The Simple Economics of Why Prescription Drug Prices Are So Darned High: Econ 101

My apologies, but a draft of this was posted when I mistakenly clicked the “publish” button when I was working on it.  It still has far to go before being a completed piece, and it may be some time before I finish it.  There is more I want to look into.  Please ignore this for now.

Frank

 

A)  Introduction

The prices of prescription drugs – drugs that are often essential to our health and well-being – are unconscionably high in the US.  Generics can be an exception, although even for these it might not always be the case.  And even with such high prices, there are nevertheless critical gaps in what drugs are developed.  Delays in the development of a new generation of antibiotics is one example, as will be discussed below.

Why is this so?  The short answer is that they price them high because they can.  A more detailed answer requires an examination of why they can, as well as a look at how they determine how high to set their prices.  This goes into some basic economics of how someone with monopoly power (as pharmaceutical companies will often have, for several possible reasons) will set prices in a market such as this, with particular features on both the demand and on the supply side.  We will examine that below.

And the prices are not simply high, but also have grown sharply in recent years.  The chart at the top of this post shows prices for baskets of the most commonly used prescription drugs, as reported in a series of analyses undertaken by the AARP (see here, here, here, and here for the most recent in the series for each category of drug).  These most recent reports cover prices from 2006 through to 2017 (with the exception of the series for brand name drugs, which is now available also for 2018).

The set of all prescription drugs cover a basket of 754 drugs with the prices as billed by pharmacy benefit managers to health insurance plans.  The prices are what the cost would be to take the drugs for a one-year period, and the drug price indices are weighted by retail prescription sales in 2014 to Americans aged 50 and above.

 

note fixed 2014 weights will bias downwards

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Top 6 US firms, both by sales revenue and by market cap

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There Have Been Real Consequences From Not Taking Covid Seriously

A.  Introduction

Earlier posts on this blog have documented that vaccination rates against Covid-19 have been systematically lower in accordance with the share of a state’s vote for Trump in the 2020 election, and that mask-wearing to protect the individuals and those around them have also been systematically lower.  The higher the share voting for Trump in a state, the lower the share vaccinated and the lower the share wearing masks.

Those choices have had consequences.  As shown in the charts above, it should not then be surprising that states with a higher share of their vote for Trump have seen, on average, a higher number of cases of Covid-19 (per 10,000 of population) as well as a higher number of deaths.  The relationship is statistically a very strong one.  While many factors affect the likelihood of being infected with Covid-19 and of dying from it (including factors such as urban density, extent of travel, health status of the population, adequacy of the health care system, and more), political identification by itself appears to be a strong and independent factor.

In what is literally a life and death issue, one would have thought that rational self-interest would have dominated.  It has not.  Following a review of the data, this post will discuss some possible reasons why.

B.  The Relationship Between the Incidence of Covid-19 Cases and Deaths and the Share Voting for Trump

The figures at the top of this post plot the relationship between the number of cases of Covid-19 in a state (per 10,000 of population), or the number of deaths (also per 10,000), and the share in the state who voted for Trump in 2020.  The Covid data come from the CDC.  It was downloaded October 26, but since case and death counts from the states may not be fully reported to the CDC for up to a week to ten days, I used October 15 as the end date for the analysis here.  “Cases” are confirmed cases, and “deaths” are deaths as a consequence of Covid-19, both as defined in the CDC guidance for how these should be recorded.

For the start date I used July 1, 2020.  This came at the end of the first wave of Covid-19 cases and deaths.  Cases and deaths in this first wave were excluded for two reasons.  One is that the first wave arrived suddenly in mid-March and with an intensity that surprised many.  The nation was unprepared, with little done to prepare for the disease that was spreading around the world as Trump was claiming it was all under control, that it was “going to disappear”, and that it would soon “go away”.  Also, the CDC had bungled the initial testing (where testing was more readily accessible in parts of Africa than in the US in the key initial months), so the full extent of the developing problem was not clear until it hit.  The response, and the then only possible response, was to quickly institute lockdowns, and this was soon done in all 50 states.  The lockdowns were effective, albeit costly, and by late April the approach had succeeded in starting to bring down the daily number of new cases.  Case numbers continued to fall in May and into June.

But starting in early May, disparate decisions were taken across the different states on how fast to lift the lockdown measures.  Some opened up early and with little guidance on or advocacy for the wearing of masks, while others opened up more cautiously.  But with the opening up, and the refusal by a significant share of the population to wear masks and to follow social distancing recommendations, the daily number of new cases stopped falling and by around mid-June began to rise again.  The daily number of deaths followed a similar pattern but with a lag of about two weeks, and so began to rise around the end of June. Thus July 1 can be taken as a turning point – the end of the first wave and the start of the second.  While differences across the states had already started to develop from early May (when decisions were taken on how rapidly to open up), the consequences of the varying approaches only became clear as the second wave started to build.  On average across the nation, this was around July 1.

The second reason to exclude this first wave is that the quality of the data for that initial period was poor.  The Trump administration was slow in launching and then ramping up testing, with testing limited even well into April to those who showed obvious symptoms or who had been in close contact with someone with a confirmed case.  Thus many cases were missed.  While testing has been far from perfect throughout this pandemic, it was much worse in the earlier months than it was later.  For this reason as well, excluding the estimates from the earlier months will provide a better measure of how successful or not the different states were as they responded to the pandemic in their different ways after the initial lockdowns.

Excluding the first wave leads to the exclusion of 6% of confirmed cases and 18% of deaths from the overall totals as of October 15, 2021.  Most thus remained.  Note also the disparity in these figures.  That the official figures recorded that just 6% of the confirmed cases in the US (as of October 15) were in this initial, first wave, period, while this same period recorded 18% of deaths, strongly suggests that cases were significantly undercounted in that first wave.

