Death in the Swiss second wave

Why so many deaths during the second wave? The second wave of the epidemic shows very different dynamics from those of the spring. In particular, the number of deaths has not kept pace with the - partial - drop in the number of new cases. A statistical analysis shows that this can be explained by the pressure on intensive care services, a pressure that more persistent than during the first wave. If the number of new cases does not decrease rapidly, we could reach the 10,000 death threshold at the end of January. Changing relations between cases, hospital stays, and deaths The relationship between the weekly number of new cases and deaths shows interesting variations. The figure below (based on figures from https://www.corona-data.ch/ ) shows the weekly number of new cases (blue line) and the weekly number of deaths (red line, right scale). 60 000 New cases and deaths per week 700 50 000 New cases 600 40 000 500 30 000 Deaths 400 20 000 300 10 000 200 100 0 0 2020-02-25 2020-03-22 2020-04-19 2020-05-17 2020-06-14 2020-07-12 2020-08-09 2020-09-06 2020-10-04 2020-11-01 2020-11-29 Until the beginning of November the death curve followed the curve of cases with a delay of one to two weeks, and the magnitude of the link has changed since the spring due to wider screening since then. A statistical analysis showed that the evolution of the number of deaths during a week was essentially explained by the evolution of the number of cases during the previous week (blog in l'Agefi of 28 October). But things have changed since: the significant drop in the number of 1

cases since the beginning of November is not reflected in the dynamics of deaths. What is happening? To look into this, we update the statistical model with the new data and refine it. One aspect that is clearly different from the first wave is the number of people in intensive care. In the spring, it peaked at 404 people on April 5, and then rapidly decreased, exceeding 300 people in only three weeks. Since the beginning of November, this number has hovered around 500 people. We therefore have a situation with greater pressure on intensive care units, both in terms of the number of patients and the persistence of the pressure. This can lead to an increase in deaths for a given number of new cases because it indicates more serious cases and/or a reduced capacity of the hospital services to cope. The table below shows the results of the statistical analysis for the flow of deaths in week t, the number of new hospitalizations (admissions minus discharges), new cases in intensive care units, and new cases under respiratory assistance. In each box the table shows the estimated coefficient for the relationship between the variables, the Student statistic which indicates whether the relationship is due to chance, and the percentage showing the probability that the relationship may be due to chance (a value of less than 5% is considered acceptable). To avoid clogging the table, the analysis only includes variables whose effect is not due to chance. In each of the four columns, the statistical model explains between 94 and 99% of the dynamics of the variables considered, as shown by the R2 statistic at the bottom of the table. Since the scope of the tests has increased significantly since the first wave, the statistical model allows the relationship between the variables to change since the beginning of May. A possible change is reflected in the lower half of the table, which shows how much the relationship has changed since the beginning of May. The first column shows that the number of deaths during a week is largely explained by the number of new cases during the previous week, and that this relationship has become more moderate since May (the coefficient going from 0.035 deaths per case to 0.007 = 0.035 - 0.028 deaths per case). However, the number of new cases does not explain everything, and in particular does not explain the gap observed since the beginning of November between a decreasing number of cases and a stable number of deaths. It is therefore necessary to extend the model by taking into account the number of people in intensive care. Indeed, we observe that the higher the number of patients in intensive care, the more deaths there are (0.372 deaths per person in intensive care). Has this changed since May? Yes, but in a subtle way. It turns out that the number of people in intensive care has since been associated with more deaths, provided there are more than 300 people in intensive care. Below this threshold, the relationship is no different since May. This threshold effect reflects the impact of the pressure on hospital services, which is stronger during the second wave. The number of new hospitalizations during a week is explained by the number of new cases during that week. Here again the relationship is weaker since May reflecting the broader screening policy. Unsurprisingly, the net flow between hospital admissions and discharges during a week is inversely proportional to the number of people in hospital at the end of the previous week (one person in hospital is associated with 0.4 additional discharges). However, this relationship has weakened 2

since May, from -0.4 to -0.34 = -0.4 + 0.06. This indicates a longer hospital stay during the second wave. New cases (t) New deaths New persons in New persons New persons (t) hospital (t) in intensive under respiratory New cases (t-1) 0.140 0.035 21.1 care (t) assistance(t) Persons in hospital (t-1) 10.7 0.0% 0.0% 0.017 0.013 Persons in intensive care (t-1) -0.400 0.372 -17.7 9.1 7.4 Persons under respiratory 7.1 0.0% assistance (t-1) 0.0% 0.0% 0.0% Post-May * New cases (t) -0.110 -0.028 -16.4 0.015 0.012 Post- May * New cases (t-1) -9.1 0.0% 0.0% 5.4 4.2 Post-May * Persons in 0.061 hospital (t-1) 0.947 2.2 0.0% 0.0% Post- May * Persons in 8.7 3.1% intensive care ( t-1) 0.0% -0.445 -0.551 Post- May * Persons in 0.97 -16.2 -12.6 intensive care beyond 300 0.99 0.0% 0.0% people (t-1) -0.013 Post- May * Persons under -0.015 -6.9 respiratory assistance ( t-1) -8.0 0.0% R2 0.0% -0.011 -0.013 -3.8 -4.4 0.0% 0.0% 0.171 5,1 0.0% 0.312 5.3 0.5% 0.97 0.94 3

