the 30% reduction in the longest diameter of the tumour comes...

the 30% reduction in the longest diameter of the tumour comes from the fundamental criteria used to define response rates in all solid tumour studies.

its called the recist criteria. it is used universally as standard practise in all solid tumour studies and defines a partial response as 30%.

you are right in thst this arbitrary cut off has never really been truly validated, such that a 25% reduction in diameter may still confer a clinically significant benefit in terms of quality of life/ pain / survival.

ill see if i can find a quick link to recist.

in the meantime, given the volume of a sphere is 4/3 x pi x r cubed then it is obvious that a 30% radial reduction will lead to a far greater volume reduction
eg for a diameter of 20mm which is a radius of 10mm, the volume would be roughly 4,000 mm3.

if the diameter drops 30% to 14, the radius drops to 7, then the volume drops to roughly 1,500 mm3. so thats a 5/8 (63%) reduction in volume for a 30% reduction in diameter.

i didnt use a calculator thats just off too of my head so correct me if im grossly wrong on this.

anyway, the point is that it makes sense that say a 15% median diameter reduction could translate to a 39% volume reduction.