The charts then show the incidence of total confirmed cases of Covid-19, or deaths from it, per 10,000 of population, over the period from July 1, 2020, to October 15, 2021, with this plotted against the share of the vote that Trump received in that state in 2020.  The relationship is a strong one:  The higher the share of the state vote for Trump, the higher the incidence of Covid-19 cases and of deaths.  Taking averages, the average number of confirmed cases over this period per 10,000 in the states won by Trump was 1,461 (i.e. 14.6% of their population) vs. 1,113 in the states won by Biden.  That is, there were on average 31% more cases in the states won by Trump.  The number of deaths from Covid-19 came to 21.2 per 10,000 in the states won by Trump vs. 15.3 in the states won by Biden, or 38% more in the states won by Trump.

But averaging across all the states won by Trump or by Biden is not terribly meaningful as there will be a mix of voters in every state.  Furthermore, there were a number of states where the vote was close to 50/50.

It is thus more meaningful to examine the trend across the different states, as a function of the share voting for Trump.  This trend is provided in the regression line shown in each chart, where simple, linear, ordinary least squares regression was used.  The statistical relationship found was very strong, and especially so for the regression for the number of cases of Covid-19.  The R-squared (a measure of how much of the variation in the values is accounted for by the regression line alone) was extremely high for such a cross-state sample as here – at 0.63 for the number of Covid-19 cases and a still high 0.36 for the number of Covid-19 deaths.  (R-squared values can vary between 1.0, in which case the regression line explains 100% of the variation across states, and 0.0, in which case the regression line explains none of the variation.)

The higher correlation (the higher R-squared) observed in the relationship for the number of cases than in the relationship for the number of deaths is what one would expect.  To die from the disease, one must first have caught it.  Hence this will depend on the number of cases in the state.  But deaths from it will then depend on additional factors such as the age structure of the population, general health conditions (obesity rates, for example), as well as the availability and quality of health care services (hospitals, for example).  These factors will vary by state, and hence add additional variation to that found for the number of confirmed cases.

The slope of the regression line is an estimate of how many additional cases of (or deaths from) Covid-19 to expect (per 10,000) for each 1% point higher share of the vote for Trump.  For each additional 1% point in the share of the vote for Trump in a state, there were on average 23.8 more cases (per 10,000 of population) of Covid-19 during the period examined, and on average 0.36 more deaths (per 10,000).  The t-statistics for these slope coefficients were both extremely high, at 9.1 for the number of cases and 5.2 for the number of deaths.  A t-statistic of 2.0 or higher is generally taken to be an indicator that the relationship found is statistically significant (as it implies that in 95% of the cases, the slope is something different from zero – a slope of zero would imply no relationship).  A t-statistic of 3.5 would raise that significance to 99.9%.  The t-statistics here of 9.1 and 5.2 are both far above even that mark.

One can also use the regression lines to address the question of what the impact would have been on Covid-19 cases and deaths if everyone behaved as Biden voters did (or as Trump voters did).  The regression lines look at how the incidence of cases or deaths change based on each additional percentage point in the vote for Trump.  If one extrapolates this to the extreme case of zero votes for Trump (and hence a “pure” Biden vote), one can estimate what cases and deaths would have been if all behaved as Biden voters did.

This is a straight line, i.e. linear, extrapolation of the effects, and the limitations from this assumption will be addressed in a moment.  But using linearity, the effects are easily calculated by simply inserting zeroes for the Trump share of the vote into the regression equations, so that one is left with the constants of +96.94 for the number of cases (per 10,000 of population) and -0.69 for the number of deaths.  That is, there would have been a predicted 97 (per 10,000) cases of Covid-19 over this period in the US rather than the actual figure of 1,261 (per 10,000).  This is 92% lower.  And the number of deaths would have been essentially zero (and indeed would have reached zero with still some share voting for Trump – based on the regression equation coefficients it would have been at the 2% point share for the Trump vote).

Are these results plausible?  Would cases and deaths have fallen by so much if all of the population had behaved (in terms of wearing masks, social distancing, getting vaccinated once vaccines became available, and other such behaviors) as the Biden voters did?  The answer is yes.  Indeed, the linear extrapolation is conservative, as infectious diseases such as Covid-19 spread exponentially.

If in some state each infected person infects, on average, two further people, the number infected will double in each time period for the disease.  This is exponential growth, with a reproduction rate of two in this example – a doubling in each period.  For Covid-19, the time period from when a person is infected to when that person may, on average, spread it to another, is a week and a half.  A person becomes infectious (can spread it to others) about one week after they became infected with the disease, and then can infect others for about a week (with the average then at the half-way point of that week).  Thus 100 cases of active infections in some region would double to 200 in that time period of a week and a half, then to 400 in the next time period, and so on.  If, in contrast, responsible behavior (such as vaccinations and mask-wearing) reduces the reproduction rate to one-half rather than two, then 100 cases will lead to 50 in the next time period, to 25 in the next, and so on down to zero.

In any given state there is a mix of Biden voters and Trump voters.  While there are many factors that matter, if these two identities reflect, on average, differing shares of people that do or do not choose to be vaccinated, wear masks, and so on, then the average reproduction rate will vary depending on the relative shares of such voters.  That average reproduction rate will be lower in states with a higher share of Biden voters, and for a sufficiently high share of Biden voters (a sufficiently low share of Trump voters), there will be an exponential decline in new infections from Covid-19.  The linear extrapolation based on the regression equations would thus be a conservative estimate of the number of cases to expect when most of the population behaves as the Biden voters have.

