Pandemic of the Unvaccinated

Here is a heat-map showing percentage of Black population in each county in the U.S.:

Original Source: https://www.reddit.com/r/MapPorn/comments/gdwty5/percentage_of_black_population_in_the_us_by_county/

I have highlighted areas of particularly dense concentration in green.

Here is a heat-map showing percentage of Hispanic population in each county in the U.S.:

Original Source: https://en.wikipedia.org/wiki/File:2010_US_Census_Hispanic_Population_by_County.svg

I have highlighted most of the areas of particularly dense concentration in purple.  For reasons I'll explain in a bit, I've left out California.  I've also highlighted one county in Oregon that has a particularly low concentration of Hispanics.

Now here is a heat-map showing the current spread-rate of Covid per county.  I have transferred those same highlights from the previous two maps to this map (by hand, in Paint, so excuse the crudity of my model):

Original Source: https://twitter.com/EricTopol/status/1426549915581251590/photo/2

My highlights from the previous maps are covering the bulk of the high-transmission counties.  So then the last piece of data is the vaccination rates of Black and Hispanics:

Original Source: https://kff.org

These vaccination rates are only national averages, and are thus not the whole story.  Vaccination rates of Blacks in the south seem particularly bad, when I look at them.  In Florida, they're terrible--high 20s if I remember correctly.

So obviously, I'm driving at a pattern here.  My hypothesis is that a very significant portion of this surge in Covid is being driven by Black and Hispanic communities with low levels of vaccinations.  Remember: diseases don't actually spread geographically so much as they spread through socially connected networks of people.  Therefore, it doesn't matter that Florida actually has an above-average vaccination rate if there exists within Florida a community of socially connected people having a shared low vaccination rate.  In this case, Covid will spread through that specific community at a rate that is high concomitantly with their lack of vaccination.

A few anomalies on the combined map

There are a few things on the Covid heatmap that might seem a bit anomalous, given my hypothesis.

1. California and Wyoming maybe seem a little reversed compared to what you would expect.  California should maybe have more Covid spread based on its high percentage of Hispanics, and Wyoming seems anomalously high, maybe.
   
   But California also has had one of the strictest anti-Covid regimes of any State in the Union, fairly consistently from early on in the pandemic.  I think we can maybe see the result of this type of policy in the heatmap.  Other places where I might see the result of public policy are Virginia--which has an interesting clear demarcation from North Carolina, and also has been more Covid-cautious in its public policies--and New York, which became much more Covid-cautious after early disaster.
   
   And as for Wyoming, I don't think it actually fits that badly with the hypothesis--its most infected county is, after all, also its county with the highest percentage of Hispanics, and the state overall does have a fair share of Hispanics.
   
   I also suspect that if you really dug into the statistics (if you could get them), you would probably find that there was an inverse correlation between social "class" and low vaccination rates, as well.  I do know that Wyoming is ranch-heavy and therefore hires an awful lot of migrant worker, and I suspect vaccination rates among them are *quite* low.
   
   
2. There is that one area in Oregon which has a very low percentage of Hispanics, but a very high Covid transmission rate.  This, it turns out, is the exception that proves the rule.  This area is comprised of two counties: Douglas and Josephine counties.  And although those two counties may not have high percentages of Hispanic populations, for whatever reason they are considerably less vaccinated than other counties around them:
   
   

   

   Vaccination Rate per 10,000: Taken from the Oregon Health Authority COVID-19 Site

   So this just highlights that the problem here isn't race or ethnicity per se: the problem is vaccination rate among socially connected persons.

So, what we have been told is in fact correct: this is--now--a pandemic of the unvaccinated.

What does this imply?

I think the implications of this reality are pretty straightforward: the highest priority for ending this pandemic in the United States should be increased vaccination, and the area where this most needs to happen is in Black and Hispanic communities.  How we increase vaccination in these communities . . . I have no idea myself.

Furthermore, I think we need to be particularly concerned with the vulnerable people in those communities: the elderly, the sick, and the immunocompromised.  Greater effort should now be exerted, I believe, to seek out those individuals for vaccination.

