Editing Therapeutic index (section)

==Types==
Based on [[efficacy (pharmacology)|efficacy]] and [[drug safety|safety]] of drugs, there are two types of therapeutic index:

;Safety-based therapeutic index
<math>TI_\text{safety} = \frac{LD_{50}}{ED_{50}}</math><br/>
It is desirous for the value of LD{{sub|50}} to be as large as possible, to decrease risk of lethal effects and increase the therapeutic window. In the above formula, TI{{sub|safety}} increases as the difference between LD{{sub|50}} and ED{{sub|50}} increases—hence, a higher safety-based therapeutic index indicates a larger therapeutic window, and vice versa.

;Efficacy-based therapeutic index
<math>TI_\text{efficacy} = \frac{ED_{50}}{TD_{50}}</math><br/>
Ideally the ED{{sub|50}} is as low as possible for faster drug response and larger therapeutic window, whereas a drugs TD{{sub|50}} is ideally as large as possible to decrease risk of toxic effects. In the above equation, the greater the difference between ED{{sub|50}} and TD{{sub|50}}, the greater the value of TI{{sub|efficacy}}. Hence, a lower efficacy-based therapeutic index indicates a larger therapeutic window.

;Protective index
Similar to safety-based therapeutic index, the [[protective index]] uses TD<sub>50</sub> (median ''toxic'' dose) in place of LD<sub>50</sub>.

<math>\text{Protective index} = \frac{TD_{50}}{ED_{50}} = \frac{1}{TI_\text{efficacy}}</math>

For many substances, toxicity can occur at levels far below lethal effects (that cause death), and thus, if toxicity is properly specified, the protective index is often more informative about a substance's relative safety. Nevertheless, the safety-based therapeutic index (<math>{TI_\text{safety}}</math>) is still useful as it can be considered an [[upper bound]] of the protective index, and the former also has the advantages of objectivity and easier comprehension.

Since the protective index (PI) is calculated as TD{{sub|50}} divided by ED{{sub|50}}, it can be mathematically expressed that:
:<math>TI_\text{efficacy} = \frac{1}\text{Protective index}</math>
which means that <math>TI_\text{efficacy}</math> is a [[multiplicative inverse|reciprocal]] of protective index.

All the above types of therapeutic index can be used in both [[pre-clinical trial]]s and [[clinical trial]]s.