There are, of course, many factors that enter into whether a person is infected by someone with Covid-19, and whether they then die from the infection they got from someone.  But the charts and the regression results suggest that the share of the population in a state voting for Biden or for Trump is, by itself, strongly correlated with how likely that was.  Why?

C.  Personal Behavior and Political Identity

The fact of, and then the consequences from, this political divide for infection by Covid should not be a surprise to anyone.  As noted before, Trump voters are far less likely to be vaccinated or to wear masks to protect themselves and others from this highly infectious, and deadly, disease.  This then translates into higher infection rates, and the higher infection rates then to higher deaths.

One sees this unwillingness to be vaccinated also in surveys.  The most recent of the regular surveys by the Kaiser Family Foundation (published on October 28) found that 90% of Democrats had received at least the first dose of the Covid vaccine, while only 61% of Republicans had.  Furthermore, 31% of Republicans declared they would “definitely not” be vaccinated, while just 2% of Democrats held that view.  Gallup surveys have found similar results, with a survey from mid-September finding that 92% of Democrats had received at least the first dose of the Covid vaccine, but that only 56% of Republicans had.  And 40% of Republicans in that survey said they are not planning on being vaccinated ever, while only 3% of Democrats said that.

Not surprisingly, one then sees this reflected in state politics.  Republican governors (such as Abbott of Texas and DeSantis of Florida) have gone so far as to issue executive orders to block private companies from protecting their staff and their customers from this disease, and even to prohibit local school boards from taking measures to protect schoolchildren.

The direct result is that the virus that causes Covid-19 has continued to spread.  An infectious disease such as Covid-19 will only persist as long as it is being spread on to others.  It cannot survive on its own.  The issue, then, is not just that someone refusing to wear a mask or to be vaccinated is highly likely to catch the disease, but that that person is likely to spread it to others.  While Republican governors such as Abbott and DeSantis have said this is a matter of “personal freedom”, it is not that at all.  No one is free to do harm to others.  It is the same reason why there are laws against drunk driving.  Drunk drivers are more likely to cause crashes (not all of the time, but often), and those crashes will harm others, up to and including killing others.  Spreading Covid-19 is similar, up to and including that those who become infected may die from it.

For whatever causal reason, the facts themselves are clear.  But why has a significant share of the population chosen to behave this way?  This is now more speculative, and goes into an area that I openly acknowledge is not my area of expertise.  With that proviso, some speculation.

It is clear that political identity has played a central role, where Trump from the start treated the then developing pandemic as an issue where you were either with him – and his assertion that he had it all under control – or against him.  This started with Trump’s assertion in an interview on January 22, 2020 (from Davos, Switzerland) that he had no worries, that “we have it totally under control”, and that “It’s going to be just fine”.  This claim continued through February (as cases were growing in the US), where on February 27 he said “It’s going to disappear.  One day it’s like a miracle.  It will disappear.”  And in campaign rallies in February, he claimed to his cheering supporters that he had been doing a superb job in stopping the virus and that any charge to the contrary was simply a “hoax” coming from the Democrats.

Thus, from the start, Trump made the issue a political one.  If you were a true supporter of Trump you could not treat the disease as something of concern – Trump had taken care of it.  Any assertion that the developing pandemic was in fact serious, and needed to be addressed, was a “hoax” perpetrated by the Democrats.

Trump then continued to assert all would soon be well, saying on March 10 that “it will go away”, on April 29 that “This is going away.  It’s gonna go.  It’s gonna leave.  It’s gonna be gone.”, on May 11 that “we have prevailed”, on June 17 that “It’s fading away.”, and on July 19 that “It’s going to disappear”.  But more than 600,000 Americans have died since July 19, 2020, not far short of the 651,000 Americans who have died in battle in all of America’s wars since 1775.  From the start of the pandemic, more than 750,000 Americans have now died.

Trump’s politicization of Covid-19 was then amplified when, at the April 3 press conference in which he announced the CDC recommendation that everyone should wear face masks when going out, he immediately then added that he would not himself wear a face mask.  Face masks are highly effective in hindering the spread from person to person of the virus that causes Covid-19, and until vaccines became available, were the best way to hinder that spread.  But wearing a face mask is also highly visible.  For those who saw themselves as supporters of Trump, and believed what he said (that the virus was going away, that he had it under control, and that any concerns over this were merely a hoax promoted by the Democrats), then it was not surprising that many would follow Trump’s highly public example and not wear a mask either.  Some even went so far as to shoot, and kill, store personnel when told they should wear a face mask inside some store.

It is not surprising that such views would then carry over to vaccination.  Having rationalized not wearing a mask, it is easy to rationalize a refusal to be vaccinated.  And rationalizations could easily be found just by watching Fox News.  In the six months from April through September this year, for example, Fox News chose to air a claim undermining vaccination on all but two of those more than 180 broadcast days.  Many were also exposed to claims that can only be described as truly bizarre, such as that the vaccination will be secretly inserting a microchip into your body for the government to track you, with Bill Gates behind it all; or that it will make you magnetic with this managed through 5G telecom towers; or that it will re-write your body’s DNA; and more.

One can therefore easily come up with rationalizations not to be vaccinated, of varying degrees of plausibility, if you are predisposed against it.  But many of those providing such rationalizations must have realized that their rationalizations often did not make much sense.  Rather, their decisions appear to have been driven more by a visceral or emotional reaction (vaccinations just “feel” wrong) than as an outcome of a rational process.  That is, the decision not to be vaccinated was made first, based on emotions or feelings, with the rationalizations then arrived at later to justify a decision that had already been made.  (Such a process is in accord with the “social intuitionist” model of Jonathan Haidt, where decisions are made first, in a visceral reaction based on emotion, while rationalizations then come later to justify that decision.)

