Lecture 3: Cost-benefit analysis#
STATS60, Stanford University Spring 2026
How should you allocate anti-Malaria funding?#
Malaria is a serious mosquito-bourne disease. It is one of the leading causes of child mortality in Africa, and even when the disease is not fatal, it can result in permanent hearing/vision loss and other disabilities.
In our scenario, you are in charge of spending a fund of $10 million dollars to combat Malaria in Africa.
You must choose between the following options:
Vaccines:
You can fund a vaccine campaign. The Malaria vaccine is effective in children who receive a course of 4 doses.
Insecticide-treated mosquito nets:
You can fund a campaign to distribute insecticide-treated mosquito nets to families. Mosquito bites can be significantly reduced by sleeping under these nets.
Question: given the current information you have, which option think we should choose? Why?
Cost/benefit analysis#
When you want to decide “should I do X or Y?”, it is useful to do a cost-benefit analysis. The steps of a cost-benefit analysis are:
Quantify the cost of doing X, and the cost of doing Y
Quantify the benefit of doing X, and the benefit of doing Y
Decide: is X or Y more attractive, given the costs and benefits?
Steps 1 and 2 are basically Fermi problems; we are trying to estimate as well as we can based on limited information. So when the stakes are high, include another step:
Was the analysis robust?
Case study: Malaria interventions#
Suppose we are trying to decide whether to invest in distributing vaccinations omosquito nets.
What are sources of benefit?
Lives saved
Disabilities prevented
Labor time saved by prevented illness
How should we quantify benefit? What units should we use?
I suggest that we use (lives saved)/net and (lives saved)/(full vaccionation). This is one of many valid choices, but it simplifies calculations.
What are sources of cost? (Direct, indirect, intangible)
Materials: vaccines/nets
Distribution
Time to practice intervention
How should we quantify cost? What units should we use?
I suggest that we use dollars/net and dollars/(full vaccionation). Again this is one of many valid choices, but it will simplify calculations
Mosquito Nets: benefits and costs#
Set up a Fermi-style calculation for
the benefit
the cost of distributing mosquito nets.
Here are some facts that Tselil compiled/condensed to help us:
An unvaccinated child in sub-Saharan Africa will experience 1-3 Malaria infections per year in early childhood.
The infection fatality rate in the population is about 1 death per 400 clinical cases.
An insecticide-treated mosquito net costs $2 to manufacture
One net remains effective in its protection for about 3 years.
On average each net is shared by 2 people.
People sleeping under a net are half as likely to contract Malaria as those sleeping without a net.
Givewell was the main source for these facts.
Mosquito nets: costs#
One of many possible ways to estimate the cost/net:
(cost/net) = (cost to manufacture one net) + (cost to distribute one net)
We know the cost to manufacture is $2.
We don’t know the cost of distribution, but it is probably between $1-$10. In class we opted to estimate it by $1.
Our estimate: cost/net = $3
Mosquito nets: benefits#
One of many possible ways to estimate the (lives saved)/net:
(lives saved)/net
= (deaths prevented)/net
= (infections prevented / net) x (deaths/infection)
We know there are 1/400 deaths/infection.
We know there are between 1-3 infections per child per year.
We know that you are half as likely to get infected if you have a net.
We also know a net lasts for 3 years, and 2 people can share a net.
So we can model the number of infections prevented per net as follows:
(infections prevented)/net
= (# infections / child / year) x ( # years a net works) x ( # children sharing a net) x (chance a net prevents an infection)
If we plug in 2 infections per child per year, we get
(infections prevented)/net
= (2 infections / child / year) x ( 3 years ) x ( 2 children / net) x (1/2 prevented infections / infectons)
= 6 infections prevented/net
Putting it together, we estimate
(# lives saved / net) = (infections prevented/net) x (deaths/infection) = 6 x 1/400 = 3/200.
Our estimate: # lives saved /net = .015
Mosqiuto nets: cost/benefit ratio#
Our cost/benefit ratio is simply the ratio:
(dollars / net) / (lives saved / net) = $3 / (3/200) = $200.
Vaccines: benefits and costs#
Set up a Fermi-style calculation for the benefit and the cost of a vaccination campaign.
Here are some facts that Tselil compiled (and, between Friday and Monday, simplified):
An unvaccinated child in sub-Saharan Africa will experience 1-3 Malaria infections per year in early childhood.
The infection fatality rate in the population is about 1 death per 400 clinical cases.
The vaccine must be given according to the following schedule: an initial dose, followed by a booster 1.5 years later
Children who receive both doses are 15-25% less likely to die of Malaria than those not vaccinated.
For the sake of simplicity, assume children who are partially vaccinated do not see any benefit.
Attrition: about 35% of children who receive one dose end up getting both doses
In other words, on average you give about 4 doses per fully vaccinated child (for each fully vaccinated child, there are .65/.35 ~ 2 children who received only 1 dose)
A single dose of the vaccine costs $20.
The vaccine must be kept cold and administered by a trained professional.
Again, Givewell was the main source for these facts. This is a simplified set of facts because (a) there are actually 4 doses needed, not 2 and (b) there is actually partial immunity when a child receives fewer than the full 4 doses of the vaccine; we ignore this for the sake of simplicity.
Vaccines: costs#
One of many possible ways to estimate the cost/vaccine:
(cost/full vaccination) = (cost / dose) x (# doses / fully vaccinated child)
We know that you need about 4 doses to fully vaccinate one child, when accounting for attrition.
The cost per dose needs to take into account the cost of the vaccine and also the cost of distribution.
The vaccine costs $20.
Distribution probably costs between $1 and $100. Let’s say it costs $10.
So (cost/dose) = (cost of vaccine) + (cost of distribution) = $30.
Our estimate: cost/full vaccination = ($30) x (4) = $120
Vaccines: benefits#
We know that for every 10 unvaccinated deaths there are only 8 vaccinated deaths.
One way we can estimate lives saved / full vaccination:
(lives saved / full vaccination) = (chance of death if unvaccinated) x (% less likely to die if fully vaccinated)
We know children are 15%-25% less likely to die if vaccinated.
We know that the chance of death if unvaccinated, over a child’s first 5 years, is
(chance of death if vaccinated) = (# cases / child / year) x (5 years) x (chance of death / case)
= (2 cases / child / year) x (5 years) x (1/400 deaths/case)
= 1/40 deaths/child
Really we may want to account for the fact that a child is probably not vaccinated at 0 years old.
Putting these together,
our estimate: (lives saved / full vaccination) = (1/40 deaths/child) x (.20 survivals / death/ full vaccination) = 1/200
Vaccines: cost/benefit ratio#
Again, our cost/benefit ratio is simply the ratio:
(dollars / full vaccination) / (lives saved / full vaccination) = $120 / (1/200) = $240,000.
Analysis#
Which option has a better (higher) benefit/cost ratio? Are you surprised? Are you convinced?
How many lives can we save with our fund of $10 million?
Robustness#
How robust is our analysis?
Which components of our calculation are we least confident in?
Does our conclusion change if we vary them?
Suppose a one-shot vaccine becomes available, with comparable cost 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).