Illustrating coronavirus waves with moving images

The New York Times put out a master class in visualizing space and time data recently, in a visualization of five waves of Covid-19 that have torched the U.S. thus far (link).

Nyt_coronawaves_title

The project displays one dataset using three designs, which provides an opportunity to compare and contrast them.

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The first design - above the headline - is an animated choropleth map. This is a straightforward presentation of space and time data. The level of cases in each county is indicated by color, dividing the country into 12 levels (plus unknown). Time is run forward. The time legend plays double duty as a line chart that shows the change in the weekly rate of reported cases over the course of the pandemic. A small piece of interactivity binds the legend with the map.

Nyt_coronawaves_moviefront

(To see a screen recording of the animation, click on the image above.)

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The second design comprises six panels, snapshots that capture crucial "turning points" during the Covid-19 pandemic. The color of each county now encodes an average case rate (I hope they didn't just average the daily rates). 

Nyt_coronawaves_panelsix

The line-chart legend is gone -  it's not hard to see Winter > Fall 2020 > Summer/Fall 2021 >... so I don't think it's a big loss.

The small-multiples setup is particularly effective at facilitating comparisons: across time, and across space. It presents a story in pictures.

They may have left off 2020 following "Winter" because December to February spans both years but "Winter 2020" may do more benefit than harm here.

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The third design is a series of short films, which stands mid-way between the single animated map and the six snapshots. Each movie covers a separate window of time.

This design does a better job telling the story within each time window while it obstructs comparisons across time windows.

Nyt_coronawaves_shortfilms

The informative legend is back. This time, it's showing the static time window for each map.

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The three designs come from the same dataset. I think of them as one long movie, six snapshots, and five short films.

The one long movie is a like a data dump. It shows every number in the dataset, which is the weekly case rate for each county for a given week. All the data are streamed into a single map. It's a show piece.

As an instrument to help readers understand the patterns in the dataset, the movie falls short. Too much is going on, making it hard to focus and pick out key trends. When your eyes are everywhere, they are nowhere.

The six snapshots represent the other extreme. The graph does not move, as the time axis is reduced to six discrete time points. But this display describes the change points, and tells a story. The long movie, by contrast, invites readers to find a story.

Without motion, the small-multiples format allows us to pick out specific counties or regions and compare the case rates across time. This task is close to impossible in the long movie, as it requires freezing the movie, and jumping back and forth.

The five short films may be the best of both worlds. It retains the motion. If the time windows are chosen wisely, each short film contains a few simple patterns that can easily be discerned. For example, the third film shows how the winter wave emerged from the midwest and then walloped the whole country, spreading southward and toward the coasts.

Nyt_winterwave

(If the above gif doesn't play, click it.)

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If there is double or triple the time allocated to this project, I'd want to explore spatial clustering. I'd like to dampen the spatial noise (neighboring counties that have slightly different experiences). There is also temporal noise (fluctuations from week to week for the same county) - which can be smoothed away. I think with these statistical techniques, the "wave" feature of the pandemic may be more visible.

 

 


Visually displaying multipliers

As I'm preparing a blog about another real-world study of Covid-19 vaccines, I came across the following chart (the chart title is mine).

React1_original

As background, this is the trend in Covid-19 cases in the U.K. in the last couple of months, courtesy of OurWorldinData.org.

Junkcharts_owid_uk_case_trend_july_august_2021

The React-1 Study sends swab kits to randomly selected people in England in order to assess the prevalence of Covid-19. Every month, there is a new round of returned swabs that are tested for Covid-19. This measurement method captures asymptomatic cases although it probably missed severe and hospitalized cases. Despite having some shortcomings, this is a far better way to measure cases than the hotch-potch assembling of variable-quality data submitted by different jurisdictions that has become the dominant source of our data.

Rounds 12 and 13 captured an inflection point in the pandemic in England. The period marked the beginning of the end of the belief that widespread vaccination will end the pandemic.