In the case of Covid-19, those decisions on vaccination (and earlier on wearing masks) were made in accordance with political identity – a perceived loyalty to Trump – rather than in recognition of the very real risks that would follow if one contracted Covid-19.  Wearing a mask or accepting a vaccination would simply be “wrong” and disloyal.

I have found it astonishing how strong this emotional reaction has apparently become.  Covid-19 is new (it did not even exist just two years ago), it is deadly (where on average about 1.5% of those infected have died – with a much higher fatality rate than this average for those who are older or who have other health issues), and may have serious long-term ill effects even for those who do not die from it.  Yet this visceral reaction appears to have been so powerful that many supporters of Trump still refuse to be vaccinated, despite the risk of genuine life and death consequences.

I should hasten to add that not all voters for Trump have refused to be vaccinated.  Indeed, according to the surveys, about 60% (a majority) have as of October.  There are also highly vocal partisans on the left who have refused to be vaccinated.  Their reasons are likely very different from that of the typical Trump voter, but the underlying cause appears still to be intuitive – the feeling that such vaccinations are simply “wrong”.  But the issue is that the relative shares of the two groups have been very different:  A far higher share of those who voted for Trump have refused vaccination than is the case for those who voted for Biden.  The consequences are as shown in the charts at the top of this post.

As noted before, the cause for this relationship cannot be known with certainty, and what I have presented here should be viewed as speculative on my part.  There may well be other explanations.  For example, a related but somewhat different explanation would be that a common third factor explains both the tendency of some to vote for Trump and also to be resistant to vaccinations.  Those in this group may put faith in conspiracy theories (including, but not limited to, terrible consequences from being vaccinated), distrust authority, proudly but stubbornly insist on doing the opposite of whatever is recommended, and for such reasons not only refuse to be vaccinated but also vote for Trump.

Whatever the explanation, the results have been tragic.  This has also been a lesson in how strongly some will keep to a held position, even as they have seen prominent figures, and sometimes friends or even family members, come down with this disease.  When an issue becomes one of identity, it appears that even with such tragic consequences there will be many who steadfastly refuse to change.

A Calculation of Covid-19 Case Rates for Those Vaccinated and Those Not Vaccinated

A.  Introduction

The vaccines available for the virus that causes Covid-19 are incredibly effective – far better than the vaccines for many diseases – but can only work if they are used.  Sadly, a substantial share of the US population, particularly those who identify as conservative and Republican, are declining the opportunity to be vaccinated.  While there are also those on the left who have indicated they will not be vaccinated against this terrible virus, a recent (June) Gallup survey found that while close to half (46%) of Republicans said they do not plan to accept the vaccinations, just 6% of Democrats said so.  A Washington Post – ABC survey in early July found almost exactly the same results, with 47% of Republicans saying they are not likely to get the vaccination, while again only 6% of Democrats said so.

It might help convince those who are reluctant to be vaccinated to see in hard numbers how effective the vaccines have turned out to be.  Part of the responsibility of the CDC is to collect and report data on disease incidence in the US as well as on the cause of all deaths in the country.  All hospitals, doctor’s offices, clinics, and other health centers in the US, are required to report these to the CDC, and the CDC in turn then consolidates the information and makes it available to the public and to researchers.  For Covid, the CDC has put together a separate online site providing extensive data on the spread of the disease in the country, calling it COVID Data Tracker, with the multiple individual data series updated daily.

For vaccinations against Covid, the CDC provides not only daily figures on the number of vaccinations given (down to the county level), but with this broken down by various demographic dimensions, including gender (male/female), age (9 different age groups), and ethnicity (7 groups).  Each of these are tracked daily, so one can also determine trends over time.  There is also daily tracking for each state (and perhaps county – I did not check) of the number of doses of each type of vaccine administered (Moderna, Pfizer, and Johnson & Johnson, and whether it was the first or second dose for Moderna and Pfizer), for key age groups (over age 65, over 18, and over 12).  Many of the charts the CDC provides are then picked up in the regular news media, so people can see daily the trends in Covid-19 cases, deaths, vaccinations, and other such important information.

But the CDC is not reporting what would be an extremely useful, and hopefully convincing, daily statistic along with these numbers.  And that would be not only the total number of new confirmed Covid cases that day, new hospitalizations due to Covid, and deaths due to Covid, but also how many of these are among those who have been vaccinated and among those who have not.  The simple figures could be provided, or, more usefully, expressed as a count per 100,000 in the relevant population (of vaccinated and unvaccinated).

The CDC is not doing this, and it is not clear why.  It may feel that the data it has is not of sufficiently high quality, but if so, one would think that a high priority would be to take whatever measures are necessary to upgrade that quality.  Indeed, it is difficult to think of anything that would be a higher priority than this.

This post will discuss what a chart with such a breakdown between vaccinated and unvaccinated may look like.  This chart (at the top of this post) is not based on directly reported data on Covid cases among the vaccinated and unvaccinated, as the CDC has not made whatever it has on this publicly available (at least among what I have been able to find – specialists in the field may have access to more of what the CDC has).  Rather, the chart presents what the rates would be, given the observed number of daily new Covid cases in the US, and assumptions on how effective the vaccines have been.

Given the high degree of effectiveness of these vaccines in preventing Covid cases, and even more so in preventing Covid deaths, why are so many people refusing to be vaccinated?  Sadly, identity politics has intervened, with many supporters of former president Trump appearing to take vaccination as a sign of disloyalty to a cause they believe in.  As we will see, there is a very strong negative correlation by state between the share of the population who have been vaccinated and the share who voted for Trump.

