The Prime Minister was addressing a COVID-19 review meeting on August 10, and India had been recording 50k+ cases each day for the past 10 days. Against the backdrop of these distressing numbers, the PM is reported to have told the Chief Ministers that an increasing recovery rate indicates that India is headed in the right direction. Over the last months, “recovery rate” has been increasingly touted as the main measure of India’s progress against COVID-19. Achievement of each recovery rate milestone has been heralded with celebratory tweets by Union ministers, the most recent one being the 70% milestone.
#COVID19Update
— Dr Harsh Vardhan (@drharshvardhan) August 19, 2020
India scales another peak !
Total recoveries cross 2 million
Recovery Rate scales a peak too
Recovery Rate races past 73%
60,091 recover in last 24 hrs
Total caseload viz active cases reduced & currently comprises less than 1/4 of total positive cases pic.twitter.com/xrrDLUaEk5
Indeed, the way the government calculates this measure, it keeps on incessantly improving. It was 60% a few weeks back when India’s total COVID-19 cases were around 10 lakh, and stands at >70% when the cases have topped 25 lakh. It surely would have led many to wonder - ‘what progress are we achieving?’. In other words, what is this measure that constantly improves when the pandemic situation worsens?
In this article, we will unpack this measure and aided by some high-school level maths (nothing more than addition and division, I promise!), we show how this measure is unrelated to the COVID-19 burden on society and is a spurious measure unworthy of any consideration whatsoever.
To keep the analysis simple, let us switch from the beastly COVID-19 to a simpler hypothetical pandemic, COVID-LITE. Unlike its senior cousin, COVID-LITE does not kill anybody, and each COVID-LITE patient recovers the day after he/she tests positive. COVID-LITE, true to its name, has a gentle infection pattern, infecting 10 new individuals each day. Let us consider how the recovery rate changes as COVID-LITE progresses through society.
Fig 1. COVID-LITE Infection Status at Day 3 and Day 5
Fig 1 illustrates a visual analysis for COVID-LITE after 3 and 5 days of onset. Each block indicates the set of 10 patients infected each day. On the third day, the first and second day patients have recovered, so are indicated in green. The active cases on the third day are the Day 3 infections, i.e., 10 cases. The situation for Day 5 is also shown, where the number of active cases remains 10, but the total cases have obviously increased.
The Central government calculates the recovery rate as the number of recovered cases expressed as a fraction of total cases. Thus, COVID-LITE recovery rate at Day 3 would be (20/30) = 66.67%. The same after Day 5 would be (40/50) = 80%. This is when the fallacy of the recovery rate starts revealing itself. The situation at Day 5, all of us would agree, is worse than the situation at Day 3. More people have suffered of COVID-LITE, and the impact of the disease on society has only increased. Yet, the recovery rate is improving!
The key to understanding this starts with the observation that the number of active cases is always 10, whatever be the day. Thus, the number of past sufferers (i.e., recovered cases) of COVID-LITE increasingly outnumber active cases as COVID-LITE spreads. This causes recovery rate to constantly improve, as illustrated in Figure 2. In fact, if COVID-LITE is still going strong at Day 1000 with the government failing to control it, 10k people would have suffered from it and the disease burden would have vastly increased, but would provide the government an opportunity to boast of an impressive 99.9% recovery rate.
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Fig 2. COVID-LITE Recovery Rate Trends
The fiercer and real COVID-19 is not as well behaved and predictable as our hypothetical COVID-LITE. COVID-19 sufferers may take anywhere between 5 and 20 days to recover, and some hapless people would succumb to it. Yet, the spirit and meaning of the COVID-LITE recovery rate holds good for COVID-19. The government’s recovery rate, as indicated above, is computed as [recovered cases/total cases], expressed as percentage. Given the vast majority of COVID-19 cases eventually recover, each person who has once tested positive for COVID-19 will continue to be counted in the numerator and denominator of the fraction long after he/she has ceased being a COVID-19 patient. Thus, with time, the numerator and denominator both will be increasingly dominated by recovered cases. Consequently, the government’s recovery rate will continue to improve, even if its efforts in mitigating COVID-19 have met with little success.
To put it in another way, the recovery rate is more indicative of how long COVID-19 has been around, and is in no way symptomatic of success of the fight against COVID-19.
If the recovery rate is meaningless and spurious, what is a meaningful measure for COVID-19 recovery? If we simply replace “total cases” in the denominator of the recovery rate formula with “completed cases” (i.e., recovered cases + deaths), we get what may be called mathematically as the “recovery likelihood”. This measure indicates, based on historical cases, the chances of successful recovery of a patient infected with COVID-19. This recovery likelihood in India is >95% as of today. Unlike recovery rate, this conveys some meaningful information to people, and serves as a crude estimate of survival if they were ever to catch COVID-19, but alas, it does not constantly improve with time.
Is the usage of a fallacious and misleading measure that always improves with time a case of deliberate deceit, or just a lack of due diligence? We can never know for sure, but there are cues which indicate that such fallacious measures are being used more and more than being phased out. Just days ago, there has been talk about decline in “percentage of active cases” as yet another measure of success. However, as this ‘decline’ is based on the recovered cases,it naturally carries with it all the fallacies of the recovery rate measure, and is no less misleading."
It is natural to wonder: are some people thinking two deceitful measures of progress are better than one! If COVID-19 were a person, I bet it won’t stop laughing at seeing measures of its longevity being used as a measure of progress by its opponents.
This brings us to the obvious question; what should we be measuring to assess progress against the pandemic? Among the natural answers would be to measure the COVID-19 burden so far, which could be the total number of cases, and total deaths. Further, the rate of change of current COVID-19 burden, measured as the number of net new cases (i.e., new cases minus recoveries) is indicative of whether the COVID-19 burden is intensifying or softening. The total number of active cases provides complementary information on the current strain on the national health system. The collection of these measures and other relevant ones serve well as a barometer of COVID-19 burden. It is no coincidence that these are the very measures that are covered within World-o-meter which many people have started to rely on, to monitor COVID-19 trends.
We would undoubtedly be better off without crafting new measures that are intended towards showing success where there is none.
Dr Deepak P is an Assistant Professor of Computer Science at Queen’s University Belfast, UK.