One thing that has puzzled me recently is how the death rate from Covid compared to infections has not really decreased *that* much since vaccination.  Data is still sketchy on this, but my initial estimations put it at 1/2 to 1/3rd what it used to be before the vaccines.  That's better--but it doesn't match up very well with the great efficacy we have been seeing in the vaccines preventing hospitalization and death, *and* the relatively high rates of vaccination among those most in danger.  If 80% of the elderly are vaccinated and the vaccines are 95% effective at preventing death, then you wouldn't expect the death rate among the elderly to drop just by 1/2 or 2/3rds--it should be a lot more.

But if the spread is happening primarily in communities in which vaccination is low, this now makes a lot more sense.  In fact, deaths from nursing home residents have fallen drastically as a percentage of overall Covid deaths since vaccinations (see New COVID-19 Cases and Deaths Among Nursing Home Residents Have Dropped Since Vaccinations Began).  But not all elderly and infirm live in nursing homes; plenty of them live at home with family among these vulnerable communities.  I believe it very likely that the bulk of the deaths from this latest surge of Covid are coming from these people: elderly, hesitant unvaccinated parents of hesitant unvaccinated children.

So none of this gives us a way forward, per se.  But I think it *does* give us a focal point and I would like to start hearing more discussion about how we are going to solve this specific problem.

Efficacy, Effectiveness, and the Prevalence of Vaccinated among the Hospitalized: Part 2

Now let's look at an example case in which the efficacy of the vaccines in preventing infection and hospitalization has seemed to be inadequate.  It has been reported (see This 900-person delta cluster in Mass. has CDC freaked out—74% are vaccinated) that an outbreak of Covid in Barnstable County, Massachusetts was a key datapoint in the CDC reversing its recommendation on mask wearing for vaccinated people.  The CDC report on the outbreak is available here, and the key worrisome facts about this outbreak is that a full 74% of the people who became sick were vaccinated, 4 out of the 5 people who were hospitalized were vaccinated, and the Ct values (i.e., roughly how many particles of virus were found from nasal pharygeal swabs of the infected) of the vaccinated and non-vaccinated were "similar".

These numbers do make it seem, on the face of it, that the vaccines aren't doing very much to limit infection spread among the vaccinated.  However, as we saw in the previous post, it is possible for those overall numbers to be misleading, especially if there is a chance that a significant proportion of those people who became infected or hospitalized were immunocompromised.  And it turns out that this is likely to be the case.

The nature of the outbreak in Barnstable County

According to the CDC paper, the outbreak in Massachusetts was the result of "multiple summer events and large public gatherings were held in a town in Barnstable County, Massachusetts, that attracted thousands of tourists from across the United States".  The Massachusetts Department of Public Health, when they interviewed people associated with the outbreak found that people "reported attending densely packed indoor and outdoor events at venues that included bars, restaurants, guest houses, and rental homes."  But the CDC paper also contains this line in the discussion on limitations of its findings at the end of the paper: 

Third, demographics of cases likely reflect those of attendees at the public gatherings, as events were marketed to adult male participants; further study is underway to identify other population characteristics among cases, such as additional demographic characteristics and underlying health conditions including immunocompromising conditions.

What sorts of events are "marketed to adult male participants"?   It turns out that Barnstable County, MA, is the most popular summer vacation destination on the East Coast for LGBT+ vacationers.  It has the highest rate of gay marriage in the entire country.  In the middle of July, they host something called "Bear Week", which is essentially a week-long party for gay men.  During this period, the town population increases 20-fold (from 3,000 people to as high as 60,000) as a result of out-of-town LGBT+ vacationers.  (Wikipedia: Providencetown, Massachusetts)

Neither the CDC report nor the Massachusetts July Covid Update (July 30, 2021 | Update: COVID-19 Cluster in Provincetown) say how many of those who fell sick were gay men.  However, the Massachusetts report *did* show that a full 89% of the people who were sick were male, mostly young.  While Covid has been shown to impact men more seriously than women if they get sick, both genders will get sick at approximately the same rate.  For the natural balance to be upset to that degree, something like 728 of the 934 people who got sick (or 78%) would have to have been gay men.

The CDC report does mention a fairly small number of the patients (30) from the outbreak whom they had already confirmed had an HIV diagnosis--but this was mentioned as being a *preliminary* finding, and they only confirmed by cross-indexing the Massachusetts index of people registered with HIV.  Given that most of the people who got sick were from out-of-town, and given that registering as HIV positive is optional, this number is certain to be too low.

