Calculation of grand median in FA

Dear DS community,

I wonder how the grand median across all data sources is computed in FA considering that the conventional computation requires the ordering of the combined observations from all data sources?

How does the computation of the grand median differ between data which cannot easily described by a theoretical, parametric distribution vs a data which can be described in such a way, ie a normal distribution?

Best regards,


Hi Wilmar,

unless it is changed, right now the function computes the sample size weighted average of the site-specific medians. Thus, you can only get a median exact per site, the aggregated one is averaged.

As an alternative, you could combine the stie-specific medians via meta-analysis techniques: McGrath S., Zhao X., Qin Z.Z., Steele R., and Benedetti A. (2019). One-sample aggregate data meta-analysis of medians. This is implemented in the R-package metamedian and the function

Best, Daniela

Hi Wilmar,

Daniela is correct. At the current version of DS we provide the weighted average of the site-specific medians as an approximation of the pooled median. However, we are working now on the development of an encryption-decryption algorithm to allow a secure federated ranking of a variable from multiple studies. When we have this algorithm, we can then get the exact pooled median, quantiles, etc.

Hi @demetris.avraam, you might want to also consider this work for what concern “encryption-decryption”:


Hi @bono,

That looks very interesting. I will read it carefully and let you know if i have any questions! By the way, I have recently developed a ds.skewness and a ds.kurtosis function that calculate both the study-specific and the pooled skewness and kurtosis. Both are included in the latest version of DS.

Best, Demetris

Hi Demetris, please feel free to contact if necessary. ds.skewness and a ds.kurtosis is definetly an update well fitting with the method in the paper … Let me know if any integration is needed.