Question:medium

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.)

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Therapeutic index = toxic dose for 50% divided by effective dose for 50%.
Updated On: Jun 25, 2026
  • 4
  • 0.25
  • 1
  • 500
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The Correct Option is A

Solution and Explanation

The graph plots two quantal (cumulative) curves: a left-shifted efficacy curve and a right-shifted toxicity curve. The 50% points on each define the two doses we need.

Therapeutic index is the ratio of the toxic dose to the effective dose:
$$TI = \frac{TD_{50}}{ED_{50}}$$

Plugging in the figure values $$TD_{50} = 400\text{ mg}, \quad ED_{50} = 100\text{ mg}$$
$$TI = \frac{400}{100} = 4$$

Checking the traps:
• $$\frac{100}{400} = 0.25$$ is the reciprocal - this would wrongly suggest the drug is unsafe.
• $$400 - 100 = 300$$ (or 500) is a difference, not the required ratio.
• A TI of 1 would mean no separation between benefit and harm.

A higher TI denotes a wider margin of safety, so the drug here has a fourfold safety margin.

\[\boxed{TI = 4}\]
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