In fact, it's been found in random surveys that more like 1 in 5 of young gay men who frequent bars have HIV, and about half of those people don't even know it yet: (cf: 1 in 5 Gay/Bi Men Have HIV, Nearly Half Don't Know).  So this means that something more like 146--not 30--of the patients in the outbreak are likely to have been immunocompromised.

How many vaccinated people in Barnstable should we have expected to be hospitalized?

The answer to this question depends very much on how many of the out-of-town vacationing gay men were fully vaccinated.  I would *think* that this number would be very high.  If I were a gay man looking to party for a week in crowded settings with other gay men, I would want to make sure I were vaccinated ahead of time.  So I think that my estimate of 90% vaccination rates from Part 1 seems very reasonable.  I admit; this is a guess.  But let's assume this is true for now.

In Part 1, the various multipliers for hospitalization that we came up with work out to a 450x greater likelihood of hospitalization for immunocompromised vaccinated individuals compared to immunocompetent vaccinated individuals.  If you applied this multiplier to the 146 likely immunocompromised people in Barnstable, then you would expect to see about 80 vaccinated patients hospitalized from that group for every single patient hospitalized outside that group.  The actual proportion of vaccinated to unvaccinated was 4 to 1.  So based on my numbers from Part 1, the vaccines seem to be working more effectively than I would have expected.

The difference is so great, in fact, that I suspect my assumptions from Part 1 are wrong.  In particular, I think that my assumption from the South African Novavax study--that the vaccines would be not effective at all for the HIV positive--might be incorrect.

If you expect 80 people to be hospitalized, but only 4 are, this translates to a vaccine efficacy of about 95%.  And indeed, this is roughly what the CDC has been reporting--that the vaccines remain something like 95-96% effective in preventing hospitalization.  So I see the numbers of hospitalized in Barnstable, even given how many immunocompromised were likely in that population, as tending to confirm the efficacy of the vaccine--as far as it goes.  There will still be more immunocompromised people being hospitalized from Covid than immunocompetent, but if you compared immunocompromised to immunocompromised only, the vaccinated will have roughly the same comparative advantage against the unvaccinated.

How many immunocompromised would we have expected to get sick?

So much is good for the issue of hospitalization.  However, the CDC did not look at the Barnstable results and say that the vaccines weren't preventing hospitalizations: they worried (apparently) that the vaccines weren't preventing infection and spread.  So let's look at the reported numbers of the symptomatic infected more closely.  

I estimated in Part 1 that immunocompromised people were twice as likely to catch a disease (at least, symptomatic disease) in the first place compared to the immunocompetent.  This, however, was just taking into account their diminished capacity to fight off a disease rapidly.  In the case of the Barnstable County outbreak, you also have a large group of people that includes (most likely) many immunocompromised people who are also engaging in much higher risk behavior: packing themselves into crowded bars and restaurants for a week-long party.  In this specific scenario, what effectiveness of the vaccine for the immunocompromised would have to obtain in order for the vaccinated to make up 74% of the infected?

I have put together another section of the spreadsheet (link again here: Efficacy vs. Effectiveness) that attempts to model this scenario.  The key assumptions for the Barnstable County outbreak that I am making are as follows:

• 50,000 visiting LGBT+ vacationers.
• 90% of visiting LGBT+ vacationers are vaccinated (compared to 69% of the locals, which was the value reported).
• A baseline vaccine efficacy of 80%
• A reduced vaccine effectiveness for HIV positive people of 50% the baseline (i.e., 40% in this case)
• A 2x multiplier for HIV positive people to come down with symptomatic Covid if they are infected.
• An 8x "exposure rate" for the vacationers compared to the locals to account for the crowded party activities.

Given these assumptions, I can come up with a percentage of the vaccinated among the total infected of 73%, which is right in line with what actually happened.  In other words, it is not necessary to conclude that vaccine effectiveness at preventing disease spread has fallen very far at all in order to see large numbers of vaccinated become ill, in this specific scenario.

VERY Important caveat on interpreting statistical results of models

If you are not very experienced with this sort of analysis, you might mistakenly think that this result is amazingly accurate and therefore must reflect reality.  That I should be able to so accurately reproduce the real-life numbers with some reasonable inputs into a model might seem proof-positive that the immunocompromised are the real reason for the vaccinated making up 74% of the infected people from the Barnstable County outbreak.  But if you thought this, you would be very wrong.

In reality, I had to tweak many of the inputs in this model in order to come up with a percentage very close to the observed percentage.  I constructed the spreadsheet, put in some initial numbers, and then tweaked those parameters that I thought could be realistically tweaked, until my end result finally said "73%".

