Dear All
I have been using a 2-parameter gamma model fitted to survival data. However I am finding the differences in parameterization rather confusing:

My first place of call was gsem's gamma family option. However I can't make much sense of the reported coefficients given. One is the "log of the scale" parameter, though it is clearly not as straightforward as that. I've gone through the entire SEM manual and the only formula description is of the survival function on page 560, involving an integral - nothing on the density function. This survival function seems hard to penetrate - I'm guessing it is some version of the upper incomplete gamma function, but trying to relate the terms to those one gets from a standard gamma parameterization is tricky. It seems the scale parameter enters the formula as 1/s^2 versus the usual alpha.

I was under the impression that constraining the ln(sigma) term (=0) from the generalized gamma in streg should give a standard gamma model. However the parameterization is still clearly different from gsem - though it doesn't help the comparison that gsem and streg give different log-likelihood values for the same model (is it whether it includes log time?), but including covariates results in slightly different estimates for these terms too so I'm not sure if the constraint is a correct one?

Now, Nick Cox and Stephen Jenkins' 'gammafit' command does fit a gamma model with the familiar gamma distribution parameterization, as per the wikipedia page for the gamma distribution. But it doesn't allow censored data. So I wrote a ml program to fit the gamma model allowing censored data using the wikipedia parameterization of shape (kappa) and scale (theta). I also fitted both terms in the log scale which gammafit doesn't do strangely (given the terms need to be >0).

So: my ml program gives exactly the same log-likelihood as gsem, so I know it is correct, but i just can't square the respective parameters, and why they are done like this in gsem? When including covariates on the (my program) theta term, the results for the covariates themselves are identical to those for gsem, so they are also AFT interpretable. Another problem I have is prediction. For gsem I can use predict and get an appropriate fit to KM data but when I try and fit my program results to a KM failure function the curve is out by a factor of about *0.863. I thought the survival function for a gamma model was basically (1-gammap(a, x)), which in my case is (1-gammap(kappa, time/theta)). This is what I used in the likelihood function of my ml program for the censored terms and it gave the correct log-likelihood value, so I am confused it doesn't appear to give the correct survival/failure prediction?!

Any illumination on the discrepancies greatly appreciated!