The chart I excerpted up top broke the data down by age groups. The column heights represent the estimated prevalence of Covid-19 during each round - also, described precisely in the paper as "swab positivity." Based on the study's design, one may generalize the prevalence to the population at large. About 1.5% of those aged 13-24 in England are estimated to have Covid-19 around the time of Round 13 (roughly early July).

The researchers came to the following conclusion:

We show that the third wave of infections in England was being driven primarily by the Delta variant in younger, unvaccinated people. This focus of infection offers considerable scope for interventions to reduce transmission among younger people, with knock-on benefits across the entire population... In our data, the highest prevalence of infection was among 12 to 24 year olds, raising the prospect that vaccinating more of this group by extending the UK programme to those aged 12 to 17 years could substantially reduce transmission potential in the autumn when levels of social mixing increase

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Raise your hand if the graphics software you prefer dictates at least one default behavior you can't stand. I'm sure most hands are up in the air. No matter how much you love the software, there is always something the developer likes that you don't.

The first thing I did with today's chart is to get rid of all such default details.

Redo_react1_cleanup

For me, the bottom chart is cleaner and more inviting.

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The researchers wanted readers to think in terms of Round 3 numbers as multiples of Round 2 numbers. In the text, they use statements such as:

weighted prevalence in round 13 was nine-fold higher in 13-17 year olds at 1.56% (1.25%, 1.95%) compared with 0.16% (0.08%, 0.31%) in round 12

It's not easy to perceive a nine-fold jump from the paired column chart, even though this chart form is better than several others. I added some subtle divisions inside each orange column in order to facilitate this task:

Redo_react1_multiples

I have recommended this before. I'm co-opting pictograms in constructing the column chart.

An alternative is to plot everything on an index scale although one would have to drop the prevalence numbers.

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The chart requires an additional piece of context to interpret properly. I added each age group's share of the population below the chart - just to illustrate this point, not to recommend it as a best practice.

Redo_react1_multiples_popshare

The researchers concluded that their data supported vaccinating 13-17 year olds because that group experienced the highest multiplier from Round 12 to Round 13. Notice that the 13-17 year old age group represents only 6 percent of England's population, and is the least populous age group shown on the chart.

The neighboring 18-24 age group experienced a 4.5 times jump in prevalence in Round 13 so this age group is doing much better than 13-17 year olds, right? Not really.

While the same infection rate was found in both age groups during this period, the slightly older age group accounted for 50% more cases -- and that's due to the larger share of population.

A similar calculation shows that while the infection rate of people under 24 is about 3 times higher than that of those 25 and over, both age groups suffered over 175,000 infections during the Round 3 time period (the difference between groups was < 4,000).  So I don't agree that focusing on 13-17 year olds gives England the biggest bang for the buck: while they are the most likely to get infected, their cases account for only 14% of all infections. Almost half of the infections are in people 25 and over.

 


Working hard at clarity

As I am preparing another blog post about the pandemic, I came across the following data graphic, recently produced by the CDC for a vaccine advisory board meeting:

CDC_positivevaccineintent

This is not an example of effective visual communications.

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For one thing, readers are directed to scour the footnotes to figure out what's going on. If we ignore those for the moment, we see clusters of bubbles that have remained pretty stable from December 2020 to August 2021. The data concern some measure of Americans' intent to take the COVID-19 vaccine. That much we know.

There may have been a bit of an upward trend between January and May, although if you were shown the clusters for December, February and April, you'd think the trend's been pretty flat. 

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But those colors? What could they represent? You'd surely have to fish this one out of the footnotes. Specifically, this obtuse sentence: "Surveys with multiple time points are shown with the same color bubble for each time point." I had to read it several times. I think it simply means "Color represents the pollster." 

Then it adds: "Surveys with only one time point are shown in gray." which simply means "All pollsters who have only one entry in the dataset are grouped together and shown in gray."

Another problem with this chart is over-plotting. Look at the July cluster. It's impossible to tell how many polls were conducted in July because the circles pile on top of one another. 

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The appearance of the flat trend is a result of two unfortunate decisions made by the designer. If I retained the chart form, I'd have produced something that looks like this:

Junkcharts_redo_cdcvaccineintent_sameform

The first design choice is to expand the vertical axis to range from 0% to 100%. This effectively squeezes all the bubbles into a small range.

