This article provides a quantitative measure for the impact of health care capacity on CFR. For this purpose, our previous method for CFR estimation  was leveraged to compare the fatality rate for critical cases who did and did not receive intensive care. Further, this work addresses the inconsistencies observed in COVID-19 CFR reported in different geographical regions.
Lower bound estimation of positive cases
Establishing high-level health care policies rely on an accurate estimation of infected cases. Respiratory, contact and aerosol transmission are the main known mechanisms by which the virus spreads. It has also been shown that the susceptibility to the infection depends mainly on viral load and exposure to an infected person [5, 7]. Therefore, the age-distribution of infected cases is expected to be similar in shape to that of region’s population. However, we observe that, in regions with relatively higher CFR, the age-distribution of infected is skewed towards the older ages (Fig.2b,2a). Further, the observed differences between CFR of regions with similar population distributions are beyond differences in health care quality and other such contributing factors.
We hypothesize that these inconsistencies are related to how these testings are conducted and that the infection in older age groups is more symptomatic and thus more detectable. Although the asymptomatic positive cases, more prevalent among younger age groups, may go unnoticed, they equally contribute to the spread of virus in the society.
To address the aforementioned inconsistencies, the data on the oldest age group (i.e. >80-year-old group) are considered. Assuming that due to the severity of symptoms, all of the positive cases in this age group are identifiable, the ratio of positive cases over the entire population for this age group was calculated. Next, the calculated ratio was applied to the populations of other age groups to estimate a lower number for the number of positive cases for them. The reason that the obtained estimation is a lower bound of positive cases is two-fold:
- The method assumes that all of the infected cases in the >80 age group are correctly identified, which is not necessarily the case; and
- The members of the >80 age group in reality have less social contacts than other age Thus, they have less chance of exposure to the virus than younger population.
Lower bound estimation results are summarized in Table 1 for different regions. It is observed from the table that the ratio of lower bound estimate of positive case to the confirmed cases, for the two countries that have lower CFRs, namely South Korea and Germany, is very close to 1.0. This is while this ratio is much greater than 1.0, for the two countries that have higher CFRs, namely Italy and Spain. Further, Fig. 2 juxtaposes the age-distribution of the resulting lower bound estimate with that of the confirmed cases and region’s population for Italy, South Korea, Germany, and Spain. Interestingly, South Korea and Germany, which have lower CFRs, show more similarity between the age-distributions of estimated positive cases and population. On the other hand, in Italy and Spain with higher CFRs, the discrepancy between the two distributions is more strongly pronounced.
The effect of health care capacity on CFR
Realizing the fact that, access to ICU is necessary for patients with critical conditions [Ref: Booth and Stewart , Arabi, Murthy, and Webb ], we studied the effect of the number of available ICU beds on CFR. The analysis was performed on the data from two regions that were severely influenced by the pandemic, namely Lombardy and the New York State, as elaborated in the following.
The region has the possession of about 18% of the total hospital beds in Italy. This is while, more than 35% of confirmed cases of Italy belong to Lombardy. Further, although Lombardy’s health care quality metrics are very similar to those of Italy’s average, the CFR for Lombardy is almost two times higher than the entire Italy excluding Lombardy (17.6% vs 9.7%, on March 27, calculated based on the number of confirmed cases).
To study how the health care capacity played a role in observing a higher CFR for Lombardy, Fig. 1a overlays the curves for CFR and intensive care rate, versus time. Here, the intensive care rate reflects the ratio of the number of patients, receiving intensive care, over the confirmed number of cases. On March 7, the intensive care rate shows a drop, which could be due to the fact that limit of health care capacity was reached, while the number of cases that needed intensive care continued to grow. Following that, one day after this drop, a sudden increase in CFR was observed for Lombardy. It is also observed that, starting on March 7, CFR surpassed intensive care rate, which means, from this date on, some patients that critically needed intensive care did not get a chance to receive it.
The effect of reaching maximum health care capacity on CFR could also be seen in Fig. 1c. Motivated by a report from the World Health Organization (WHO), which provided numerical percentages for mild, severe, critical and fatal cases, a best fit curve was obtained to overlay shifted curve for fatal cases and the curve for a fraction of critical cases. World Health Organization (WHO) provided numerical percentages for mild, severe, critical and fatal cases . Motivated by this, we investigated the possibility of correlating the number of fatal cases to the number of cases that received intensive care. For this purpose, first, the fatal cases were shifted based on the phase lag value obtained from CFR calculations . Next, a percentage factor that could correlate the shifted number of fatal cases to the number of intensive care cases was obtained. This was done by minimizing an error describing the difference between the two curves. The resulting percentage value was ~40%. Accordingly, we compared, in the chart of Fig 1c, the numbers for fatality cases versus 40% of cases that received intensive care. In this chart, the horizontal line represents 40% of intensive care capacity. It is observed that, fatal cases and 40% of intensive care receivers, which fairly overlap until March 5, start to diverge on March 6, when the maximum capacity of intensive care is reached. The 40% factor used for intensive care capacity is for the normalization purpose, to assure that the numbers of intensive care receivers and intensive care capacity are compared on the same scale. Note that, the number of intensive care receivers continues to grow after it reaches the ICU cap, which implies that additional ICU beds have continuously been added but with a rate slower than required to accommodate all cases in need of it.
To quantify the importance of ICU beds in reducing fatality, the expected number of fatal cases in the hypothetical scenario that no cap existed on the number of ICU bed, was compared with the actual number of fatal cases. Such expected number of fatal cases was estimated using the number of confirmed cases and an average CFR value calculated from the days prior to reaching the cap of ICU beds. This CFR number was ~8.45% as can be construed from Fig. 1a. The resulting expected number of fatal cases is shown in Fig. 1c, which follows the actual number of fatal cases, before ICU bed cap is reached, but remains below the actual number of cases ever since. The numbers for actual fatal cases, the expected fatal cases as well as the number of cases that receive intensive care are used to quantitatively estimate the effect of shortage of ICU beds on exacerbation of fatality rate. For this purpose, the fatality rate was estimated for critical cases who did not have access to standard ICU beds and was compared with that of those who had access to them, which are assumed to form ~40% of the cases.
This result is presented in Fig. 1d. Note that, as opposed to the fatality rate for the group that had access to ICU beds, the fatality rate of the group that did not have access to ICU is graphed only after March 8. The reason for doing so is that, the latter group essentially was non-existing before March 8, as the cap of ICU beds was not reached yet. The fatality rate for the group, without access to ICU, spiked to ~96% right after the cap was reached and slowly stabilized at ~76%. This means that the chance of living for cases in need of intensive care, but not having access to it, was only about ~24% as opposed to the ~60% chance of living for the group that received the intensive care. The fatality rate of the group with no intensive care never reached 40%.
Based on an 82% occupancy rate for ICU beds in New York, as reported in Wunsch et al. , we have estimated the number of available ICU beds in New York to be 850. Similar to Lombardy’s case, by assuming a 40% fatality rate for critical cases who receive intensive care, it is estimated that the cap of health care is reached when the fatality cases are 340, which occurs on March 26. Figure 1b depicts the CFR for New York over time. Interestingly, it is evident, that on March 26, there is a sudden raise in CFR value, which supports the hypothesis that reaching health care cap immediately exacerbates CFR.