B.  Covid Case Rates Among Those Vaccinated and Those Unvaccinated 

Despite its extensive reports on Covid cases and vaccinations, one key dimension that the CDC does not report is the breakdown of the daily number of new Covid-19 cases, hospitalizations, and deaths, between those who have been vaccinated and those who have not.  Given the high degree of effectiveness of the vaccines (as observed in the clinical trials and in numerous studies since), one should expect huge disparities in such rates between these two groups.  And seeing such disparities daily in the news might convince at least a few, and hopefully many, of those hesitant to be vaccinated to accept that they should indeed be vaccinated.  It truly is a matter of survival.

So why doesn’t the CDC report this?  One would think that if the CDC does not obtain such reports already, that their highest priority would be to set up the system to ensure such numbers are gathered.  Anyone being tested for Covid-19 will certainly be asked if they have been vaccinated.  And the first question that will likely be asked of anyone entering a hospital for suspected Covid-19 (even before they are asked their name and medical insurance number) is whether they have been vaccinated.  Such information would then be recorded in (or certainly could be recorded in) the reports sent to the CDC on the number testing positive for Covid-19, and would certainly be available for anyone who has been hospitalized and then dies from Covid-19.

The CDC does appear to obtain at least partial information on the number of Covid-19 cases, hospitalizations, and deaths where vaccination status is known.  But they have evidently not sought to organize a more complete and reliable system.  In late May they issued a brief, non-technical, summary of data obtained on cases of Covid-19 among individuals who had been vaccinated (there were a total of 10,262, in reports from 46 states), covering the period between January 1 and April 30, 2021.  But they did not put this in any context, and while they noted that 101 million Americans had been fully vaccinated as of April 30, there were far fewer (essentially zero) as of January 1.  By itself, this report was basically useless.  And then the CDC announced that as of May 1, it would no longer even seek to collect comprehensive data on the vaccination status of confirmed cases of Covid-19, but rather seek this only for those hospitalized due to Covid-19 or who had died from it.

It is difficult to understand why the CDC would scale back the reporting of Covid-19 cases to it, rather than upgrade the quality and completeness of what is reported.  Furthermore, even with incomplete data on vaccination status of confirmed cases of Covid-19, as well as of hospitalizations and deaths from Covid-19, the CDC could still report the figures for those known to be vaccinated, those known not to be vaccinated, and those where vaccination status was not known.  Such a breakdown would still show the (likely huge) disparities in the rates between those known to be vaccinated and those not.  And gathering such data is critically important not only in determining the continued effectiveness (or not) of the vaccines overall against Covid-19 as mutations of the virus develop, but also the continued effectiveness (or not) of the several individual vaccines that have been approved (i.e. Moderna, Pfizer/BioNTech, and Johnson & Johnson, so far in the US).

In the absence of such real world data, the chart at the top of this post presents what the Covid-19 case rates would be under specific assumptions (based on the clinical trial results and more recent studies of efficacy among different groups) of what the effectiveness rates are.  Specifically, based on the clinical trial results as well as numerous studies undertaken for various special groups since, plus being conservative (given the new mutations that have developed and spread over this time period) and rounding down, I assumed effectiveness rates of:

a)  90% for those fully vaccinated (both shots) with either the Pfizer or Moderna vaccines (and with a lag of 14 days from the second shot).

b)  70% for those partially vaccinated (one-shot) with either the Pfizer or Moderna vaccines (and with a lag of 14 days from that shot).

c)  70% for those vaccinated with the one-shot Johnson & Johnson vaccine (again with a 14-day lag).

[Side note:  One will often see the terms “efficacy” and “effectiveness” used interchangeably in describing how well vaccines work.  Technically, efficacy refers to how well (how effective) the vaccines perform in clinical trials, while effectiveness is the term used for how well the vaccines perform in the real world.  For non-specialists, the distinction is not important.]

The chart at the top of this post shows what the respective number of daily newly confirmed Covid-19 rates would be for those fully vaccinated with the Pfizer or Moderna vaccines and for those not vaccinated with any vaccine (per 100,000 of population in each group) from December 27, 2020 (14 days after vaccinations began for the general public on December 13) to July 12, 2021.  To reduce clutter in the chart, I did not show the respective curves for those partially vaccinated or those vaccinated with the Johnson & Johnson vaccines, but those numbers were part of the calculations as the fact that some were vaccinated in this way will affect the position of the curves.  One has to solve a small algebra problem, as the data one has to work with are only the daily number of new cases, the number fully or partially vaccinated with one of the vaccines, and the assumed effectiveness rates (where effectiveness is defined relative to those not vaccinated).  The curves for the groups who had been partially vaccinated (as of a particular date) or who had had the Johnson & Johnson vaccine, would be in between the two curves shown (given the assumed 70% effectiveness rates for each).

The chart presents what the curves would be for daily new cases of Covid-19.  Also of interest are the number of those being hospitalized (indicating severe cases) and those dying from this disease.  In principle, one could prepare similar charts.  But here there is not as much data to go on to underlie the assumptions to be made on vaccine effectiveness.  It is however clear that, given how they function, the vaccines will likely be a good deal more effective in preventing serious cases of Covid-19 (those that require hospitalization) and of deaths than their effectiveness in preventing any type of case.  The reason is that exposures to the virus will be similar for those who are vaccinated and for those who are not:  The virus is floating in the air (due to a contagious person nearby) and it passes up the nose of some of those passing by.  But the difference then is that as the virus starts to replicate in the person’s lungs and body, the immune system of a vaccinated person will be primed and prepared to respond quickly, thus (in most cases) stopping the virus before it has replicated to levels that lead to a detectable illness.  But with 90% effectiveness, a detectable illness will still occur in 10% of such cases.

