# Efficacy and costs of medical treatments

There is an easy to grasp formula which combines the efficacy and the costs of a medical treatment, however these may be determined. I wonder if this formula (and the approach) has a name, and which role it plays in public health economics. The bigger context surely is cost-effectiveness analysis and its special case cost-benefit analysis.

Consider the following scenario: There is a population in which at any time some N individuals suffer from some disease X ("patients"). Let there be an established therapy or treatment T1 (pharmaceutical or other) which costs c1 per patient. Let there be a new therapy T2 with efficacy ε which costs c2 per patient. Efficacy ε shall mean that a proportion ε of patients is cured by the therapy. Let all patients receive a treatment, either T1 only (scenario 1), or first T2 and only if it doesn't help T1 (scenario 2).

Note that for our purposes c1 may as well be considered the subsequent costs per patient when there is no treatment T1 at all and T2 is the first treatment in the market.

The total costs in the two scenarios are:

• C1 = N · c1

• C2 = N · c2 + N · (1 - ε) · c1

Normalizing with respect to N and c1, i.e. N → 1, c1 → 1, c2 → c2/c1 gives

• C1 = 1

• C2 = c2 + (1 - ε)

The additional costs of scenario 2 compared to scenario 1 are

• ΔC = C2 - C1 = c2 - ε

where c2 and ε are dimensionless numbers which it makes sense to compare.

If c2 > ε ("the costs are higher than the efficacy") scenario 2 may be considered uneconomical, if c2 < ε ("the costs are lower than the efficacy") it may be considered economical.

Next to the difference c2 - ε one may consider the ratio ε / c2 as the cost-effectiveness of treatment T2.

Starting from these considerations one may take into account:

To repeat my question from above:

• Where, in which disguise and under which name can I find these considerations (based on ΔC) in textbooks on health economics or the literature?
• I'm not sure I understand your question. Are you asking what the general term for &Delta;C is? Do any of these help: en.wikipedia.org/wiki/… ?
– JMP
Jun 11 at 4:15
• @JMP: Thanks for the hint. Does this book still play a role, e.g. in education? Yes, it's about &Delta;C - but as a difference between a (relative) price and an efficiacy! Jun 11 at 15:11