Since none of my parameters are outlandish, but all could potentially be realistic and true, it is correct to say that my theory (that immunocompromised are almost completely the cause of the scary proportion of vaccinated individuals from Barnstable) is consistent with the available data.  "Consistent with" is a very different statement from "proof of", and it is important to be aware of the difference between a study claiming one and a study claiming the other.

Sensitivity Analysis

It is for this reason that whenever I do a rough-model like this, I provide the link to the spreadsheet, and I encourage anyone who reads my estimates to look at the spreadsheet and make changes--play around with different parameters to see what sorts of result are generated with the new numbers.

When you do this formally and rigorously, this sort of thing is called "sensitivity analysis": you systematically change each parameter--individually and in groups--and determine which parameters are the important ones that actually make a difference on the outcome.  Good statistical packages can do this for you automatically nowadays--though you have to be sure you include all of the relevant parameters as inputs to the program!  "Garbage In, Garbage Out" is still a very true dictum.

Understanding the dynamics of which parameters make a difference to the outcome can do several things for you:

First, it allows you to see what aspects of the problem are more important to get clarity on.  For example, in my toy model, I found that although I accounted for the difference between the local population and the vacationing population, I really didn't need to bother.  The vacationing population is so much bigger, the effects of the local population on the outcome doesn't really matter.  This tells me that the "69% vaccinated" rate of Barnstable County that was reported in the CDC paper and in a lot of news outlets, is really irrelevant. 

Second, it allows you to see how reliable your result is.  In the case of my toy model, I am able to see that my result is not very reliable at all--I have some excessively sensitive parameters that are also too much of a raw guess on my part.  The key number here that makes all the difference is the vaccination rate of the vacationers.  I set that at 90%; if instead you set if lower (to 80%, for example), you have to set the effectiveness of the vaccine way down (to somewhere around the 40% level) in order to still end up in the neighborhood of 74% vaccinated among the infected, if you keep all the other parameters the same.

Likewise, the proportion of HIV positive individuals among the vacationers has a huge impact on the result, and my proportion of 1/5 is taken from a single study of general trends, not any sort of specific survey of this particular population.

Therefore, what this model really proves is only that the events of Barnstable County are currently capable of multiple interpretations.  If we want to know what is really going on in this outbreak, we need more information.  In particular, the prevalence of both vaccination and HIV in the vacationing population are very important for a correct interpretation: both of which might be very difficult to obtain at this point.

Bottom Line

The bottom line conclusion of this must be that we cannot make firm conclusions about the real-world effectiveness of the vaccines from the Barnstable data as it has been reported to us so far.  We would need a far better knowledge of other variables at play--other risk factors--in order to know which variables aside from vaccination effectiveness may have caused different people to end up infected or in the hospital.

This conclusion is especially true in the case of the Barnstable data given that the outbreak there occurred under circumstances far from normal for the national population in ways that are materially relevant to disease spread and vaccine efficacy.  But the conclusion is also true for a lot of other data that has been bandied about by many people.  In general, the prevalence of vaccinated among the hospitalized is a very bad statistic on which to make conclusions.  There are far too many confounding variables that are in play--far too many risk factors which dramatically change the likelihood of hospitalization independently of vaccination status--for this bare statistic to be of any use without a whole lot of other data about those people.

The gold standard for judging the effectiveness of a vaccine is the ability to compare vaccinated people versus unvaccinated people when you are able to control for all other variables.  You want to compare vaccinated sick old men with unvaccinated sick old men, vaccinated teenage girls with no health problems with unvaccinated teenage girls with no health problems, vaccinated middle-aged gay party-goers with HIV to unvaccinated middle-aged gay party-goers with HIV.  And so forth, and so on.

Simply comparing the raw numbers of hospitalized vaccinated to hospitalized unvaccinated people--with no differentiation--is going to be comparing apples to oranges with a vengeance.

Efficacy, Effectiveness, and the Prevalence of Vaccinated among the Hospitalized: Part 1

There has been a lot of angst, recently, over how many vaccinated people are coming down with Covid, even to the extent of being hospitalized.  A lot of people are coming to the conclusion that vaccine effectiveness has been waning--either because the new Delta variant is escaping suppression, or because the vaccines are losing effectiveness over time, or both.

