# Commenting on the Statistics of COVID Blood-Type Associations

*Views and opinions expressed are solely my own.*

## Introduction

In the early days of the COVID-19 pandemic in the U.S., news around an article in medRxiv caught the attention of many of my peers, generating headlines such as:

People with blood type A might be more susceptible to coronavirus, study finds

Does blood type matter when it comes to coronavirus? A Chinese study says yes

Let’s examine the results section of the original article. One excerpt worth noting:

The proportion of blood group A in patients with COVID-19 was significantly higher than that in normal people, being 37.75% in the former vs 32.16% in the later (\(P < 0.001\)). The proportion of blood group O in patients with COVID-19 was significantly lower than that in normal people, being 25.80% in the former vs 33.84% in the later (\(P < 0.001\), Table 1). These results corresponded to a significantly increased risk of blood group A for COVID-19… and decreased risk of blood group O for COVID-19… in comparison with non-A groups and non-O groups, respectively.

From the above, the claim that people with type-A blood may be more susceptible to COVID-19 is due to calculations yielding small \(p\)-values. **One must look at claims solely based on \(p\)-values with extreme skepticism.** **\(p\)-values are not infallible:** just because a small \(p\)-value indicates that people with type-A blood have an increased risk of COVID-19 compared to their counterparts does **not** mean that an increased risk *actually* exists.

In fact, the authors of this paper go on to give a possible explanation to this phenomena to which they state:

This speculation will need direct studies to prove. There may also be other mechanisms underlying the ABO blood group-differentiated susceptibility for COVID-19 that require further studies to elucidate.

and then, in the conclusions section, state:

It should be emphasized, however, that given the above limitations, it would be premature to use this study to guide clinical practice at this time.

All of this information, unfortunately, is lost in the headlines. Furthermore, in my opinion, it is unreasonable to expect a member of the general public to pick up all of these nuances.

### What do these \(p\)-values actually tell us?

Let’s assess both of these claims on their own.

The proportion of blood group A in patients with COVID-19 was significantly higher than that in normal people, being 37.75% in the former vs 32.16% in the later (\(P < 0.001\)).

In Table 1 of the original article, we can see that the \(p\)-value obtained above is a result of a \(\chi^2\) (chi-squared) test. The \(\chi^2\) test, in this case, is a test for independence between the “blood-type A” status and the “normal/COVID” status. Independence of these statuses means each of the following four statements must be true:

- The probability of a person having type-A blood remains unchanged from the probability of this occurring in the overall group if you know that the person is “Normal.”
- The probability of a person having type-A blood remains unchanged from the probability of this occurring in the overall group if you know that the person is a COVID-19 patient.
- The probability of a person being a COVID-19 patient remains unchanged from the probability of this occurring in the overall group if you know that the person has type-A blood.
- The probability of a person being a COVID-19 patient remains unchanged from the probability of this occurring in the overall group if you know that the person does not have type-A blood.

For example, to illustrate this in the context in the second bullet above, suppose we know that 35% of people in general have type-A blood (a statistic I’ve made up). Consider a single person who is a COVID-19 patient. Then the probability that this person has type-A blood is also 35%, by the independence assumption we have made.

**By providing a small \(p\)-value for a \(\chi^2\) test for independence, the \(\chi^2\) tests that there is evidence that these two statuses are not independent.** That means, therefore, that there is *evidence* (note: it is **not** certainty) that these two statuses are dependent. In the context of our example, if someone is a COVID patient, dependence means that the probability that this person has type-A blood would change from the overall type-A blood probability. While the \(\chi^2\) test *provides evidence* of dependence, it does **not**:

- mean there is an
**actual**dependence between these two statuses, and - tell us the
**direction**of said dependence. For example, if someone is a COVID patient, while there is evidence the probability that they have type-A blood is different from the overall percentage due to dependence, the \(\chi^2\) does**not**tell us whether the type-A probability for this COVID patient is greater than the type-A probability for the overall population.

**Thus, the explanation associated with this \(p\)-value is incorrect.** It should really say something like:

There is evidence of a dependence between COVID-19 status and whether a person has type-A blood (\(P < 0.001\)).

Similar principles apply to the other statement given in the original quoted text:

The proportion of blood group O in patients with COVID-19 was significantly lower than that in normal people, being 25.80% in the former vs 33.84% in the later (\(P < 0.001\), Table 1).

which should be reworded as:

There is evidence of a dependence between COVID-19 status and whether a person has type-O blood (\(P < 0.001\)).

One can quite easily observe how the original statements are not as definitive as they may seem to be with appropriate rewording.^{1}

### What does one do with regard to COVID-19 guidance?

In the prior section, I explained what the \(\chi^2\)-test \(p\)-values actually suggest. However, it’s unreasonable for the general public to be able to take apart the statistical techniques like I’ve done here.

Here is how I handle hearing about new COVID-19-related guidance in the news:

- Find the original source of research. As much as I can, I ignore all news media and social media commenting on said research.
- Find the results and discussion sections of said research article.
- If the only rationale for the final conclusion is a \(p\)-value calculation and/or confidence interval calculation, keep in mind the association(s) found, but don’t trust the conclusions for definite advice.
- If \(p\)-values and confidence intervals are supplemented with an explanation of the scientific mechanism supporting why said associations would occur, assign the article higher credibility. If the scientific mechanism isn’t available, a randomized controlled trial (RCT) would be ideal; however, seek other studies with RCTs to see if similar results have been replicated.

The point in 4 is to emphasize that one of the most important aspects of how to live with COVID-19 in our society is that it is essentially a problem of **causality**. Many statistical aspects of issues end with \(p\)-values.^{2} Causality requires a step *beyond* the statistics, options including a number of RCTs which support similar results, or an explanation of the scientific mechanism behind a particular phenomena.^{3}

## Conclusion

Do not rely on \(p\)-values as the ultimate source of truth, especially during a pandemic. In future posts, I will explain the details behind the calculation of \(p\)-values.

Granted, the authors of the original article also calculated odds ratios in attempting to give an idea of the direction, but they should have provided \(p\)-values with these. Even if they used a more appropriate test with \(p\)-values to give an idea of the direction, it is not appropriate to use “significantly higher” or “significantly lower” to describe such conclusions; they should be reworded to “higher” or “lower.” Such tests give an idea of the

*direction*of such differences, but not necessarily the magnitude of such differences.↩︎Not that I agree this should be the case.↩︎

Or, if you’re feeling especially ambitious, see

*Causality*by Judea Pearl for a framework. I haven’t had a chance to dig into this book in depth yet.↩︎