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Yes, let’s vaccinate twice as many people against covid-19

I am very sympathetic to Robert Waldmann’s argument that we should give twice as many people one dose of the new Pfizer/Moderna vaccines, at least until supply constraints are eased, instead of following the FDA approved vaccination protocol and giving everyone two doses right from the beginning. What follows is a rough way of thinking about the logic and perhaps the magnitudes involved. Let me emphasize that this is just a finger exercise and I am not an epidemiologist, but with those important caveats I will share my work.

Here are my assumptions. The reproduction number of the virus is currently 1. This means that if behavior, transmissibility, and natural and vaccine acquired immunity are all unchanged, the number of people getting infected each day will remain the same. I assume that there are 300 million people in the United States, 40 million of whom are currently immune due to prior infection, and 260 of whom are susceptible. There are 400,000 new actual infections each day (two times the reported number of cases). These infections lead to 3,000 deaths per day (roughly the current number).

Covid 19 Vaccination: One Dose or Two ?

I am going to write more on the topic of Covid 19 vaccines. I will argue that it would be better to give second (booster) shots only when vaccine supplies are plentiful. I think that so long as the vaccine is in short supply, people should be given one dose. I criticise the current policy of withholding vaccine to make sure that everyone who gets a first dose gets the scheduled booster either 3 weeks later (for the Pfizer vaccine) or 4 weeks later (for the Moderna vaccine). I argue that more lives will be saved with the one dose until supplies are plentiful strategy (even if many people don’t show up for the booster when supplies are plentiful). I think that the current policy will lead to tens of thousands of un-necessary deaths in the US alone with worse consequences for countries further back in line for vaccine supplies.

The post will have two sections. One will be an attempt to analyse the published data, which are mostly Kaplan and Meier plots with numbers read off by eyeballing. I will conclude that the best (poor) estimate of the reduction of infections from the first dose is more than 18 times the reduction due to the second dose. This calculation requires the key unproven assumption that the effect of one shot is weaker than but as durable as the effect of two shots.

This would mean that efficient deployment is one dose for as many as possible as soon as possible and second doses when giving them doesn’t interfere with this. I will go on to bore people with some p-values. I think that the null that it is as efficient to give second doses on schedule is rejected at at the 5% level (given published data). I note that benefits probably include the (unproven) prevention of transmission as well as benefits for the vaccinated people. I also note that giving two to some and zero to others is unfair especially given the difficulty of deciding who gets vaccinated first and the necessarily partly arbitrary decisions. The second section will come back to arguing about public policy and ethics as I just did.

SCOTUS: States Can Regulate Insurance Plan Contractors

While briefly discussing (accessible link below for addition information) this decision, keep in mind this is a big deal in lowering the costs of pharmaceuticals as it goes right to the source of some of the excess takings involved in the distribution of drugs from manufacturer to drug stores.

December 10, 2020: the Supreme Court handed a win to states and broadened the path for state health care cost control efforts. In Rutledge v. Pharmaceutical Care Management Association, the Court ruled 8-0 that the Employee Retirement Income Security Act (ERISA) did not preempt Arkansas’s law regulating pharmacy benefit managers (PBMs), the intermediaries that administer prescription drug benefits for health plans.

Speaking for an unanimous Court, Justice Sonia Sotomayor, held that “state laws requiring PBMs to pay pharmacies no less than their acquisition costs for prescription drugs was not preempted by ERISA (the federal statute governing employee benefits). ERISA does not pre-empt state rate regulations that merely increase costs or alter incentives for ERISA plans without forcing plans to adopt any particular scheme of substantive coverage.”

Liveblogging the FDA hearing on the Moderna Covid 19 vaccine

So Far the efficacy data has been presented. As reported in the press earlier, the vaccine is roughly 95% effective, that is roughly 95% of people who got Covid 19 during the trial were participants who received the placebo.

Importantly, the null hypothesis that just one dose is just as good as two was not rejected. The test of this null had extremely low power as almost all participants received both doses, so basically this means cases less than 4 weeks after the first dose (so one week after the second dose). However, note the extreme rigidity of the FDA.

Before allowing vaccination, the FDA required proof of efficacy. Before allowing a modification from two doses 4 3 weeks apart to one dose, the FDA requires … I don’t know maybe if Jesus Christ returned and petitioned them for some flexibility, they would give Him a hearing, but I guess they would tell him he needed to propose (and fund) a new Phase III trial.

update: incorrect assertion of fact crossed out

It is also true that there is no evidence of benefit from the second dose of Pfizer’s vaccine. It is clear that people who have received one dose of either vaccine are among those least at risk of Covid 19.

