As part of an email conversation about testing, Paul Romer sent the following message. He so beautifully encapsulated the case for testing, I asked for permission to post his email. Here it is. Here is a short summary of the case for testing.1. A program of "test and isolate" will reduce the effective reproduction number, R.2. ...
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As part of an email conversation about testing, Paul Romer sent the following message. He so beautifully encapsulated the case for testing, I asked for permission to post his email. Here it is.
Here is a short summary of the case for testing.
1. A program of "test and isolate" will reduce the effective reproduction number, R.
2. A combined policy of (i) more "test and isolate" which reduces R and (ii) more social interaction and more economic activity which increases R can be designed so that the net effect on R is zero.
3. The ratio of the cost of the additional testing to the additional economic activity that this combined policy will allow offers one way to estimate of the "rate or return" to spending on tests. My rough estimate is that this rate of return lies in the range of 10x to 100x so there is no doubt that test and isolate would be cost effective. To reach the higher end of the range, the cost of the test would have to be relatively low, say $10.
4. The combined plan under #2 will lead to more total cases. If the main measure of policy success or failure were deaths, an increase in the number of cases would not matter. Under the current circumstances, an increase in the number of cases is likely to be interpreted as a sign of a policy failure. This increases the political cost to the administration of increasing the number of tests. A second-best solution that avoids this cost might be to use at home tests and encourage people to self-isolate. This way, the results from the tests need not generate any new confirmed cases.
[JC Comment: one reluctance that the president or governors may have is that more testing naturally produces more measured cases, and the media don't seem all that good about recognizing this fact
Details on Targeting, Timing, and Compliance:
- Under the program in #3, the benefit created when more infectious people are isolated is received by unknown others who are free to resume normal activities. This is a classic case of an external effect. As a result, it makes sense for the government to pay for the tests and perhaps even to pay for "supported isolation" to increase the compliance rate. Because the fraction of the population that is infected is relatively small and because the required period of isolation is short, it would be relatively inexpensive to pay the few people who are in isolation, for example by making up any lost wages. Because transmission in the household is likely, it would make sense to offer a choice of isolation in a hotel or isolating the entire family at home. However, implementing this would require some way to confirm that someone is infectious, which precludes its use in the at-home approach noted under #4 above.
- For purposes of calculating the rate of return in the combined program described in #3, it is useful to consider a thought experiment of testing people at random. But in any practical program, the efficient way to use more tests is to start by targeting populations that have high ex ante probability of being infected. This could be done by concentrating the tests in high prevalence geographical regions, in high exposure populations, or on people identified by contact tracing. I am skeptical that contact tracing is the cost effective way to identify a large number of people who have a higher ex ante probability of being infected.
- For reducing R, what matters is the average number of infectious-person-days in isolation per test. This depends on (a) the number of true positives that are isolated and (b) when in the course of their infection they are isolated. The way to increase (a) is to target populations with a high ex ante probability of infection. The way to increase (b) is to use tests with a shorter time from sample to result.
- The choice between centralized lab testing and POC tests depends in part on an easily quantified tradeoff between a reduction in the sample-to-result time of most POC tests and a reduction in their sensitivity. But in the early months of any program for expanding the number of tests, the most important differentiator is likely to be the supply response. Many people are convinced that there is a large amount of lab capacity on university campuses that could rapidly be mobilized so that this path probably offers the lowest-cost path of expansion until manufacturing capacity increases for the POC or at home tests.
- There is a synergy between the frequency of testing in a population and the use of pooling to increase lab capacity. As the frequency increases, the frequency of positives will go down so that pooling becomes more cost effective.
- A large fraction of the total cost of a test comes from the discomfort experienced by the person who gives the sample and the time it takes for a healthcare professional to collect the sample. On both grounds, saliva samples will almost surely have the lowest cost.
- To reduce the cost from isolating false positives, any initial positives could be retested. Because the number of positive results will be a small fraction of the number of tests, retesting adds only a small amount to the cost of the program.
- As long as any true positives are isolated, the net effect of the combined program described in #2 will be to increase the total amount of social interaction by people who are not infectious, even if there are some false positives.
I hope this is helpful.