Turning two doses into one safety number
If a drug becomes toxic at a dose only slightly above the one that helps, it is dangerous to use even if it works beautifully. So we compare the toxic dose to the effective dose. The classic ratio is the therapeutic index (TI): TD50 divided by ED50 (in animal lethality studies, LD50 divided by ED50). A larger number means a wider gap and a more forgiving drug.
Therapeutic index (TI) = TD50 / ED50 (or LD50 / ED50) Drug A: ED50 = 10 mg, TD50 = 1000 mg -> TI = 100 (very safe) Drug B: ED50 = 10 mg, TD50 = 20 mg -> TI = 2 (treacherous) Same effective dose, wildly different safety: Drug B leaves almost no room for error in dosing.
Why the index alone can lie
The therapeutic index compares two midpoints, but patients are not all average. What matters in practice is whether the dose that helps the last few patients overlaps the dose that harms the first few. A safer comparison is the margin of safety, which pits a high-effect dose against a low-toxicity dose — for example, the dose toxic to 1% of people (TD1) versus the dose effective in 99% (ED99). A related idea is the certain safety factor, LD1 divided by ED99, which asks the blunt question: can a dose that helps nearly everyone ever kill anyone?
From doses to concentrations: the therapeutic window
At the bedside we often think in blood concentrations rather than ratios. The therapeutic window is the band of plasma concentration that sits above the minimum effective concentration — below which the drug does too little — and below the concentration where toxicity begins, near the maximum tolerated dose. Stay inside the window and the drug both works and is tolerated. Drift below and the patient is undertreated; drift above and toxicity appears.
When that window is narrow — think of drugs like digoxin, warfarin, lithium, or many antiepileptics — even small day-to-day changes can push a patient out of it. Those are exactly the drugs for which clinicians order therapeutic drug monitoring, measuring blood levels to steer the dose and keep the patient safely inside the window.