Most of these illnesses will then be mild, as the immune system in a vaccinated person is already acting to drive down the virus.  But some share of these will not be, possibly due to how the individual’s body had responded to the vaccine.  Still, since it will be some share (well less than 100%) of the 10%, the number will be small.  And it will likely be an even smaller share for those cases that turn out to be so severe that the patient dies.

With such small numbers, the effects will not be easily picked up in clinical trials.  For the clinical trial used to assess the efficacy of the Pfizer/BioNTech vaccine in the US, for example, one had 43,000 volunteers enrolled, of which half received the vaccine and half received a similar looking shot but which had just saline (salt water) in it.  Neither the patient nor the doctor overseeing the shots knew which it was – there was simply an identifying number to be revealed later.  The volunteers would then go about their lives as they had before.  Over time, some would then come down with Covid-19 (as Covid-19 was present in the country and spreading).  Those that did were treated as any other Covid-19 patient would be.  Once a certain number of cases arose (determined based on statistics, with 170 the trigger in the Pfizer/BioNTech trial), the identifying numbers were then, and only then, revealed.  When they were, they found in this trial that 162 of those cases were of individuals who had received just saline (i.e. no vaccine) while 8 had received the vaccine.  This thus showed 95% efficacy (as 8 is 5% of 162, the case burden among those not vaccinated).  Note this is for the effectiveness against getting a case of Covid-19, whether mild or severe.

For hospitalizations, the numbers will be far smaller.  In the Pfizer/BioNTech trial, only 10 of the 170 cases were “severe”, and of these 9 occurred in those who had the shot of saline while just one was in the vaccinated group.  This is far too small a sample to come up with a figure for how effective the virus is against severe cases requiring hospitalization, although it is clear that it helped.  And with no deaths at all among the 170, one can say even less.

There should, however, now be data on this in CDC files as close to half of the US population has been fully vaccinated.  The CDC has not reported on this.  But the Associated Press, working with experts, was able to find relevant data in the CDC files (possibly in files accessible to researchers with special software – I could not find them).  The AP reported that for the month of May, only 1,200 (1.1%) of the 107,000 patients who had been hospitalized for Covid had been vaccinated.  And only 150 (0.8%) of the 18,000 who had died from Covid in the month had been vaccinated.  Since one-third (34%) of the US population had been fully vaccinated as of May 1 (and 43% as of May 31), the shares of those vaccinated will not be small because the number who had been vaccinated were few.  Rather, the numbers give an indication that the vaccines are highly effective against severe cases of Covid developing, and even more effective against patients dying from the disease.  The numbers may well be imperfect, as the CDC has warned, but the impact of vaccination is still clear.

The figures are also consistent with public statements that have been made.  In late June, CDC Director Dr. Rochelle Walensky said that the vaccine is so effective the “nearly every death, especially among adults, due to Covid-19, is, at this point, entirely preventable.”  On July 1, Dr. Walensky said at a White House press briefing that “preliminary data” from certain states over the last six months suggested that “99.5 percent of deaths from COVID-19 in these states have occurred in unvaccinated people”.  On July 8, the White House coordinator on the coronavirus response, Jeff Zients, said “Virtually all Covid-19 hospitalizations and deaths in the United States are now occurring among unvaccinated individuals”.  And on July 12, Dr. Anthony Fauci said “99.5% of people who die of Covid are unvaccinated.  Only 0.5% of those who die are vaccinated” (with his source for these figures probably the same as Dr. Walensky’s).

I am sure all these statements are true.  But many would find them far more convincing if they would show us the actual numbers.  They could be partial, as noted above, with figures for those known to be vaccinated, known not to be vaccinated, and not known.  But the CDC should make public what it has.  And it would be even more convincing to show the numbers updated daily, to drive home the point, repeatedly, that vaccinations are highly effective in protecting us from suffering and possibly dying from this terrible disease.

C.  The Simple Dynamics of Pandemic Spread

As the chart indicates, the likelihood of becoming a victim of Covid-19 is far less for those vaccinated.  I would stress, however, that one should not jump to the conclusion that if by some miracle all of the US had been vaccinated as of December 27, that the path followed would have been the one shown in the chart for those fully vaccinated.  That would not be the case.  Rather, what the curves show is what the case rates would be for each such group where, as has in fact been the case, a substantial share of the population had not been vaccinated, and hence the virus continued to spread (primarily among the unvaccinated).  With a substantial number of people still infecting others with the virus, a certain number of vaccinated people will still catch the virus as the vaccines, while excellent at an effectiveness of 90% or even higher, are still not 100% effective.

The dynamics would be very different, and far better, if everyone (or even just most Americans) were fully vaccinated.  Indeed, under such a scenario the pandemic would soon end completely, and the line depicting cases of Covid-19 would not simply be low but at zero.

This is due to the mathematics of exponential spread of a virus in a pandemic.  The virus that causes Covid-19 cannot live on its own, but only in a living person.  When a person is exposed to the virus, with viral particles floating into their nose, the virus will take about a week to incubate.  The person is then infectious to others for about another week.  If an infected person spreads the virus on average to two others, then the number of cases will double every reproduction period (one and a half weeks on average for Covid-19).  This reproduction rate is called R0 (or R-naught, or R-zero) by epidemiologists, and refers to the reproduction rate in a setting where no measures are being taken to contain the spread of the virus (no vaccines, no masks, no social distancing).  For the original (pre-mutation) virus that causes Covid-19, the R0 was estimated to be between 2 and 3.  With the more recent – more easily spread – delta variant of the virus, it is believed the R0 is above 3.

