converting Risk ratio from quantiles to tertiles

[hatem ali]

We summarize the associations corresponding to the top versus bottom third of the baseline FGF-23 concentrations. In studies where different measures of association were reported, we
are trying to calculate a measure of association corresponding to the top versus bottom third of FGF-23concentration .
in some studies, associations were reported for top versus bottom quintile, quartile or half of the FGF-23 distribution. in some other studies, associations were reported per unit of standard deviation (SD)

I wonder if you can help me to convert the risk ratio as reported in the studies and calculate the risk ratio and confidence interval of top versus bottom tertiles?
(ln/unit=per unit on lnFGF-23 scale; Q4vsQ1=top quartile vs bottomquartile; log/SD or ln/SD=per SD on logFGF-23/lnFGF-23 scale)

Example of the data I got is :

Author	Risk ratio (95% CI) as reported in study report1; comparison
Parker 2010	1.05 (0.85, 1.3); ln/unit
di Giuseppe 2015	1.62 (1.07, 2.45); Q4vsQ1
Ix* 2012	1.19 (0.77, 1.83); Q4vsQ1
Ix** 2012	1.29 (0.75, 2.22); Q4vsQ1
Kendrick 2011	2.44 (1.25,4.76); Q4vsQ1
Moe 2015	1.2 (1.02,1.41); log/SD

[Nick Cox]

I don't think there is any way to convert your results to those for different bins without going back to the raw data.

[hatem ali]

Dear Nick Cox, Thanks for getting back to me.
I have found a paper that did this conversion without getting back to the raw data.
They did the following:
For example, in studies where associations were
reported for top versus bottom quintile, quartile or half of the FGF-23 distribution, the log hazard
ratios were scaled by factors of 0.779, 0.858 and 1.371, respectively, to reflect the respective
ratios of the distance between the means of the baseline FGF-23 measurements in top and
bottom third and the distances between means in top and bottom quintile, quartile or half in a
normal distribution (2.18/2.80, 2.18/2.54 and 2.18/1.59, respectively). Similarly, in studies
where associations were reported per unit of standard deviation (SD) increase (e.g.,logtransformed
FGF-23), the scaling factor used was 2.18 (as the distance between the means of
baseline FGF-23 measurements in top and bottom third of a normal distribution is 2.18x SDs).
For studies reporting associations per unit (or multiples thereof) increase in log-transformed
FGF-23, the respective units were converted to SDs (provided the SD of log-transformed
FGF-23 for the population was also reported) and the above approach employed. Where the
SD was required but not reported, it was estimated from the interquartile range


I am trying to do exactly the same but do not know how to do this on STATA . Also I am not sure if the way and the factors they used to scale the log hazard can be standardized
and used the same to do a similar analysis or not?

Looking forward to hear back from you

Hatem Ali

[hatem ali]

hello, i would appreciate if somebody can help