Convert T-values from Poisson regression to Standard Errors

Question

I am trying to summarize results from an article for a review (available for free here, I am looking at table 3), and thus want to find Standard Errors (SE) to compute confidence intervals. The article I am looking at gives the results of a Poisson regression as Incidence Rate Ratios (IRR) (that comes from exponentiating the calculated coefficients) - and t-values, which is not what I am used to.

From my interpretation of this article, $$\mathrm{SE}=\frac{\mathrm{IRR}-1}{\mathrm{Tvalue}}.$$ After a few tests, I get reasonable confidence intervals for this - eg. when the article says the result is significant, the confidence interval does not include 1 - but am I right? Or should I derive the $\mathrm{SE}$ from $\log(\mathrm{IRR})$ instead? Or use a different formula? I am a bit out of my league here.

Here is an example of my calculations - for example using an IRR of $0.76$ and a t-value of $1.96$:

$$0.76 - 1 = -0.24 \implies \mathrm{SE} = \frac{-0.24}{1.96} = -0.122$$

The confidence interval is then given by: $$\exp(\log(\mathrm{IRR}) \pm 1.96 \cdot \mathrm{SE}),$$ results in: $$0.76 \left[0.60 ; 0.97\right]$$

Answer 1

I contacted a statistics professor at my faculty and the author of the paper - the solution is:

SE_logIRR = log(IRR)/Tvalue

and the example calculation becomes:

SE_logIRR = log(0.76)/1.96 = -0.14002

and the corresponding result using the formula from the question:

0.76 [0.60 ; 0.97]