Researchers around the world have used the case fatality rate (CFR) to determine how many people with COVID-19 are dying of it. CFR has also been used to understand how well India is responding to the pandemic.
The CFR is equal to the cumulative number of patients who died divided by the cumulative number of patients infected.
Using the same approach, the case recovery rate (CRR) is equal to the number of patients who recovered divided by the number of patients infected.
The CFR and the CRR can help evaluate the response of a country’s health system to the COVID-19 pandemic. India’s CFR, of 3.03%, is much lower than that of many developed nations. However, the CRR of 40.97% is rather poor compared to, say, Germany, which has a CFR of 4.64% but a CRR of 88.82%, or even China, which has a CFR of 5.99% and a CRR of 94.32%. The mystery deepens when we consider Russia: its CFR is 0.98% and its CRR, 29.19%. Pakistan’s numbers tell a similar story: CFR 2.10% and CRR 29.99%.
The metrics don’t say what has happened, or will happen, to the remaining 56% in India, the 69% in Russia or the 68% in Pakistan. This difference arises because of the way CFR and CRR are calculated – both use the total number of cases in the denominator, so they’re bound to yield an incomplete picture. Specifically, these numbers don’t account for the stage of the pandemic in any given country.
That is, CFR and CRR together explain the fate of only 44.27% of those infected in India, 32.1% in Pakistan, or 31% in Russia. Globally, the CFR + CRR = 46.5%. This is very different from the stage of the pandemic in Germany, where the CFR + CRR is 93.46% or in China – where the pandemic has more or less levelled off – it is 99.91%. Given that Germany’s and China’s CFRs are 4.64% and 5.59%, respectively, it would be wrong to conclude that India has fared better than Germany or China.
So how does one estimate the stage of the pandemic that a given country is currently in?
An alternative to CFR and CRR is to measure whether the number of daily COVID-19 cases is growing, steady or declining. Consider the graph below, which shows the number of confirmed cases with time. Clearly, the number of new cases in China, Germany and Spain appear to have stabilised. These are also countries where the CFR + CRR is over 80% (i.e. fewer than 20% of those infected are still in hospital or under quarantine).
The number of new cases appears to have steadied in France and Italy as well, although their numbers of “active” cases are still large, at 50% and 65%, respectively.
Iran seems to be a special case: there was a recent spike in the number of cases even though fewer than 17% of patients are in hospital or quarantine. The number of daily cases in Pakistan and Iran is similarly growing.
In other words, the CFR and the CRR give a reasonably complete picture only when (a) the number of active cases is small as well as (b) few new cases are registered each day. But the debate is misled when a majority of patients are still under treatment – as in India – or when the number of new cases every day is high, as in Russia and Brazil.
The CFR or the CRR are, therefore, poor metrics to use to assess a country’s success with treating its COVID-19 patients, particularly in comparison with other countries.
Given that a significant fraction of infected persons are still under treatment, the correct measure of recovery or fatality is to estimate these by computing the cumulative number of persons who have recovered as a fraction of the cumulative number of closed cases, which is the number of people who have recovered plus the number of people who have died. One should similarly compute the fraction of cumulative number of cases that have resulted in deaths as a fraction of the number of closed cases. In other words:
Closed case recovery rate (CCRR) = [no. of patients who recovered] ÷ [no. of patients who recovered + no. of patients who died]
Closed case fatality rate (CCFR) = 100 – closed case recovery rate
People whose cases are “open” are still in hospitals or in homes recovering from COVID-19.
With these metrics, based on the number of closed cases as well, India (CCRR 93.12%) will fare better than the US (79.87%), Spain (87.58%), and others. However, it will still have a way to go before it catches up with Germany (95.03%) and China (94.41%).
The fatality rate based on closed cases in India (CCFR 6.88%) again compares favourably to several developed nations, including the US and France. But India’s response to the pandemic is not as great when compared to those of China (CCFR 5.59%), Germany (4.97%) and, surprisingly, Russia (3.24%).
Outliers including France, the US and Italy contribute significantly to the world’s combined closed cases fatality rate, i.e. the world’s CCFR is 13.84%.
Recovery and fatality rates based on closed cases indicate that Kerala (CCRR 99.22%), Tamil Nadu (98.53%) and Delhi (96.63%) lead the way. On the other hand, Madhya Pradesh (91.33%), Maharashtra (88.97%), Gujarat (87.65%) and West Bengal (82.16%) have fallen behind. The all-India average CCRR is 93.13%.
That the CCFR is relatively higher in West Bengal, Gujarat, Maharashtra and Madhya Pradesh is of some concern. It’s also surprising that a few states with higher populations, such as Bihar, Punjab, Karnataka, etc., have reported relatively fewer cases.
In sum, case-based fatality and recovery rates — CFR and CRR — give the complete picture only when the number of active cases is small and few new cases are registered each day. In such situations, the rates of recovery and fatality based on closed cases – CCRR and CCFR – may be used to get a sense of the response of a country’s health system to the COVID-19 pandemic irrespective of the extent to which the pandemic has stabilised or is in its early stages.
And the estimated values of these figures indicate India’s health system has responded well to the pandemic, even if it has some distance to go before it matches up with the responses of other countries. What should worry us is that India is still in the early stages of its COVID-19 outbreak. The same metrics also suggest what we thought to be true based on existing data as well as anecdotal reports: Maharashtra, Gujarat and West Bengal need to do better than they have done thus far.
Bijendra Nath Jain was a professor of computer science at IIT Delhi in 1975-2019, and vice-chancellor of BITS Pilani from 2010 to 2015. He is currently a visiting distinguished professor at IIIT Delhi and an honorary professor at IIT Delhi.