See the raw data below from Polack et all 2020 . Can anyone see from the Kaplan Meier plot when the second dose was given ?

The vaccines are in very short supply. People are anxiously waiting for vaccination. Because the protocol had two doses, half of the vaccine will be reserved for the people who will benefit least.

Here there is a difference between careful science and optimal policy. In science it is crucial to write the protocol first then follow it mechanically. This is necessary so that the experimental interventions are exogenous and one can be sure they cause the observed outcomes and are not caused by observations.

However, it is not optimal policy to reduce the possible decisions to two, a priori with extremely limited data. This is what the FDA does. I think they should approve a single dose. Their rule is always to only act on extremely firm knowledge. It is, in this case, not going to be first do no harm. The second dose has side effects (mild but not zero). There is, I think, no weak evidence of benefits. (Again, the test has extremely low power (and I’m not sure protocol did not say the question would be addressed — if it didn’t then there is a problem — the rule decide what to do in advance applies to data analysis too — it is vital that the data not be dredged looking for a significant coefficient)). I think the point estimate is pretty much exactly zero benefit. of a benefit of the second dose much lower than of the first (and without proof of any benefit.

I think that people should be given a single dose. After everyone who wants one dose has been vaccinated, then it makes sense to give people a second dose. There is no reason to think spacing 4 3 weeks apart is optimal — the spacing was decided in advance (and it was 4 weeks for the Moderna vaccine hence my mistake).

Covid update

I seem to be through the worst of it. My fever is down and my cough is subsiding. If I hadn’t gotten a covid test I would have thought I had a moderately bad cold. With a bit of luck, it’s all over except the quarantine. Thanks to everyone for their good wishes.

Paying people to get vaccinated?

Apparently there are proposals circulating to pay people to get vaccinated. (Summary here.) The pro/con story is familiar enough. Monetary incentives might increase the uptake rate; but they might also increase suspicion and backfire, or at least not be very effective. Given the large cost involved – the number cited in the linked article is $1,000, which could cost well over a hundred billion depending on eligibility – a small increase in vaccination rates might not be worth it.

Here is an alternative suggestive. When people get vaccinated, give them cash cards worth $100 that can only be used to purchase restaurant food for 10 days, beginning 5 days after they get vaccinated. The framing of this might be more positive than a simple cash incentive – we are paying you to go out and help jump start your local economy, especially the businesses that have been struggling so much in the epidemic. It helps to emphasize the pro-social aspect of getting vaccinated. Plus it would be much cheaper than giving everyone $1,000, and support from restaurants might help push it into the end zone in Congress.

I have covid . . .

I’m fairly certain I picked it up this past Tuesday.   Wednesday night I had a slight throat-clearing cough.  Not sure if this was covid related or not.  Saturday I had a fever of 100.5, along with some achiness.  I got tested on Saturday and received the positive test result on Sunday.  Last night was a bit worse than the night before.  I had chills and aches.  When I am not sick I am usually more or less pain free; when I get a cold or flu all my old aches and pains come back for an encore.  That happened last night.  In addition, the cough moved into my lungs and became deeper, and I got just a bit wheezy.  This morning with the help of acetaminophen I feel pretty good – if you dropped me into my body without telling me that I had covid it might take me a while to notice that I was sick.  I don’t have any other symptoms.

My initial reaction to my diagnosis was fairly optimistic.  I thought it was likely I would have a mild case and would soon be able to visit family and friends again, including a favorite uncle who is quite sick.  Having read a bit on disease progression, I think my initial take may have been a bit optimistic.  I am still early in the course of the disease; things could definitely go south over the next 3 to 5 days.  My sense is that I have a small chance (maybe 10% to 20%) of ending up in the hospital, and other than that an even chance of skating through relatively unscathed or spending several days struggling to breath but pulling through at home. Having the cough move to my chest last night was sobering.

Although I hope to get through this relatively easily and to enjoy a real benefit from immunity (I would not be vaccine-eligible for months) I would not have chosen to get sick.  The prospect of gasping for breath for a several days at home is very unappealing, choking to death alone would be oh-so-much worse.  I would rather have waited for a vaccine.  Be careful out there!

The Failure of the Public Health Establishment

Prof. Peter Dorman of Evergreen College writes at EconoSpeak and portrays Matt Yglesias’s retrospective on how the healthcare establishment failed the public when passing information on facemasks, hand-washing, distancing, etc., and how Covid is transmitted.

The direct result of not following these practices or casting doubt upon them is an elevation of Covid cases which strains the capacity and logistics of healthcare facilities, the equipment used on patients, and the supply of medicines.