There is some truth to those fears, for sure.  However, I believe that neither fear plays as much a role in uncomfortable numbers of vaccinated people getting sick as a lot of people think.  A third factor that you need to consider when you look at the number of people who are vaccinated who are also getting sick or being hospitalized is the difference between vaccine "efficacy" and vaccine "effectiveness".

I am going to explain what the difference is between these terms and why it matters in Part 1.  In Part 2, I am going to look at an important case study in which this distinction might be very important.

Efficacy vs. Effectiveness

These two words--"Efficacy" and "Effectiveness"--are technical terms in immunology.  Briefly, "efficacy" refers to how well a vaccine reduces disease in an ideal, properly balanced clinical trial.  "Effectiveness" refers to how well a vaccine reduces disease in the real world, given a distribution of recipients that is limited by real world constraints rather than the artificial constraints of a clinical trial.

When a vaccine (or any other medication, for that matter) is tested in a clinical trial, the goal is to identify how well the vaccine works compared to non-vaccination, all other things being equal.  A well-designed clinical trial will identify all characteristics of a subject that might have an effect on the outcome of the trial.  The trial runners will then balance the trial vs. the placebo groups so that an equal proportion of each characteristic appears in each group.  That is, both the placebo and trial groups should contain the same proportion of elderly to young people, of each race and gender, of sickly vs. healthy people, and so forth.  If there is a certain population that is more (or less) susceptible to the disease in your trial, and you do not balance that population properly between your trial and placebo groups, then your final results will be biased by the properties of this particular population.

If a clinical trial is properly balanced, then you can take the difference between how many people get sick in the vaccinated group vs. how many get sick in the unvaccinated and calculate your vaccine *efficacy*.

In the real world, however, there is no one balancing out the vaccinated vs. the unvaccinated populations.  People get vaccinated or not for reasons other than balanced, random chance.  Therefore it is quite possible (and actually inevitable) that, in the real world, the group of people who are vaccinated will have different characteristics from the group of people who are unvaccinated.  This means that you should not expect that the difference between the vaccinated and the unvaccinated who get sick in the real world to reflect the same efficacy as was found in the clinical trials.  What you get from this calculation is the *effectiveness*, and this can be skewed from the "efficacy" number for a lot of reasons.

Risk Averse Behavior

The most critical reason effectiveness can be skewed from efficacy (or at least the reason that *I* think is the most important) is the very nature of human behavior relating to risk.  Simply put, it is pretty obviously true (if you think about it), that those people who are more naturally at risk from a disease will choose to take a vaccine against that disease at a much higher rate compared to people who do not feel similarly at risk.  Given that this is true, you should expect, in the real world, that the group of all vaccinated people will contain many more naturally at-risk people that the group of all unvaccinated people.

How large of an effect will this have?  Well, it could actually have quite a large effect, depending on the specifics.  I think there are, broadly, two different types of person this distinction applies to, which I will now describe.  Then I will try to estimate the magnitude of this effect with some reasonable guesses and a spreadsheet.

At-Risk of Exposure

One type of person is more at risk of catching Covid because of an occupation.  This type of person may have a job that brings him into close contact with a lot of potentially sick people on a regular basis.  The classical example here is health care workers; they are obviously exposed to Covid (at least potentially) a lot more than other people are.  Now, some early studies showed that health care workers weren't getting sick all that more often than other people (see Prevalence of SARS-CoV-2 Infection Among Health Care Workers in a Tertiary Community Hospital)--but those studies were done during a time in which rather extreme Personal Protective Equipment (PPE) practices were in place.  Nowadays, practice has tended to relax a lot further and we are looking at close to business-as-usual behavior.  So I think it is fair to say that healthcare workers will very likely be exposed to a lot more Covid virus than other people.

For this type of person, both natural immunity and vaccination would be expected to work as well for them as for anyone else.  However, given that they will be exposed so much more, the vaccination will be given much more opportunity to fail for these people than for others.

