date Thu, 14 May 2009 10:57:40 -0400

```--

"can I take the multiplicative inverse of the time ratio and report it
as a hazard ratio?"

No, The (log) Weibull is the  only probability distribution for which
this is true.

It's a good idea to consider multiple probability distributions, as
you have done. but reporting the regression results is not enough.
Have you evidence that these distributions fit the data?  (using a
-linktest- or diagnostic plots, for example); that one fits any better
or worse than the others?  You can compare directly the likelihoods of
the log-logistic and log-normal, and those of the log-normal and
Weibull models.

For hazard ratio models, I rarely see anything but a Cox model these
days, because the Weibull has a very restrictive shape. Patrick
Royston's -stpm-  (from SSC) offers a flexible parametric version.
For the log-linear regression models , the generalized Gamma in Stata
has the most flexible shape, and its likelihood can be compared
directly to those of the Weibull and log-normal.   See:  Stephen
Jenkins's  book “Survival Analysis”, available from his website
(http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/pdfs/ec968lnotesv6.pdf
).

-Steve

On Wed, May 13, 2009 at 7:16 PM, Emory Morrison
<Morrison@soc.msstate.edu> wrote:
> I am reporting different specifications of event history models within the same paper.
>
> In some of the models (for example the log logistic specification and the log normal specification) stata reports coefficients as time ratios.
>
> In the Weibull model stata report coefficients as hazard ratios.
>
> While the direction of effects are clearly inverted in these two ways of reporting the coefficients, I need to know if these coefficients are precisely inverse.  In other words, can I take the multiplicative inverse of the time ratio and report it as a hazard ratio?
>
> It would be very helpful in writing up the results of the paper, if the coefficients could be read and interpreted in a standardized fashion.
>

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```