Junkcharts_redo_cdcvaccineintent_startatzero

The second design choice is to enlarge the bubbles causing copious amount of overlapping. 

Junkcharts_redo_cdcvaccineintent_startatzero_bigdots

In particular, this decision blows up the Pew poll (big pink bubble) that contained 10 times the sample size of most of the other polls. The Pew outcome actually came in at 70% but the top of the pink bubble extends to over 80%. Because of this, the outlier poll of December 2020 - which surprisingly printed the highest number of all polls in the entire time window - no longer looks special. 

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Now, let's see what else we can do to enhance this chart. 

I don't like how bubble size is used to encode the sample size. It creates a weird sensation for anyone who's familiar with sampling errors, and confidence regions. The Pew poll with 10 times the sample size is the most reliable poll of them all. Reliability means the error bars around the Pew poll outcome is the smallest of them all. I tend to think of the area around a point estimate as showing the sampling error so the Pew poll would be a dot, showing the high precision of that estimate. 

But that won't work because larger bubbles catch more of the reader's attention. So, in the following version, all dots have the same size. I encode reliability in the opacity of the color. The darker dots are polls that are more reliable, that have larger sample sizes.

Junkcharts_redo_cdcvaccineintent_opacity

Two of the pollsters have more frequent polling than others. In this next version, I highlighted those two, which reveals the trend better.

Junkcharts_redo_cdcvaccineintent_opacitywithlines

 

 

 


Simple charts are the hardest to do right

The CDC website has a variety of data graphics about many topics, one of which is U.S. vaccinations. I was looking for information about Covid-19 data broken down by age groups, and that's when I landed on these charts (link).

Cdc_vaccinations_by_age_small

The left panel shows people with at least one dose, and the right panel shows those who are "fully vaccinated." This simple chart takes an unreasonable amount of time to comprehend.

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The analyst introduces three metrics, all of which are described as "percentages". Upon reflection, they are proportions of the people in specific age ranges.

Readers are thus invited to compare these proportions. It's not clear, however, which comparisons are intended. The first item listed in the legend states "Percent among Persons who completed all recommended doses in last 14 days". For most readers, including me, this introduces an unexpected concept. The 14 days here do not refer to the (in)famous 14-day case-counting window but literally the most recent two weeks relative to when the chart was produced.

It would have been clearer if the concept of Proportions were introduced in the chart title or axis title, while the color legend explains the concept of the base population. From the lighter shade to the darker shade (of red and blue) to the gray color, the base population shifts from "Among Those Who Completed/Initiated Vaccinations Within Last 14 Days" to "Among Those Who Completed/Initiated Vaccinations Any Time" to "Among the U.S. Population (regardless of vaccination status)".

Also, a reverse order helps our comprehension. Each subsequent category is a subset of the one above. First, the whole population, then those who are fully vaccinated, and finally those who recently completed vaccinations.

The next hurdle concerns the Q corner of our Trifecta Checkup. The design leaves few hints as to what question(s) its creator intended to address. The age distribution of the U.S. population is useless unless it is compared to something.

One apparently informative comparison is the age distribution of those fully vaccinated versus the age distribution of all Americans. This is revealed by comparing the lengths of the dark blue bar and the gray bar. But is this comparison informative? It's telling me that people aged 50 to 64 account for ~25% of those who are fully vaccinated, and ~20% of all Americans. Because proportions necessarily add to 100%, this implies that other age groups have been less vaccinated. Duh! Isn't that the result of an age-based vaccination prioritization? During the first week of the vaccination campaign, one might expect close to 100% of all vaccinations to be in the highest age group while it was 0% for the other age groups.

This is a chart in search of a question. The 25% vs 20% comparison does not assist readers in making a judgement. Does this mean the vaccination campaign is working as expected, worse than expected or better than expected? The problem is the wrong baseline. The designer of this chart implies that the expected proportions should conform to the overall age distribution - but that clearly stands in the way of CDC's initial prioritization of higher-risk age groups.