At-Risk of Infection

Another type of person is not necessarily more exposed to Covid, but might be more naturally at risk of catching the disease when they are exposed.  The most important group here, I think, is the immunocompromised.  This is a larger group of people than most realize: it includes the HIV positive, people on a whole array of immunosuppresive drugs, people undergoing cancer treatment, and people with Down syndrome--to name just a few.  Randomized surveys have shown that a full 2.7% of Americans at any given time have been diagnosed as immunosuppressed. (Prevalence of Immunosuppression Among US Adults, 2013).  And I think this number might be understating the total effect, because there are certain conditions that typically don't get you outright diagnosed as "immunocompromised", but which actually do have some compromising effects on immunity.  The two most important of these conditions are age and obesity, both of which are known to exert some suppressing force on immunity (see Impact of Obesity and Metabolic Syndrome on Immunity) and which are together the two most important "comorbidities" for Covid.

How much effect immunocompromising conditions might have on the effectiveness of vaccines is not completely known--but it might be rather severe.  The Novavax study in South Africa included a cohort of known HIV positive test subjects in its vaccine trial.  The sample size was not large--which makes its results here uncertain because of lack of statistical power--but insofar as the results are reliable, they indicate that the Novavax vaccine was not at all effective in the HIV cohort (Efficacy of NVX-CoV2373 Covid-19 Vaccine against the B.1.351 Variant).  The trial found the vaccine pretty effective for other people, but did not see any effectiveness for the HIV positive--in fact, slightly more vaccinated HIV subjects came down with Covid than unvaccinated HIV subjects.

Immunocompromised also have a two-fold problem: not only are they more prone to catching a disease, since their bodies are not well equipped to fight a disease once it gains a foothold, they are much more likely to be hospitalized from a disease once they catch it.

How much of an effect could these special cases have?

But, you might say, even if the vaccines don't work very well for the immunocompromised, that's only roughly a 3% portion of the population.  That couldn't mess up the numbers that badly, could it?  Yes, it could.  Covid attacks people very unevenly; the more vulnerable people aren't just a little bit more likely than everyone else to suffer badly from Covid, they are far more likely to suffer badly from Covid.  This uneven distribution of adverse effects means that even a pretty small population of very vulnerable people can have a very substantial effect on the makeup of the total hospitalized and dead.

To illustrate this, I have put together this spreadsheet with what I considered simplified but still reasonable numbers, here: Efficacy vs. Effectiveness

In this spreadsheet, I setup a group of 1 million people, and then determine who gets sick and who gets hospitalized based on various parameters.

Here are the assumptions I make for this spreadsheet:

• The average person will have a 1% chance of catching Covid.
• 5% of the population will be in "high exposure" occupations, which I set to 4x the regular exposure to the virus.
• 3% of the population will be immunocompromised.
• The immunocompromised will be 2x as likely to catch the disease compared to everyone else (a guess, but I think reasonable based on my experiences with an immunocompromised daughter).
• The vaccine will be 88% efficacious for normal people.  
• It will be 0% efficacious for immunocompromised people.  (This is consistent with the Novavax trial results even if not proven by them.)
• 5% of unvaccinated people with functional immune systems who catch Covid will end up hospitalized
• The vaccine will be 96% effective at keeping people who come down with Covid from being hospitalized.
• 40% of immunocompromised who catch Covid will end up being hospitalized.
• 80% of people in high-exposure occupations will be vaccinated.
• 90% of immunocompromised people will be vaccinated.
• 60% of everyone else will be vaccinated.

These are all reasonable assumptions.  They may not be quite accurate and some of them are fairly bald guesses, but nothing here is outlandish and nothing contradicts anything I actually know to be true.

With these assumptions, what you will see as far as numbers of actual infections and hospitalizations is that 1394 people who are vaccinated will become infected, whereas 4140 who are unvaccinated will be.  This translates to an effectiveness of approximately 66%.  Meanwhile, 218 vaccinated people will be hospitalized, whereas 228 unvaccinated people will be--which makes it seem as if the effectiveness of the vaccine at preventing hospitalization is basically 0%.

And remember--these results are assuming a very robust protection from the vaccine for 97% of the population: 88% protection against infection and 96% infection against hospitalization over and above that protection.  So we have a seemingly paradoxical result that even with a vaccine that is highly effective, as many vaccinated as unvaccinated are seen to be suffering badly from the disease.

Bottom line conclusion: It is very easy for important sub-groups of your population to completely throw off your bottom-line numbers if you do not interpret the results correctly.  So make sure you understand the sub-groups of your population and account for their characteristics in any study that you do.

In the case of how many people are vaccinated yet also hospitalized, we need to pay careful attention to what other risk factors these people have.  It is not necessarily the case that high numbers of vaccinated people in the hospital implies inefficacy of the vaccine.