# Comparing Dose/Response Curves

You have learned that dose is a measure of exposure that accounts for body size, and you saw examples of typical dose/response curves. You also heard about how important dose/response curves are to regulatory decisions in both toxicology and pharmacology.Remember, in a dose/response curve, the X-axis represents dose and the Y-axis represents the percentage of test subjects that have a particular biological response at that dose. Note that the X-axis is often plotted on a logarithmic scale—which just means that each step represents a power of ten, rather than a single unit, so we can compare a very wide range of doses in a single graph.You may have noticed in previous examples that half of the subjects fall above, and half fall below, a median dose. Because different individuals can have different sensitivities to the same molecule, there is a distribution around this median. So this median dose, at which half the subjects exhibit the response, and half the subjects do not exhibit the response, is a useful reference dose.Let’s examine aspirin. Like all drugs, it has both beneficial, and possibly harmful, effects. One measure of toxicity—and a rather crude measure, at that—is death. If we plot a dose/response curve that reflects the number of lab animals that die because of an overdose of aspirin, we observe a curve centered over a fairly high dose range. The dose that is lethal to fifty percent of the test subjects is referred to as the median lethal dose, or LD50. LD50 is a very common measure of toxicity used by drug companies and regulatory agencies, and it is calculated by measuring a dose/response curve. The median lethal dose for aspirin is about 500 milligrams per kilogram of body weight.But we aren’t only interested in a drug’s harmful effects; we also need to know what dose of a drug is effective for its medical purpose. So, if we plot a dose/response curve that reflects the number of lab animals that exhibit pain relief due to aspirin, we observe a curve centered at a lower dose range. The dose that is effective in fifty percent of the test subjects is referred to as the median effective dose, or ED50. Potency is the word pharmacologists use to mean beneficial effectiveness of a drug. ED50 is a very common measure of potency used to evaluate drugs, again, calculated by measuring a dose/response curve. The median effective dose for aspirin is about 25 milligrams per kilogram of body weight. Obviously, it’s a good thing that the median effective dose is much lower than the median lethal dose for aspirin. But we can quantify how big this safety margin between ED50 and LD50 is with a ratio called the therapeutic index.Therapeutic index is the ratio of median lethal dose to median effective dose. We put median lethal dose in the numerator so that the farther away it is from the median effective dose, the higher the therapeutic index. Higher therapeutic index means a higher margin of safety from an accidental overdose. For aspirin, the therapeutic index is 20. In other words, a patient would have to take 20 times the recommended dose of aspirin in order to be at risk for a lethal overdose, which would be unlikely to happen by accident. Let’s look at another example. Digitalis is a drug prescribed to people who have suffered heart attacks. The median effective dose of this drug is roughly 15 mg/kg. But the median lethal dose is only about twice as much! In other words, the therapeutic index of this drug is just 2! Needless to say, it is not out of the question that a patient might accidentally take a lethal overdose of this drug, so it is administered only under very close supervision.Remember, for any particular substance, there are as many different dose/response curves as there are biological responses that we can measure. Curing a headache and causing death by overdose are very different endpoints. Potency and lethality are two responses that are commonly used to evaluate drugs, but they are not the only responses that might be important to measure.