Lecture 3: Cost-benefit analysis

Lecture 3: Cost-benefit analysis#

STATS60, Stanford University Spring 2025

Making good decisions#

Researchers have developed a new medication which, in double-blind randomized trials of individuals with cholesterol levels above 240 mg/dL, reduces the incidence of heart attack by 30%: for every 100 heart attacks in the control group, there were only 70 heart attacks in the treatment group.

The medication needs to be taken every month, and each dosage costs $ 500.

Decide: is it worth it to broadly deploy this medicine?

Cost/benefit analysis#

When you want to decide “should I do X?”, it is useful to do a cost-benefit analysis. The steps of a cost-benefit analysis are:

  1. Quantify the cost of doing X

  2. Quantify the benefit of doing X

  3. Decide: does the benefit outweigh the cost?

Steps 1 and 2 are basically Fermi questions; we are trying to estimate as well as we can based on limited information. So when the stakes are high, include another step:

  1. Is your analysis robust?

Case study: Preventative care#

Suppose we are trying to decide if we should deploy the heart medication from the previous slide (details loosely based on statins).

  1. How should we quantify cost/benefit? What units should we use?

  • It is easy to quantify the cost of medication in dollars/year.

  • The benefits are harder to quantify in dollars/year.

  • To make a comparison, we are going to need to come up with a way of measuring the benefits (lives saved, quality of life) in the same units as the cost.

  • It is conventional to do this in dollars as well, though the conversion is inherently subjective.

(2) What are sources of cost? (Direct, indirect, intangible)

  • Medication

  • Consultation and screening

  • Indirect costs: time spent on treatment (measure in wages?)

(3) What are the benefits? How can we measure them?

  • Lives saved ($ contributed to society by working for rest of life? Life insurance payout?)

  • Cost of treatment for prevented attacks

  • Labor time saved by prevented attacks

Costs#

Set up a Fermi-style calculation for the cost of putting all U.S. adults over the age of 40 with cholesterol \(\ge 240\) on this medication.

Here are some facts that Tselil compiled to help us calculate the cost:

  • The medication must be taken monthly, and each month’s dose costs \(\$500\).

  • 10% of U.S. adults over the age of 20 have cholesterol levels above 240 mg/dL (source: CDC).

Remember to account for indirect costs.

In class, we broke it up as follows:#

Cost = (Medication cost) + (Screening cost) + (wages lost in time spent on treatment)

(Medication cost) = (monthly dose) x (months / year) x (# treated)

( # treated) = (# US adults over 40) x (fraction with high cholesterol)

(Screening cost) = (# US adults over 40) x (fraction screened per year) x (cost of screening)

(wages lost to treatment) = (# treated) x ( hours treated / year) x ( average hourly wage)

Values estimated in the spreadsheet.

Benefits#

Set up a Fermi-style calculation for the benefit of putting all U.S. adults over the age of 40 with cholesterol \(\ge 240\) on this medication.

Here are some facts that Tselil compiled to help us calculate benefit:

  • In trials of US adults with cholesterol \(\ge 240\) mg/dL, for every 100 heart attacks in the control group, there were only 70 heart attacks in the treatment group.

  • More than \(8 \times 10^{5}\) people in the U.S. have a heart attack each year. (source: CDC)

  • The fraction of heart attacks that occur in people with high cholesterol is 1/4.

  • The cost of treating a heart attack in 2010 was around \(\$1.8 \times 10^{4}\).

  • A 2010 US dollar is worth \(\$1.46\) today.

How can you account for intangible benefits?

In class, we broke it up as follows:#

Benefits = (attack treatment cost saved) + (wages of treatment time saved) + (cost of lives saved)

(attack treatment cost saved) = (cost of treatment) x (# attacks prevented per year )

(wages saved) = (# attacks prevented per year) x (hours spent on treatment per person) x (average hourly wage)

(cost of lives saved) = (# attacks prevented per year) x (fraction attacks fatal) x ($ value of life)

Values estimated in the spreadsheet.

Analysis#

Let’s put together our cost-benefit analysis. Do the benefits outweigh the costs?

Compute the cost/benefit ratio. If > 1, then no.

Robustness#

How robust is our analysis?

  • Which components of our calculation are we least confident in?

  • Does our conclusion change if we vary them?

  • What affects costs most: treatment, or screening?

  • Suppose a generic drug becomes available, with a cost of \(\$5\) per dose. Does the conclusion change?

Try varying our estimates in the spreadsheet.

(The class copy of the spreadsheet is not editable; download a copy to vary the values).

What does the cost of screening and/or medication need to be for the cost/benefit ratio to drop below 1?

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