Bayesian Decision Theory and Coronavirus

2020 March 4
by Daniel Lakeland

You’d have to seriously be living under rock to not know about Coronavirus… But not matter how much you know about it at the moment, you probably don’t really know what we should do about it as a society. I mean, what are the various factors involved, should we close schools, churches, sporting events… what to do at nursing homes? Who should go to work and who should stay home? How would they afford it?

This is because all those questions are actually answerable to some extent (probabilistically at least) but there isn’t a group tasked with doing the analysis. It would be a good idea. Like, what the heck is the WHO doing if not at least staffing say 10 people who develop disease modeling software, and have several racks of computers to run MonteCarlo scenarios?

Well, whatever, if they were going to hire some people to do this stuff, what does the analysis look like? Here’s the general idea:

  1. Describe the factors that are associated with costs…
    1. Loss of Quality Adjusted Life Years (QALYs). This is the cost associate directly with “you don’t feel well for N days” all the way up to early death… The direct real-world cost of loss of healthy time.
    2. Loss of productivity: people who are sick don’t provide services to other people, they don’t produce goods, etc.
    3. Cost of treatment: people who are sick require other people to take care of them. They require medicines. Etc etc.
  2. Describe the factors associate with reduction of cost, or creation of benefits (or increasing costs above what they otherwise might be):
    1. Treatment of a person may shorten their sickness time.
    2. Treatment of a person may avoid them spreading the disease.
    3. Quarantine or Social Distancing may reduce spreading rate.
    4. Fast spreading rate may result in overwhelming local medical care, resulting in lack of care and much worse symptoms even death.

Once we put all these different factors into a model of the costs of any given scenario, we have the structure for a decision, but we still don’t know what the right values are for the parameters. For example, what’s the right cost of loss of worker time in India, how about in Vietnam… in Canada? How about the cost of health care, or the number of hospital beds etc? One needs to collect data, and estimate quantities. Some quantities will need to be estimated during the outbreak, like the growth rate of the number of cases in each country and the effect on this growth rate of different kinds of responses… Some numbers we will never know particularly accurately, but we will need to “borrow strength” from estimates across nearby regions, or similar cultures.

So, after specifying all that… we need to run a tremendous number of simulations, using the posterior distribution of the estimated quantities, predict the costs of different responses. From this we will get a variety of distributions over costs for different scenarios, and can calculate what seems to be the best response choice. If we make that choice, we continue to collect data and figure out what is going on, going forward, and continue to estimate what is the best choice… possibly changing the response through time as things become clearer whether they work. There’s some reason to think that that we should try different responses in different places, so as to collect information about what might work, and then switch people to the apparently most effective thing as time goes on.

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