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In my version of the chart, I illustrate the proportion of people in each age group who have been fully vaccinated.

Junkcharts_cdcvaccinationsbyage_1

Among those fully vaccinated, some did it within the most recent two weeks:

Junkcharts_cdcvaccinationsbyage_2

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Elsewhere on the CDC site, one learns that on these charts, "fully vaccinated" means one shot of J&J or 2 shots of Pfizer or Moderna, without dealing with the 14-day window or other complications. Why do we think different definitions are used in different analyses? Story-first thinking, as I have explained here. When it comes to telling the story about vaccinations, the story is about the number of shots in arms. They want as big a number as possible, and abandon any criterion that decreases the count. When it comes to reporting on vaccine effectiveness, they want as small a number of cases as possible.

 

 

 

 

 


Check your presumptions while you're reading this chart about Israel's vaccination campaign

On July 30, Israel began administering third doses of mRNA vaccines to targeted groups of people. This decision was controversial since there is no science to support it. The policymakers do have educated guesses by experts based on best-available information. By science, I mean actual evidence. Since no one has previously been given three shots, there can be no data on which anyone can root such a decision. Nevertheless, the pandemic does not always give us time to collect relevant data, and so speculative analysis has found its calling.

Dvir Aran, at Technion, has been diligently tracking the situation in Israel on his Twitter. Ten days after July 30, he posted the following chart, which immediately led many commentators to bounce out of their seats crowning the third shot as a magic bullet. Notably, Dvir himself did not endorse such a claim. (See here to learn how other hasty conclusions by experts have fared.)

When you look at Dvir's chart, what do we see?

Dvir_aran_chart

Possibly one of the following two things, depending on what concern you have in your head.

1) The red line sits far above the other two lines, showing that unvaccinated people are much more likely to get infected.

2) The blue line diverges from the green line almost immediately after the 3rd shots started getting into arms, showing that the 3rd shot is super effective.

If you take another moment to look, you might start asking questions, as many in Twitter world did. Dvir was startlingly efficient at answering these queries.

A) Does the green line represent people with 2 or 3 doses, or is it strictly 2 doses? Aron asked this question and got the answer (the former):

AronBrand_israelcases_twoorthreedoses

It's time to check our presumptions. When you read that chart, did you presume it's exactly 2 doses or did you presume it's 2 or 3 doses? Or did you immediately spot the ambiguity? As I said in this article, graphs attain efficiency at communication because the designer leverages unspoken rules - the chart conveys certain information without explicitly placing it on the chart. But this can backfire. In this case, I presumed the three lines to display three non-overlapping groups of people, and thus the green line indicates those with 2 doses but not 3. That presumption led me to misinterpret what's on the chart.

B) What is the denominator of the case rates? Is it literal - by that I mean, all unvaccinated people for the red line, and all people with 3 doses for the blue line? Or is the denominator the population of Israel, the same number for all three lines? Lukas asked this question, and got the answer (the former).

Lukas_denominator

C) Since third shots are recommended for 60 year olds and over who were vaccinated at least 5 months ago, and most unvaccinated Israelis are below 60, this answer opens the possibility that the lines compare apples and oranges. Joe. S. asked about this, and received an answer (all lines display only 60 year olds and over.)

Joescholar_basepopulationquestion

Jason P. asked, and learned that the 5-month-out criterion is immaterial since 90% of the vaccinated have already reached that time point.

JasonPogue_5monthsout

D) We have even more presumptions. Like me, did you presume that the red line represents the "unvaccinated," meaning people who have not had any vaccine shots? If so, we may both be wrong about this. It has become the norm by vaccine researchers to lump "partially vaccinated" people with "unvaccinated", and call this combined group "unvaccinated". Here is an excerpt from a recent report from Public Health Ontario (link to PDF), which clearly states this unintuitive counting rule:

Ontario_case_definition

Notice that in this definition, someone who got infected within 14 days of the first shot is classified as an "unvaccinated" case and not a "partially vaccinated case".