A virus that then spreads from one person to three every reproduction period (every week and a half on average for Covid) means that if left unchecked, 100 cases to start (week 0) would grow to 8,100 cases by week 6 and to over 650,000 cases by week 12.  it is tripling every week and a half  However, if everyone has had a vaccine that is 90% effective, then the reproduction rate would be reduced from 3 to 0.3.  That means 100 cases to start would lead to only 30 cases in the next reproduction period and to less than one case by week 6, by which point it will have died out.

However, not everyone is vaccinated.  As of the day I am writing this (July 20), the share of the population fully vaccinated is 49%.  Using, for simplicity, a figure of 50%, and assuming the R0 for the mutations currently circulating in the US is 3, then the reproduction rate would fall not to 0.3 but only to 1.65 (the weighted average of half of the population at 0.3 and half still at 3).  With any reproduction rate above 1.0, the spread of the virus will grow, not diminish.  At a rate of 1.65, one will find by simple arithmetic that 100 cases initially (in week 0) would grow (if nothing else is done) to over 700 cases by week 6 and over 5,000 cases by week 12.  While far less than with a reproduction rate of 3, it is still growing.  And that is indeed what has been happening.

These numbers should be taken as illustrative as the modeling is simplistic.  True modeling would take much more into account.  Simple averages are assumed here, as well as no changes in other factors that affect the trends (in particular no change in the use of masks or social distancing).  Also, simple averages may not work that well for Covid-19, as it appears that some people will be far more contagious than others, plus it will depend on how such individuals behave.  A contagious person might spread the disease to dozens or even hundreds of others if they are in an enclosed hall, with a crowd of others who might be chanting or singing, such as at a political rally or a church service.

But the point here is that if 100% of the population were vaccinated, the curve in a chart showing the case rate among those vaccinated would not follow the curve in the chart at the top of this post.  Rather, it would very quickly drop to zero.  The reason why there are still cases among those vaccinated in the US is that, with only about half of the population vaccinated, the virus continues to spread among the unvaccinated.  It will then spread to a certain share of the vaccinated (about 10% of those who are exposed, for vaccines that are 90% effective).

D.  Why Are Some Not Accepting Vaccination?

Despite the high degree of safety and effectiveness of the vaccines, a significant share of Americans are still refusing to be vaccinated.  As noted at the top of this post, recent Gallup and Washington Post – ABC polls found the almost identical results that close to half (46 or 47%) of Republicans say they are unlikely to (or definitely will not) accept vaccination, while 6% of Democrats (in both polls) said that.

Why this opposition to vaccinations, particularly among Republicans?  It is always hard to discern motives and often the individuals themselves may not really know why they are opposed – they just are.  Surveys may provide an indication, but are limited as the survey questionnaire will typically provide a list of possible reasons and ask the person to check all that might be a factor for them.

For example, a survey conducted by Echelon Insights, a Republican firm, in mid-April asked those surveyed who had said they will not accept a vaccination, or were not sure, to choose from a list of possible reasons for why.  The top responses were (with the percentage saying yes, where one could choose multiple reasons):

a)  The vaccine was developed too quickly:  48%

b)  The vaccine was rushed for political reasons:  39%

c)  I don’t have enough information about side effects:  37%

d)  I don’t trust the information being published about the vaccine:  34%

e)  I’m taking enough measures to avoid Covid-19 without the vaccine:  30%

f)  I wouldn’t trust the vaccine until it’s been in use for at least a few years:  28%

g)  I don’t trust any vaccines:  26%

h)  I wouldn’t trust the vaccine until it’s been in use for at least several months:  20%

i)  I believe I’m personally unlikely to suffer serious long term effects if I contract the coronavirus:  17%

But it is not possible to say the extent to which these were in fact the primary reasons for their hesitancy (or direct opposition) to being vaccinated, and to what extent these were just convenient responses to provide to the person conducting the survey.

There are also more bizarre reasons given by some.  For example, a very recent Economist/YouGov poll (conducted between July 10 and 13) found that among those who say they will not be vaccinated, fully half (51%) said that the vaccinations are being used by the government to inject microchips into the population.  A common variant of this conspiracy theory is that Bill Gates will be using the microchips to monitor and/or control us.  It is hard to believe that half of those refusing to be vaccinated really believe this.  Rather, it appears they have decided they do not want to be vaccinated, and then they come up with various rationalizations.  Consistent with this, the Economist/YouGov poll also found that 85% of those who say they will not be vaccinated believe that the threat of the coronavirus has been exaggerated for political reasons (this despite over 600,000 Americans already having died from Covid).

This opposition has also been fed by such media groups as Fox News, with repeated segments that denigrate vaccination against this disease.  As one example, In early May, Tucker Carlson, the most watched political commentator on Fox News, told his audience that as of April 23, a CDC system had recorded that 3,362 people had died following their vaccination.  His report implied the vaccines caused those deaths, when this was not at all the case.  Numerous fact-checkers and commentators in the media almost immediately investigated and concluded that the Carlson allegations were false (see, for example, here, here, and here).  But the damage had been done.

Tucker Carlson took the figures from the Vaccine Adverse Events Recording System (VAERS), an on-line system set up by the CDC where anyone who had been vaccinated (and indeed anyone else) could make a report if they encountered some adverse event following their vaccination.  It is a voluntary system, open to anyone, and you may have noticed a description of how to use it in the papers you received when you were vaccinated (at least I received it as part of the instructions when I was vaccinated in Washington, DC).  Carlson’s report was that the VAERS showed 3,362 deaths between late December and April 23 (which he then extrapolated to 3,722 as of April 30).

But as the fact-checkers and commentators in the media immediately noted, just because a death was recorded by someone in the VAERS does not mean that the death was caused by the vaccine.  There are a certain number of deaths every year in the US, particularly among the elderly, and one should have taken that into account before jumping to a conclusion that a 3,362 figure (or 3,722 as of end-April) was abnormal and a consequence of the vaccinations they received.