t and t-1 indicate the specific week. Each cell of the table shows the estimated coefficient the value of the Student t- statistic, and the likelihood that the coefficient differs from zero simply by chance (p-value). It is commonly considered that a p-value of 5% or less indicates that the estimated relation is robust. The change in the number of people in intensive care reflects the number of new cases during the week and the previous week, and decreases with the number of people in intensive care at the end of the previous week due to discharges. Again we observe that since May a given number of people in intensive care is associated with a reduced number of discharges, indicating longer hospital stays. The situation for the change in the number of people on respiratory assistance is similar to that observed for intensive care. The model accounts well for flows Although the model is based on a limited number of variables, it captures well the evolution of the pandemic. The figure below shows the evolution of the weekly number of deaths (blue line) and the value estimated by the model (red line). We can see that the two lines follow each other, including since the beginning of November. This stability at a high level reflects the number of people in intensive care (a variant of the model based solely on the number of new cases misses this stability). New deaths per week 800 700 600 500 400 300 200 100 0 2020-02-25 2020-03-22 2020-04-19 2020-05-17 2020-06-14 2020-07-12 2020-08-09 2020-09-06 2020-10-04 2020-11-01 2020-11-29 actual data Estimated values The model also accounts for the change in the number of people in hospital, in intensive care, and under respiratory assistance, as shown in the following three graphs. It should be noted that the 4

model has some difficulty in explaining the change in the number of people on respiratory assistance in recent weeks. New hospital cases per week (inflow - outflow) 1 200 2020-02-25 1 000 2020-03-22 2020-04-19 800 2020-05-17 600 2020-06-14 400 2020-07-12 200 2020-08-09 2020-09-06 0 2020-10-04 -200 2020-11-01 -400 2020-11-29 -600 actual data Estimated values New intensive care units cases per week (inflow - outflow) 200 150 100 50 0 -50 2020-02-25 2020-03-22 2020-04-19 2020-05-17 2020-06-14 2020-07-12 2020-08-09 2020-09-06 2020-10-04 2020-11-01 2020-11-29 -100 actual data Estimated values 5

New respiratory assistance cases per week (inflow - outflow) 120 100 80 60 40 20 0 -20 2020-02-25 2020-03-22 -40 2020-04-19 2020-05-17 -60 2020-06-14 2020-07-12 2020-08-09 2020-09-06 2020-10-04 2020-11-01 2020-11-29 -80 actual data Estimated values What’s next ? The model makes it possible to project the evolution of deaths and hospitalizations. To do this, all that is required is to provide it with a scenario on the evolution of new cases. Such a scenario is presented in the curve below until the end of January. It considers a stable number of new cases until January 10, followed by a gradual decrease. New cases per week 60 000 50 000 40 000 30 000 20 000 10 000 0 2020-02-25 2020-03-22 2020-04-19 2020-05-17 2020-06-14 2020-07-12 2020-08-09 2020-09-06 2020-10-04 2020-11-01 2020-11-29 2020-12-27 2021-01-24 6

In this scenario, the number of deaths remains at a high level, and only begins to fall at the end of January. This translates into a total number of deaths since the beginning of the epidemic reaching almost 10,000 people at the end of January. The high number of deaths can be explained in particular by a lasting pressure on hospital services. New deaths per per week 800 700 600 500 400 300 200 100 0 2020-02-25 2020-03-22 2020-04-19 2020-05-17 2020-06-14 2020-07-12 2020-08-09 2020-09-06 2020-10-04 2020-11-01 2020-11-29 2020-12-27 2021-01-24 Number of persons in hospital 4 000 3 500 3 000 2 500 2 000 1 500 1 000 500 0 2020-02-25 2020-03-22 2020-04-19 2020-05-17 2020-06-14 2020-07-12 2020-08-09 2020-09-06 2020-10-04 2020-11-01 2020-11-29 2020-12-27 2021-01-24 7

2020-02-25 Number of persons in intensive care 2020-03-22 2020-04-19600 2020-05-17500 2020-06-14400 2020-07-12300 2020-08-09200 2020-09-06100 2020-10-04 2020-11-010 2020-11-29 2020-12-27Number of persons under respiratory assistance 2021-01-24 300 250 200 150 100 50 0 A simple statistical analysis clearly shows that Switzerland will continue to be under pressure, especially if the festive season leads the curve of new cases to rise again. Moreover, as the pressure on hospital services lasts much longer than during the first wave, we cannot rule out the possibility that this will lead to an increase in deaths for a given number of cases. 8 2020-02-25 2020-03-22 2020-04-19 2020-05-17 2020-06-14 2020-07-12 2020-08-09 2020-09-06 2020-10-04 2020-11-01 2020-11-29 2020-12-27 2021-01-24