Someone who tweets under the handle @enn_nafnlaus cautioned that it is easy to make a mistake when comparing trajectories with different exponential growth rates.

In fact, this mistake can bias down the measure of severity that is raising hopes that an omicron infection will be less serious. The bias can be large, off by something closer to a factor of 10 than a factor of 2.

The underlying problem is that fast growth dramatically increases the ratio of any quantity that we measure today compared to its value only a few days ago.

What follows is a timeline of events leading up to the World Bank’s decision to stop publishing the Doing Business report because of manipulation of the data used in the 2018 and 2020 reports. The timeline relies primarily on the report by the WilmerHale law firm, which is available here. I encourage anyone who wants to express an opinion about the actions of Kristalina Georgieva to read the WilmerHale report first. Failing that, and at a bare minimum, they should at least read this summary of its findings.

I was responsible for the 2017 report but was not involved in any of the events that make up this timeline. They do show that I was right to express deep concern about the ease with which country rankings could be manipulated and the likelihood that this type of manipulation could be undertaken inside the World Bank, but I will not elaborate here on my findings from the 2017 and earlier reports. Justin Sandefur has a helpful post that goes into the some of the specifics.

When I was asked back in June of 2021 about lessons for science from the pandemic, the gist of what I said was:

In a democracy, the community of science can be a uniquely valuable source of objective facts, but assertions by scientists will be trusted only if they are careful not to overreach by advocating on behalf of their preferred political outcomes.

(See below for my detailed response.) Three months later, in the wake of a debate about booster shots, we can see the risk associated with overreach. In the United States, no one making decisions about boosters is paying any attention to what the people who claim to be the scientific authorities are saying.

Two opposing interpretations of the evidence about waning vaccine protection are grounded in two very different models of the course of a Covid-19 infection. In two masterful tweets, John Burn-Murdoch captured and named them: the dice model and the two-walls model.

Under the dice model, waning protection against infection implies waning protection against severe disease. Because there are fewer instances of more serious outcomes, it is more difficult to tease out statistically significant evidence of waning against a more serious outcome than against infection. But if the dice model is right, the two always go together.

Under the two-walls model, it would be possible to have waning protection for infections without waning protection for severe disease, but there is a problem with this model. Part of the beauty of the stripped-down characterization by Burn-Murdoch is that it is precise enough to surface its intrinsic logical contradiction. There is a way to patch the model to remove this contradiction, but what remains is a biologically implausible model that is starkly inconsistent with the data.

As a result, the the default presumption should be that statistically significant evidence of waning against infection also implies waning against more serious outcomes. This presumption could be overturned by tight estimates that show no waning of protection against these more serious outcomes, but not by low-powered tests that generate big uncertainty intervals.

Suppose that a drug company is trying to get approval for a new pain medication that might have some serious negative side effects. How can the company keep regulators from finding any?

Even if you have no training in statistics it is easy to understand that the sure-fire strategy is to focus attention on side effects that are rare. The smaller the number of events, the easier it is to dismiss the few that arise as chance outcomes.

This same strategy for avoiding a discovery is being used now by people who want to keep us from finding that the protection from vaccines diminishes over time.