It is straightforward to calculate what the expected number of deaths would be in a normal year for the number of individuals who were vaccinated between late 2020 and the April 30 date that Carlson focussed on.  About 2.9 million Americans died in 2019 (i.e. before any Covid cases or vaccinations), and simply assuming an average mortality rate of those vaccinated, the number that would be expected to die in this period in a normal year would be more than 100,000.  And since those being vaccinated over this period were disproportionately the elderly (as the elderly were prioritized in these early months), the far higher mortality rates of the elderly (compared to the entire population) would lead to a number several times higher.  Some of these deaths were then recorded by someone in the VAERS, but that does not mean the vaccinations caused them.  Indeed, there is no evidence so far that the vaccines have caused any deaths at all (although a very small number are being investigated).

[Technical note for those interested in the details of how this calculation was done:  I used the CDC numbers of those who had been fully vaccinated (as of end-December, 2020, and then daily through to April 30, 2021), the US population (332 million, from the Census Bureau), and the number of deaths in the US in 2019 (i.e. before Covid) of 2.9 million (from the CDC).  From this, one can easily calculate on a spreadsheet the number of person-days (through to April 30) of those vaccinated (i.e. starting at 120 days for those vaccinated as of December 31, and then counting down to zero for those vaccinated on April 30), and take the sum of this.  Dividing this total by the number of person-days in a year for the full US population (i.e. 332 million times 365) yields 3.7%.  Applying this share to the 2.9 million number of deaths in a pre-Covid year means that one would have expected 108,000 of those who had been vaccinated during this period to have died during this period for reasons that had nothing to do with Covid or the vaccines.  And the number dying of normal causes would likely be far higher than this 108,000, as that number is calculated assuming those being vaccinated during this period would have had the average mortality rate of the US as a whole.  But a disproportionate share of those vaccinated during this period were the elderly, as they were given priority, and the elderly will of course have naturally higher mortality rates than the population as a whole.  If one adjusted for the ages of those being vaccinated and then used age-specific mortality rates for these groups, the true number to expect would not be 108,000 but something far higher, and likely several times higher.]

It is not just the media, however.  A number of Republican politicians are saying the same.  And it is not only Republican politicians on the more extreme end of their party (such as Representative Marjorie Taylor Greene of Georgia, where Twitter has just suspended her account for 12 hours due to the misleading information she has posted on Covid-19 and the vaccines for it).  One also sees this among Republican office-holders who have been perceived as coming from the party’s establishment.  A prominent example is Senator Ron Johnson of Wisconsin.  In early May, for example, Senator Johnson also cited the VAERS as indicating “over 3,000” had died following their being vaccinated – implying causation.  And despite being called out on this by fact-checkers, Senator Johnson has continued to make these claims.  The fact-checkers at the Washington Post have recently given Senator Johnson their “highest” rating of four Pinocchios for his ongoing campaign of vaccine misinformation.

It is not clear, however, the extent to which vaccine hesitancy and/or outright opposition originated in the reports and statements of media figures such as Tucker Carlson or political figures such as Senator Ron Johnson, or whether the media and political figures found it advantageous to build on such perceptions and then spur along the concerns.  Which came first is not clear.

What is clear is that the issue of vaccination has become politicized, with vaccination being taken as a sign of political loyalties.  One saw the same politicization with the wearing of masks.  Comparing the share of state populations that have been vaccinated (fully or partially) to the share of the 2020 presidential vote in that state for Trump, one finds:

The correlation is incredibly high, with an R-squared of 0.77.  On average, the regression line indicates that for every additional percentage point in the vote share of Trump, the share of the population in the state that was fully or partially vaccinated (as of July 13) was 0.8 percentage points lower.  Furthermore, almost all of the states that voted for Biden have a higher share vaccinated than all of the states that voted for Trump (with the only significant exception being Georgia, and with a few states where the election was close – Arizona, Wisconsin, Michigan, and Nevada – having similar vaccination shares as some of the higher-end Trump states).

E.  Conclusion

The political division is stark, and it is not clear what might change this.  But with the vaccines so highly effective – against cases of Covid-19, more so against severe cases requiring hospitalization, and even more so against death – releasing hard numbers on what the rates have been among the vaccinated versus the unvaccinated may help.  The numbers currently available might be imperfect, and hence require releases with three categories (vaccinated, unvaccinated, and not known), but this would still tell the story.  If everyone saw each day that 995 out of 1,000 deaths had been among the unvaccinated, with only 5 among those who had been vaccinated (as Dr. Walensky’s 99.5% figure implies), self-interest in one’s own health might eventually win out.

This is obviously urgent.  The chart at the top of this post was based on case data downloaded on July 13 (for Covid-19 cases as of July 12).  As one can see in that chart, the daily number of new cases of Covid-19 has been rising over the last month.  It reached a trough around June 20 (using a 7-day moving average of the daily cases).  By July 12, the number of cases had more than doubled from this trough.  As I write this on July 20, it has increased by a further more than 50% since July 12, so it is now more than triple what it was on June 20.  It is spreading especially rapidly in the states with a relatively low rate of vaccination.

This increase has been due, in part, to new mutations (in particular the delta variant) that spread more rapidly than the original form of the virus.  This is what one would expect from standard evolutionary theory – mutations develop and those that spread more easily will soon dominate.  Adding to this is that social distancing and mask mandates have been sharply eased over the last month, leading many to act as if the virus is no longer a threat.  While that would be true if everyone were vaccinated, and is greatly reduced for those who have been vaccinated, the disease will continue to spread and the threat will remain real when half the population is not.