If you are going to use a frequentist analysis for this, Hartaung Knapp has been reported to have better coverage for small sample sizes compared to the DerSimonian-Laird approach. But you might want to read this:
The problem – you only have 3 studies. So of course the CI is going to be wide.
You will need to find more studies, but I think a meta-regression approach would be more useful to explore the heterogeneity.
Addendum This will be a great start to doing a meta-analysis in a rigorous way, in that it doesn’t naively substitute estimates of components for variance, and treat them as population parameters.
Think carefully about the effect size measure. Maybe using the log odds instead of the hazard ratio will reduce heterogeneity?
Ignore the “significance” of the aggregate CI. If you extracted the one tailed p-values from each of the CI and used a combination procedure, I’m sure it would indicate that there is a positive association before a CI would reject the null.
I put together a thread with a lot of references on statistical issues related to meta-analysis. Suffice it to say – the common textbook procedures will lead you astray if you are not careful.