I am working with a dataset of 5298 women with DXA-scans (Dual-energy X-ray absorptiometry) in which three different machines were used for measurement: HOLOGIC_2000 (n=2275), HOLOGIC_4500 (n=1485) and LUNAR (n=1538).
The three populations have the same distribution in terms of age, weight, height, BMI. Therefore, I would expect the DXA measurement, between the three groups, to have the same distribution as well but this is not the case.
I would like to calculate a ratio between the weight and the “total lean” of each person. But since the “total lean” depends on which machine was being used, I can’t calculate the ratio directly, as it would introduce a bias.
Here are two plots of “total lean” and “total fat” respectively. As you can see, the LUNAR machine measures “total lean” a bit higher than the other two machines. When looking at “total fat”, the machines seem to disagree especially for the women with more fat.
In order to treat these three groups as one group, and make the DXA-measurements comparable, I have calculated z-scores for each population, and thereby normalized them.
Is this a reasonable thing to do? Will I still be able to calculate a ratio using these values?
I would like to know if there is a better way to correct for the fact different machines have been used without having reference values/ double measurements.
Someone suggested I use EM but im not certain how I would do this.