In the following tweet, Dvir gave a hint of what he plotted:

Dvir_group_definition

In a previous analysis, he averaged the rates of people with 0 doses and 1 dose, which is equivalent to combining them and calling them unvaccinated. It's unclear to me what he did to the 1-dose subgroup in our featured chart - did it just vanish from the chart? (How people and cases are classified into these groups is a major factor in all vaccine effectiveness calculations - a topic I covered here. Unfortunately, most published reports do a poor job explaining what the analysts did).

E) Did you presume that all three lines are equally important? That's far from true. Since Israel is the world champion in vaccination, the bulk of the 60+ population form the green line. I asked Dvir and he responded that only 7.5%, or roughly 100K are unvaccinated.

DvirAran_proportionofunvaccinated

That means 1.2 million people are part of the green line, 12 times higher. There are roughly 50 cases per day among unvaccinated, and 370 daily cases among those with 2 or 3 doses. In other words, vaccinated people account for almost 90% of all cases.

Yes, this is inevitable when over 90% of the age group have been vaccinated (but it is predictable on the first day someone blasted everywhere that real-world VE is proved by the fact that almost all new cases were in the unvaccinated.)

If your job is to minimize infections, you should be spending most of your time thinking about the 370 cases among vaccinated than the 50 cases among unvaccinated. If you halve the case rate, that would be a difference of 185 cases vs 25. In Israel, the vaccination campaign has already succeeded; it's time to look forward, which is exactly why they are re-focusing on the already vaccinated.

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If what you worry about most is the effectiveness of the original two-dose regimen, Dvir's chart raises a puzzle. Ignore the blue line, and remember that the green line already includes everybody represented by the blue line.

In the following chart, I removed the blue line, and added reference lines in dashed purple that correspond to 25%, 50% and 75% vaccine effectiveness. The data plotted on this chart are unadjusted case rates. A 75% effective vaccine cuts case rate by three quarters.

Junkcharts_dviraran_israel_threeshotschart

This chart shows the 2-dose mRNA vaccine was nowhere near 90% effective. (As regular readers know, I don't endorse this simplistic calculation and have outlined the problems here, but this style of calculation keeps getting published and passed around. Those who use it to claim real-world studies confirm prior clinical trial outcomes can either (a) insist on using it and retract their earlier conclusions, or (b) admit that such a calculation was, and is, a bad take.)

Also observe how the vaccinated (green) line is moving away from the unvaccinated (red) line. The vaccine apparently is becoming more effective, which runs counter to the trend used by the Israeli government to justify third doses. This improvement also precedes the start of the third-shot campaign. When the analytical method is bad, it generates all sorts of spurious findings.

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As Dvir said, it is premature to comment on the third doses based on 10 days of data. For one thing, the vaccine developers insist that their vaccines must be given 14 days to work. In a typical calculation, all of the cases in the blue line fall outside the case-counting window. The effective number of cases that would be attributed to the 3-dose group right now is zero, and the vaccine effectiveness using the standard methodology is 100%, even better than shown in the chart.

There is an alternative interpretation of this graph. Statisticians call this the selection effect. On July 30, the blue line split out of the green: some people were selected to receive the 3rd dose - this includes an official selection (the government makes certain subgroups eligible) as well as a self-selection (within the eligible subgroup, certain people decide to get the 3rd shot earlier.) If those who are less exposed to the virus, or more risk averse, get the shots first, then all that is happening may be that we have split off a high VE subgroup from the green line. Even if the third shot were useless, the selection effect itself could explain the gap.

Statistics is about grays. It's not either-or. It's usually some of each. If you feel like Groundhog Day, you're getting the picture. When they rolled out two doses, we lived through an optimistic period in which most experts rejoiced about 90-100% real-world effectiveness, and then as more people get vaccinated, the effect washed away. The selection effect gradually disappears when vaccination becomes widespread. Are we starting a new cycle of hope and despair? We'll find out soon enough.


What metaphors give, they take away

Aleks pointed me to the following graphic making the rounds on Twitter:

Whyaxis_covid_men

It's being passed around as an example of great dataviz.

The entire attraction rests on a risque metaphor. The designer is illustrating a claim that Covid-19 causes erectile dysfunction in men.

That's a well-formed question so in using the Trifecta Checkup, that's a pass on the Q corner.

What about the visual metaphor? I advise people to think twice before using metaphors because these devices can give as they can take. This example is no exception. Some readers may pay attention to the orientation but other readers may focus on the size.

I pulled out the tape measure. Here's what I found.

Junkcharts_covid_eds

The angle is accurate on the first chart but the diameter has been exaggerated relative to the other. The angle is slightly magnified in the bottom chart which has a smaller circumference.

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Let's look at the Data to round out our analysis. They come from a study from Italy (link), utilizing survey responses. There were 25 male respondents in the survey who self-reported having had Covid-19. Seven of these submitted answers to a set of five questions that were "suggestive of erectile dysfunction". (This isn't as arbitrary as it sounds - apparently it is an internationally accepted way of conducting reseach.) Seven out of 25 is 28 percent. Because the sample size is small, the 95% confidence range is 10% to 46%.

The researchers then used the propensity scoring method to find 3 matches per each infected person. Each match is a survey respondent who did not self-report having had Covid-19. See this post about a real-world vaccine study to learn more about propensity scoring. Among the 75 non-infected men, 7 were judged to have ED. The 95% range is 3% to 16%.

The difference between the two subgroups is quite large. The paper also includes other research that investigates the mechanisms that can explain the observed correlation. Nevertheless, the two proportions depicted in the chart have wide error bars around them.

I have always had a question about analysis using this type of survey data (including my own work). How do they know that ED follows infection rather than precedes it? One of the inviolable rules of causation is that the effect follows the cause. If it's a series of surveys, the sequencing may be measurable but a single survey presents challenges. 

The headline of the dataviz is "Get your vaccines". This comes from a "story time" moment in the paper. On page 1, under Discussion and conclusion, they inserted the sentence "Universal vaccination against COVID-19 and the personal protective equipment could possibly have the added benefit of preventing sexual dysfunctions." Nothing in the research actually supports this claim. The only time the word "vaccine" appears in the entire paper is on that first page.

"Story time" is the moment in a scientific paper when the researchers - after lulling readers to sleep over some interesting data - roll out statements that are not supported by the data presented before.

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The graph succeeds in catching people's attention. The visual metaphor works in one sense but not in a different sense.

 

P.S. [8/6/2021] One final note for those who do care about the science: the internet survey not surprisingly has a youth bias. The median age of 25 infected people was 39, maxing out at 45 while the median of the 75 not infected was 42, maxing out at 49.


Hanging things on your charts

The Financial Times published the following chart that shows the rollout of vaccines in the U.K.

Ft_astrazeneca_uk_rollout

(I can't find the online link to the article. The article is titled "AstraZeneca and Oxford face setbacks and success as battle enters next phase", May 29/30 2021.)

This chart form is known as a "streamgraph", and it is a stacked area chart in disguise. 

The same trick can be applied to a column chart. See the "hanging" column chart below:

Junkcharts_hangingcolumns

The two charts show exactly the same data. The left one roots the columns at the bottom. The right one aligns the middle of the columns. 

I have rarely found these hanging charts useful. The realignment makes it harder to compare the sizes of the different column segments. On the normal stacked column chart, the yellow segments are the easiest to compare because they share the same base level. Even this is taken away from the reader on the right side.

Note also that the hanging version does not admit a vertical axis

The same comments apply to the streamgraph.

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Nevertheless, I was surprised that the FT chart shown above actually works. The main message I learned was that initially U.K. primarily rolled out AstraZeneca and, to a lesser extent, Pfizer, shots while later, they introduced other vaccines, including Johnson & Johnson, Novavax, CureVac, Moderna, and "Other". 

I can also see that the supply of AstraZeneca has not changed much through the entire time window. Pfizer has grown to roughly the same scale as AstraZeneca. Moderna remains a small fraction of total shots. 

I can even roughly see that the total number of vaccinations has grown about six times from start to finish. 

That's quite a lot for one chart, so job well done!

There is one problem with the FT chart. It should have labelled end of May as "today". Half the chart is history, and the other half is the future.

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For those following Covid-19 news, the FT chart is informative in a different way.

There is a misleading statement going around blaming the U.K.'s recent surge in cases on the Astrazeneca vaccine, claiming that the U.K. mostly uses AZ. This chart shows that from the start, about a third of the shots administered in the U.K. are Pfizer, and Pfizer's share has been growing over time. 

U.K. compared to some countries mostly using mRNA vaccines

Ourworldindata_cases

U.K. is almost back to the winter peak. That's because the U.K. is serious about counting cases. Look at the state of testing in these countries:

Ourworldindata_tests

What's clear about the U.S. case count is that it is kept low by cutting the number of tests by two-thirds, thus, our data now is once again severely biased towards severe cases. 

We can do a back-of-the-envelope calculation. The drop in testing may directly lead to a proportional drop in reported cases, thus removing 500 (asymptomatic, or mild) cases per million from the case count. The case count goes below 250 per million so the additional 200 or so reduction is due to other reasons such as vaccinations.


Did prices go up or down? Depends on how one looks at the data

The U.S. media have been flooded with reports of runaway inflation recently, and it's refreshing to see a nice article in the Wall Street Journal that takes a second look at the data. Because as my readers know, raw data can be incredibly deceptive.

Inflation typically describes the change in price level relative to the prior year. The month-on-month change in price levels is a simple seasonal adjustment used to remove the effect of seasonality that masks the true change in price levels. (See this explainer of seasonal adjustment.)

As the pandemic enters the second year, this methodology is comparing 2021 price levels to pandemic-impacted price levels of 2020. This produces a very confusing picture. As the WSJ article explains, prices can be lower than they were in 2019 (pre-pandemic) and yet substantially higher than they were in 2020 (during the pandemic). This happens in industry sectors that were heavily affected by the economic shutdown, e.g. hotels, travel, entertainment.

Wsj_pricechangehotels_20192021Here is how they visualized this phenomenon. Amusingly, some algorithm estimated that it should take 5 minutes to read the entire article. It may take that much time to understand properly what this chart is showing.

Let me save you some time.

The chart shows monthly inflation rates of hotel price levels.

The pink horizontal stripes represent the official inflation numbers, which compare each month's hotel prices to those of a year prior. The most recent value for May of 2021 says hotel prices rose by 9% compared to May of 2020.

The blue horizontal stripes show an alternative calculation which compares each month's hotel prices to those of two years prior. Think of 2018-9 as "normal" years, pre-pandemic. Using this measure, we find that hotel prices for May of 2021 are about 4% lower than for May of 2019.

(This situation affects all of our economic statistics. We may see an expansion in employment levels from a year ago which still leaves us behind where we were before the pandemic.)

What confused me on the WSJ chart are the blocks of color. In a previous chart, the readers learn that solid colors mean inflation rose while diagonal lines mean inflation decreased. It turns out that these are month-over-month changes in inflation rates (notice that one end of the column for the previous month touches one end of the column of the next month).

The color patterns become the most dominant feature of this chart, and yet the month-over-month change in inflation rates isn't the crux of the story. The real star of the story should be the difference in inflation rates - for any given month - between two reference years.

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In the following chart, I focus attention on the within-month, between-reference-years comparisons.

Junkcharts_redo_wsj_inflationbaserate

Because hotel prices dropped drastically during the pandemic, and have recovered quite well in recent months as the U.S. reopens the economy, the inflation rate of hotel prices is almost 10%. Nevertheless, the current price level is still 7% below the pre-pandemic level.

 



 


Plotting the signal or the noise

Antonio alerted me to the following graphic that appeared in the Economist. This is a playful (?) attempt to draw attention to racism in the game of football (soccer).

The analyst proposed that non-white players have played better in stadiums without fans due to Covid19 in 2020 because they have not been distracted by racist abuse from fans, using Italy's Serie A as the case study.

Econ_seriea_racism

The chart struggles to bring out this finding. There are many lines that criss-cross. The conclusion is primarily based on the two thick lines - which show the average performance with and without fans of white and non-white players. The blue line (non-white) inched to the right (better performance) while the red line (white) shifted slightly to the left.

If the reader wants to understand the chart fully, there's a lot to take in. All (presumably) players are ranked by the performance score from lowest to highest into ten equally sized tiers (known as "deciles"). They are sorted by the 2019 performance when fans were in the stadiums. Each tier is represented by the average performance score of its members. These are the values shown on the top axis labeled "with fans".

Then, with the tiers fixed, the players are rated in 2020 when stadiums were empty. For each tier, an average 2020 performance score is computed, and compared to the 2019 performance score.

The following chart reveals the structure of the data:

Junkcharts_redo_seriea_racism

The players are lined up from left to right, from the worst performers to the best. Each decile is one tenth of the players, and is represented by the average score within the tier. The vertical axis is the actual score while the horizontal axis is a relative ranking - so we expect a positive correlation.

The blue line shows the 2019 (with fans) data, which are used to determine tier membership. The gray dotted line is the 2020 (no fans) data - because they don't decide the ranking, it's possible that the average score of a lower tier (e.g. tier 3 for non-whites) is higher than the average score of a higher tier (e.g. tier 4 for non-whites).

What do we learn from the graphic?

It's very hard to know if the blue and gray lines are different by chance or by whether fans were in the stadium. The maximum gap between the lines is not quite 0.2 on the raw score scale, which is roughly a one-decile shift. It'd be interesting to know the variability of the score of a given player across say 5 seasons prior to 2019. I suspect it could be more than 0.2. In any case, the tiny shifts in the averages (around 0.05) can't be distinguished from noise.

***

This type of analysis is tough to do. Like other observational studies, there are multiple problems of biases and confounding. Fan attendance was not the only thing that changed between 2019 and 2020. The score used to rank players is a "Fantacalcio algorithmic match-level fantasy-football score." It's odd that real-life players should be judged by their fantasy scores rather than their on-the-field performance.

The causal model appears to assume that every non-white player gets racially abused. At least, the analyst didn't look at the curves above and conclude, post-hoc, that players in the third decile are most affected by racial abuse - which is exactly what has happened with the observational studies I have featured on the book blog recently.

Being a Serie A fan, I happen to know non-white players are a small minority so the error bars are wider, which is another issue to think about. I wonder if this factor by itself explains the shifts in those curves. The curve for white players has a much higher sample size thus season-to-season fluctuations are much smaller (regardless of fans or no fans).

 

 

 

 


Probabilities and proportions: which one is the chart showing

The New York Times showed this chart (link):

Nyt_unvaccinated_undeterred

My first read: oh my gosh, 40-50% of the unvaccinated Americans are living their normal lives - dining at restaurants, assembling with more than 10 people, going to religious gatherings.

After reading the text around this chart, I realize I have misinterpreted it.

The chart should be read by columns. Each column is a "pie chart". For example, the first column shows that half the restaurant diners are not vaccinated, a third are fully vaccinated, and the remainder are partially vaccinated. The other columns have roughly the same proportions.

The author says "The rates of vaccination among people doing these activities largely reflect the rates in the population." This line is perhaps more confusing than intended. What she's saying is that in the general population, half of us are unvaccinated, a third are fully unvaccinated, and the remainder are partially vaccinated.

Here's a picture:

Junkcharts_redo_nyt_unvaccinatedundeterred

What this chart is saying is that the people dining out is like a random sample from all Americans. So too the other groups depicted. What Americans are choosing to do is independent of their vaccination status.

Unvaccinated people are no less likely to be doing all these activities than the fully vaccinated. This raises the question: are half of the people not wearing masks outdoors unvaccinated?

***

Why did I read the chart wrongly in the first place? It has to do with expectations.

Most survey charts plot probabilities not proportions. I haphazardly grabbed the following Pew Research chart as an example:

Pew_kids_socialmedia

From this chart, we learn that 30% of kids 9-11 years old uses TikTok compared to 11% of kids 5-8.  The percentages down a column do not sum to 100%.