Geometric means for longitudinal data

[Erin Mead-Morse]

I have a longitudinal data set of pregnant women nested within trimesters. We measured biomarkers of toxicant exposure, for example toluene (bzma_im below). I examined the means using xtsum without any issues. A colleague recommended that I examine geometric means instead. I see there is a command, ameans. Is there an equivalent for longitudinal data? I have not been able to find one. Thank you.

* Example generated by -dataex-. For more info, type help dataex
clear
input long pid float(trimester bzma_im)
7511014 1       .
7511014 2 23.1728
7511014 3 22.2623
7511015 1       .
7511015 2 24.3935
7511015 3 35.6095
7511016 1  3.4852
7511017 1       .
7511017 2  4.6753
7511017 3  3.2963
7511018 1       .
7511018 2       .
7511018 3   12.88
7511019 1       .
end

[Andrew Musau]

The geometric mean of 1, 2, 3 and 4 is \((1\times2\times3\times4)^{\frac{1}{4}}= 24^{\frac{1}{4}}\approx 2.213\). As we cannot easily multiply over observations but can sum, a trick is to take the log of these values, calculate the mean and then take the exponent.

$$e^{\frac{1}{4}(\log(1) + \log(2) + \log(3) + \log(4))} \approx 2.213$$

Therefore:

gen logbzma_im = log(bzma_im)
bys pid: egen sum=total(logbzma_im)
bys pid: egen count= total(!missing(logbzma_im))
gen wanted= exp(sum/count)

[Nick Cox]

Andrew Musau 's method is what I would use too: witness the gmean() function for egen from 1999 in egenmore from SSC. You need to install that package, or at least copy _ggmean.ado, before you can use it.

The route from first principles is generally preferable. It's the same recipe: exp(ave(log())). Here is a demonstration:

* Example generated by -dataex-. For more info, type help dataex
clear
input long pid float(trimester bzma_im)
7511014 1       .
7511014 2 23.1728
7511014 3 22.2623
7511015 1       .
7511015 2 24.3935
7511015 3 35.6095
7511016 1  3.4852
7511017 1       .
7511017 2  4.6753
7511017 3  3.2963
7511018 1       .
7511018 2       .
7511018 3   12.88
7511019 1       .
end

egen gmean1 = gmean(bzma_im), by(pid)

egen numer = total(log(bzma_im)), by(pid)

egen denom = total(!missing(log(bzma_im))), by(pid)

gen gmean2 = exp(numer/denom)

list, sepby(pid)


     +-----------------------------------------------------------------------+
     |     pid   trimes~r   bzma_im     gmean1      numer   denom     gmean2 |
     |-----------------------------------------------------------------------|
  1. | 7511014          1         .   22.71299   6.245874       2   22.71299 |
  2. | 7511014          2   23.1728   22.71299   6.245874       2   22.71299 |
  3. | 7511014          3   22.2623   22.71299   6.245874       2   22.71299 |
     |-----------------------------------------------------------------------|
  4. | 7511015          1         .    29.4727   6.766929       2    29.4727 |
  5. | 7511015          2   24.3935    29.4727   6.766929       2    29.4727 |
  6. | 7511015          3   35.6095    29.4727   6.766929       2    29.4727 |
     |-----------------------------------------------------------------------|
  7. | 7511016          1    3.4852     3.4852   1.248525       1     3.4852 |
     |-----------------------------------------------------------------------|
  8. | 7511017          1         .   3.925709   2.735094       2   3.925709 |
  9. | 7511017          2    4.6753   3.925709   2.735094       2   3.925709 |
 10. | 7511017          3    3.2963   3.925709   2.735094       2   3.925709 |
     |-----------------------------------------------------------------------|
 11. | 7511018          1         .      12.88   2.555676       1      12.88 |
 12. | 7511018          2         .      12.88   2.555676       1      12.88 |
 13. | 7511018          3     12.88      12.88   2.555676       1      12.88 |
     |-----------------------------------------------------------------------|
 14. | 7511019          1         .          .          0       0          . |
     +-----------------------------------------------------------------------+

[Erin Mead-Morse]

Thank you very much Andrew and Nick!