Why is therapeutic index a ratio instead of an interval?

Question

The therapeutic index of a drug is defined as its toxic dose ($TD_{50}$) divided by its effective dose ($ED_{50}$). Why is it defined as a ratio rather than the difference $TD_{50} - ED_{50}$?

For example, if drug A has an effective dose of 1 ml and a toxic dose of 2 ml, and drug B has an effective dose of 50 ml and a toxic dose of 100 ml, then they both have the same therapeutic index (2), but intuitively, I would say drug A is much more dangerous, which is reflected if we take the difference instead.

Answer 1

Most drugs are measured by mass - they are then dissolved in some solution or incorporated with fillers into pill form.

If you are worried only about a difference, say from measuring out a volume to be given intravenously, then it would be trivial to solve that issue by dilution: you could take your drug that was dissolved in 1 mL, dilute it so that you are giving 50 mL instead, and make the difference unimportant. The ratio, however, stays the same, regardless of formulation.

A ratio is also much more likely to come up in clinical practice. Take your example, where the toxic dose is only 2X the effective dose. That means that an error where a drug is accidentally given twice could be a serious problem. It doesn't really matter if the volume delivered is small or large, just that someone doesn't realize the drug was already given.