Question

From the quantal dose-response curves shown, the median toxic dose \(TD_{50}\) is 400 mg and the median effective dose \(ED_{50}\) is 100 mg. Calculate the therapeutic index.
(Refer to the figure.)

• A. 4
• B. 0.25
• C. 1
• D. 500

Hint:

Therapeutic index = toxic dose for 50% divided by effective dose for 50%.

Answer 1

The Correct Option is A

Step 1: Recall the definition of therapeutic index (TI).
The therapeutic index is a measure of drug safety, defined from quantal dose-response curves as:
\[ TI = \frac{TD_{50}\ (\text{or } LD_{50})}{ED_{50}} \]
where \(TD_{50}\) is the dose toxic in 50% of the population and \(ED_{50}\) the dose effective in 50%.

Step 2: Read the values from the curves.
From the figure: \(ED_{50} = 100\) mg (efficacy curve) and \(TD_{50} = 400\) mg (toxicity curve).

Step 3: Substitute.
\[ TI = \frac{400}{100} = 4 \]

Step 4: Interpret and eliminate.
A larger TI means a wider (safer) margin between effective and toxic doses. A value of \(4\) is the answer.
• \(0.25\) is the inverted ratio (\(ED_{50}/TD_{50}\)) - wrong direction.
• \(1\) would imply effective and toxic doses are identical - not the case here.
• \(500\) is the simple difference of the doses, not a ratio.

Key fact: \(TI = TD_{50}/ED_{50}\); the higher the value, the safer the drug.