Matt Yglesias has an excellent retrospective on the absurd reversals over mask usage that arose in the early stages of the pandemic.  You will recall that the public health establishment, amplified by mainstream media outlets like the New York Times, told us all to ditch our masks and concentrate instead on frequent, vigorous hand-washing.  This was transparently absurd at the time, since from the beginning it appeared that coronavirus transmission had something to do with airborne virus exposure.

We were told masking didn’t protect us.

We were told only N95 masks worked, and only if they were taken on and off just so, in a complex procedure us untrained mortals could never execute.

And we were told we had to save these precious masks so health care workers could protect themselves, even though that was in direct contradiction to argument #1.  (Later, Anthony Fauci told us that conserving the inadequate supply of N95’s was the underlying motivation, and the rest was mostly persuasion.)

Should we worry about hospitals being overwhelmed with COVID-19 Patients? Libertarian: Nah.

Our friend Donald Boudreaux is at it again, dispensing misleading statistics that just so happen to favor libertarian outcomes.

Two days ago Boudreaux posted some data on hospital capacity that seem to suggest that we do not need to worry about hospitals getting overwhelmed with COVID patients because capacity utilization over time is flat.  As Boudreaux puts it:

The bottom line is that, when broken down to the state level – at least for the period November 4th through December 4th – there is no evidence that hospitals in the U.S. are close to running out of beds for patients.

Of course, there are other possibilities that Boudreaux does not flag for his readers.  For example, to take a wild possibility at random, it may be that hospitals are not admitting as many sick COVID patients as they fill up. 

Ashish Jha in the Washington Post:

What is happening is pretty simple: As hospitals fill up, they are admitting fewer and fewer people. As any doctor or nurse will tell you, as the demand for beds soars, the threshold for admission rises with it. . . .

One theory that some have advanced is that better treatment is leading to fewer hospitalizations or that more testing is identifying milder cases, and that’s why hospitalization rates are dropping. But outpatient treatment of covid has not changed meaningfully in the past month. The most promising potential outpatient treatment, monoclonal antibodies, has yet to see wide usage. Testing has increased, with more than 2 million tests conducted on some recent days, but case numbers and test positive rates have been rising even more steeply, indicating that we are still missing many more cases — especially mild and asymptomatic cases — so there is no evidence that more testing explains the change in rates of hospitalization.

What is happening is that patients who would have been admitted to hospitals earlier in the year are not being admitted now. Indeed, by my best calculation, between a third and half of covid-19 patients who would have been admitted in the beginning of October are now being sent home instead. This is really bad for patients. Some will get much sicker at home. Some may die there.

And from the Grey Lady:

More than a third of Americans live in areas where hospitals are running critically short of intensive care beds, federal data show, revealing a newly detailed picture of the nation’s hospital crisis during the deadliest week of the Covid-19 epidemic.

Hospitals serving more than 100 million Americans reported having fewer than 15 percent of intensive care beds still available as of last week, according to a Times analysis of data reported by hospitals and released by the Department of Health and Human Services. . . . 

There is some evidence physicians are already limiting care, Dr. Tsai said. For the last several weeks, the rate at which Covid-19 patients are going to hospitals has started decreasing. “That suggests that there’s some rationing and stricter triage criteria about who gets admitted as hospitals remain full,” he said.

We can debate what is happening and how the government should respond.  But Boudreaux just can’t seem to acknowledge that there might, possibly, be a reasonable case for aggressive public health measures to slow the epidemic.  Instead, he keeps the anti-government rhetoric dialed up to 11 (“tyranny!”), and continues to stoke outrage with misleading statistics.  This is especially perverse given the rise in right wing extremism and the fact that vaccines will soon become widely available.  

Coronavirus dashboard for November 30

Coronavirus dashboard for November 3

Total US confirmed infections: 13,383,320*

Average US infections last 7 days: 162,365 (vs. latest low of 34,354 on Sept 12)
Total US deaths: 266,873
Average US deaths last 7 days: 1,430 (vs. latest low of 701 on Oct 16)

*I suspect the real number is 18-19,000,000, or between 5 to 6% of the total US population
Source: COVID Tracking Project

Infections are out of control over much, if not most, of the country. North and South Dakota, the 2 worst States, now have had confirmed infections in over 10% and over 9% of their entire populations (and probably much worse than that since many asymptomatic cases go undetected):

While the earliest hard hit States, NY and NJ, still have had the highest death tolls, 8 more States have suffered fatalities in excess of 1 in 1000 of their total populations: