Update on mobility and COVID-19 data in Spain: The bias in retrospective consolidation and the Stockdale paradox

We announced a prediction one month ago about the forthcoming fourth wave in Spain. This prediction was based on the empirical observation that the number of COVID cases and deaths increase two and three weeks after the median of the radius of mobility crosses a critical value (70% of its pre-pandemic score).

The radius of mobility measures the dispersion in our displacements and captures the most relevant features in our daily mobility. We can see peaks in the radius for those special dates in 2019 (Easter, summer, national’s day, etc.) and valleys in the lockdowns of 2020 and 2021, as well as the peaks in the relaxation of the measures that systematically preceded each COVID-19 wave.

Our team made an extraordinary effort collecting the daily radius of gyration of more than 10 million users, every day since 1st of January 2018 until yesterday, and updating it every 24 hours. We obtain a daily distribution from those users with very low to those with very high radius. We see here the evolution in time of the percentiles of such distribution, with the mean an the median. Thanks David Mateo, Jordi Bayer and Jordi Escrich for the effort.

Indeed, we found that is correlated with the number of daily contacts based on the fact that most of our displacements are mean to meet with other people, or to do activities where there are also other people. Thus, more dispersion in our mobility is statistically correlated with having more contacts which is statistically correlated with increasing the number of positive COVID-19 cases. This chain of correlations makes the radius of mobility an earlier predictor of the evolution of the pandemic.

It is still early to confirm the accuracy of our prediction as data is still consolidating, but some comments in the media this week push us to make an update on this topic. This is our analysis of the present situation in Spain regarding mobility and COVID-19.

1. Confirming the prediction from the radius of mobility

The median of the radius of mobility crossed the critical value the last week of February, and the number of cases had the tipping point in the second week of March. Hospitalizations also had their tipping point three weeks later as expected (typically at the same week as for the cases or one week later). At the regional level, we see that the Community of Madrid crossed the critical value earlier, and thus all COVID metrics show an earlier increase in their values. For the rest of the provinces, cases and deaths were going down in almost all of the 50 main provinces in the week of our prediction. Last week, we had an increase in the number of positive cases in 46 of these provinces, and an increase in the number of hospitalizations, UCI cases and deaths in 20 of them. The situation is not good, and the radius is still above the critical value.

Spain:

Madrid:

Legend:

There is a relevant data story behind these tables: The radius of mobility peaked during Easter and decreased the weeks after but still stays above the critical value. However:

1)      Hospitalizations and ICU cases decrease in the last couple of weeks at the national level even if positive cases continue growing;

2)      the number of deaths did not stop decreasing in all the period at the national level, and the tipping point in Madrid is 5 weeks after crossing the critical value.

3)      the growth in the number of cases looks slower than in the previous waves.

One candidate to explain this apparently contradictory behavior is the vaccination campaign. We expect positive effects indeed, but we expect them in the absolute values and not in the trends. We are facing here other effects related with the data itself, one related with the nature of the data and the other related with its harvesting process: scale invariance and retrospective consolidation.

2. Interpretation of the data

Scale invariance

When a system shows scale invariance, the natural way to check the data involves logarithmic scale. We learned with the pandemic the relevance of using the appropriate representation to see the data to get conclusions. Is the number of cases growing slower? Yes, in linear scale; no, in logarithmic scale:

The expansion of an epidemic is a multiplicative process and thus show scale invariance. Conclusions should be made by looking the numbers in logarithmic scale. When we do that, we find the growth of the third wave has the same rate as the previous one (right panel, dashed lines to guide the eye), what is not obvious in linear scale (left panel).

In view of this plot, we can expect that the cases will skyrocket in the next weeks if it follows the same trend, as it looks like each peak and valley is more extreme that the previous one. Are we entering into a resonance?

Retrospective consolidation

The process of consolidating this data is complex and involves thousands of people. It is not easy, and it takes time, in some places more than others. Every day we get updates in the number of cases and deaths, but many of these cases are actually from days, weeks and months ago. It is also easier to consolidate a trend when numbers are very high since those complex situations have less relative weight to the total, but every contribution is relevant at low numbers as the weight of these fluctuations are higher in relative terms. In other words: it is harder to accurate update the data when numbers are low.

