Every z-score assumes a shape for the healthy distribution. Near the middle the shape barely matters; for a severely dilated aorta it can double the z-score. Move the slider to see how.
A z-score needs three things: the expected (median) diameter, the spread, and the shape of the distribution. The shape is set by the Box-Cox power, λ. With λ = 0, diameters are log-normal, so being 20% above the median counts the same at any size. With λ = 1 they are normal in millimetres, which is the assumption behind ratio z-scores such as diameter ÷ BSA0.5. With λ = 2 they are normal on the scale of an area, as with CSA/height.
The calculator estimates λ from the healthy children for each level instead of assuming it. Here the median and spread stay at the fitted values for the child below, and only λ changes.
Enter a diameter, height and age.
| Shape | z | Band | D at z +2 | +3.5 | +5 |
|---|
Percent of expected does not change with λ. The z-score and the cutoffs do, and the differences grow the further out you go.
Colored horizontal lines mark z = 2, 3.5 and 5. The dotted vertical line is the entered diameter. The curves agree near the median and spread apart in the tail, where the reference data run out (beyond about z ±4). Hover to read values.
The fitted λ is about 0.05 at the sinuses (essentially log-normal), and about 0.4 at the sinotubular junction and the ascending aorta. A shape of 2 was strongly rejected at every level. Because the median and spread here stay fixed while λ moves, the alternative shapes are illustrations rather than refitted models; a full refit at a fixed λ also adjusts the spread slightly.
No healthy child in the reference data sits much beyond z ±4, so past that point any z-score, from any calculator, depends on the assumed shape rather than on data. That is why the calculator also reports percent of expected.