Efficacy and costs of medical treatments

Question

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:

• other benefits of a treatment than monetary ones, e.g. quality-adjusted life years

• marginal costs c₂ instead of costs at some given point in time

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?

Answer 1

Your analysis looks similar to:

Incremental Cost-Effectiveness Ratio (ICER)

which:

ICER ... is used in cost-effectiveness analysis to summarise the cost-effectiveness of a health care intervention. It is defined by the difference in cost between two possible interventions, divided by the difference in their effect.

In your case, because of your normalization, ε is effectively a measure of relative cost, and so the denominator is ignored.