Heterogeneity with two studies With data from two centres I want to account for potential heterogeneity or confounders between two centers. So the analysis will initially be stratified by clinical center and a chi square test performed with one degree of freedom.  Is this appropriate with just two centres? Or is there an alternative?
 A: Are you calculating your chi-square statistic by squaring the difference between the logHRs and dividing by the variance of this diff? If so, that sounds absolutely fine to me. With only two centres, perhaps I wouldn't usually think of this a test for (between-centre) heterogeneity - i might call it a test for interaction with centre, or a test for between-centre difference in the effect (i.e. in the hazard ratio in this case). That's just terminology though. 
One thing that probably wouldn't be appropriate would be to estimate the between-centre variance, as with only two centre you really enough information for a meaningful estimate.
Another possible mistake to avoid: if the result of the test is 'not statistically significant' do not drop the centre effects, i.e. do still stratify by centre. Even if the HRs are the same in the two centres there could still be confounding by centre, i.e. the pooled HR could still be different from both. And even if that's not a 'significant' difference, avoiding any possibility of confounding by centre characteristics is always worth the loss of 1 degree of freedom. (In any case, it's usually a mistake to decide the method of analysis based on the results of statistical tests, an approach sometimes called 'data snooping' - see this earlier topic). 
(Note that I'm not suggesting the questioner was going to do either of those things, i'm just taking the opportunity to be particularly pedagogical.)