We can check how the time series change comparing historical data from different updates: confirmed cases are typically consolidated in a few days, but ICU and deaths may take weeks and months to get the actual picture. Madrid consolidates the number of deaths faster than the national level and already shows an increase in the last weeks (this is normal since the national level will update data as slower as the slowest region). 

Number of cases are typically updated faster than number of deaths, that may take weeks or months to consolidate, as seen when we compare the updates at different previous dates.

In summary, what we know now is:

-         Regions with faster consolidation are already registering an increase in hospitalizations, ICU cases and deaths.

-         Consolidation takes longer as the numbers are lower.

To understand better where we are now respecting the emergence of the fourth wave, let’s see what we knew during the emergence of the third one as data got retrospectively consolidated (let’s use logarithmic scale since we know it gets a better picture): 

Spain crossed the critical value in its radius of mobility in the first week of December, peaking just before Christmas. The tipping point in the number of deaths between the second and third wave took place around mid December (according to consolidated data we have today). However, the 14-days average of the data we had available on the 28th of December just showed a constant decline trend. We only noticed a stabilization in the number of deaths some weeks later, around 15th of January, but the picture changed completely in only five days, when the effects of the wave in the number of deaths become obvious in the update on 20th of January. This represents 7 weeks of difference between the early alarm of the radius of mobility and the consolidation of the data.

3. Conclusions

 Is this fourth wave growing slower?

No, it is growing at the expected rate given the scale of the numbers, which are lower now than in the previous valley.

Should we expect an increase in the number of deaths?

We need to wait to consolidate the data, but yes, we can expect an increase. As we just shown for the previous wave, the picture dramatically changed in just 5 days with the new updates.

We should take decisions based on data, but we should care about where this data comes from and the bias it has. If we do not do that, we could spread misinformation. It is plausible that the vaccination campaign is now keeping the number of deaths low. And it is also plausible that the increase in mobility in Easter is not having any consequence in the number of deaths of COVID-19. However, it is highly probable that this is a superfluous effect of the data consolidation.

Fernando Simón (director at CCAES at the Ministry of Health) declared yesterday that “Right now it seems that the effect that we could have expected due to the increased mobility in Easter is not occurring, according with the data that we have as of today” [1]. He knows what he is saying, and he is right with “with the data that we have as of today”: the effect is not visible because the data is not consolidated.

Not consolidated data will always give the impression that the situation is much better that what it really is. We appreciate Fernando's effort in keeping the motivation high and recognizing the massive effort that the people is doing. However, this is sending a message of false optimism to the tired population that will push them to underestimate the danger of the fourth wave, and most important: burn and frustrate them psychologically once they realize that the fight is not over, over and over again.

This is known as the Stockdale paradox [2]: you should be optimistic in the long term to make it, but you will fail if you are naively optimistic in the short term, cumulating frustration after frustration.

Admiral Jim Stockdale was a war prisoner for 8 years at Vietnam and these were his words in his famous interview with author Jim Collins:

Finally I asked, “Who didn’t make it out?”

“Oh, that’s easy,” he said. “The optimists.”

“The optimists? I don’t understand,” I said, now completely confused given what he’d said earlier.

“The optimists. Oh, they were the ones who said, ‘We’re going to be out by Christmas.’ And Christmas would come, and Christmas would go. Then they’d say, ‘We’re going to be out by Easter.’ And Easter would come, and Easter would go. And then Thanksgiving, and then it would be Christmas again. And they died of a broken heart. This is a very important lesson. You must never confuse faith that you will prevail in the end–-which you can never afford to lose–-with the discipline to confront the most brutal facts of your current reality, whatever they might be.”

I am naturally optimistic (you do not start a PhD or create a start-up if you are not stupidly optimistic) and I know this situation will come to an end. But not yet, not now. We still need to hold some extra weeks.

Take care.

[1] https://www.20minutos.es/noticia/4664409/0/tres-autonomias-mas-entran-en-riesgo-extremo-por-covid-pero-simon-es-optimista-hay-que-estar-satisfechos

[2] https://www.huffpost.com/entry/the-stockdale-paradox_b_5897ca82e4b02bbb1816bc38