Reading the Covid-19 numbers right

Talking about doubling-time between given periods without taking into account whether the underlying testing/case identification factors are comparable or not, or comparing case fatality ratios of countries without age-standardisation etc, is fallacious interpretation.

As Covid-19 spreads, spiralling upward in many parts of the world, several indicators are frequently discussed by experts and TV anchors to assess the state and rate of progression, stabilisation, and reversal of the epidemic in a population. These numbers are often used for decision making by policymakers, for crafting the response at different stages of the epidemic.

Doubling Time

This indicates the time taken, in days, for the number of diagnosed cases to double. If this interval is long, it is often interpreted to mean that the infection is spreading slowly. If it is short, it is often interpreted as a rapidly spreading infection. The media frequently discusses questions like when the doubling time rose from three to five days, or why it then fell to four days.

These questions are sometimes unmindful of a fallacy of interpretation, especially with respect to Covid-19 cases in India. Cases are based on defined criteria, which may be purely clinical, or lab test based, or a combination of both. These criteria may have false positives, or false negatives. In the case of Covid-19, which has high infectivity and where our intent is to block its spread, we prefer not to miss cases and, therefore, use highly sensitive methods for case detection, even if it results in some false positives.

To attach value to this measure, the number of tests performed each day, the criteria for selection of individuals for testing, and the type of tests performed over a period of time have to be constant, or at least closely comparable. If we increase daily testing numbers, relax testing criteria, and employ an additional type of test in a shift from the earlier strategy, we will rapidly uncover more cases. The doubling interval will then shrink. Only if the test criteria and test numbers hold constant can we compare doubling rates of infected cases over time. If we use a bigger fishing net today than we did yesterday, we will catch more fish, but that does not indicate that the number of fish in the pond has suddenly increased.

This is currently the problem with the tracking of the progression of Covid-19 in India. The number of tests performed per day has recently shot up substantially, with more centres performing them and an expanded list of indications for testing. Further, apart from the RT-PCR testing for the viral antigen, we are now starting rapid tests for the antibodies the body produces when infected. Obviously, the number of new cases detected will jump up, and result in a shortening of the doubling time in the near term. Only when the number and type of tests performed, as well as the criteria of selection of persons to be tested, remain stable over time in the days to come will the doubling time become a good indicator of whether or not the epidemic is ebbing. Our test numbers are now rising daily. If the doubling time remains static, or actually lengthens, despite a larger number of tests being performed, it will be a very good sign indeed.

There is yet another fallacy. The case counts reported nowadays count both old and new cases, while talking about the pace of the epidemic. It will be more meaningful if we look only at the number of new cases detected during a defined period as a fraction or percentage of the tests performed during that period. The doubling time of this smaller number will be more accurate. It would be even better to estimate the number of new cases detected as a fraction of the number of new tests performed on a daily basis. Ideally, these rates should be measured in different zones of the country rather than being lumped in an aggregate number for the whole country.

A note of caution is warranted. We should not hold the number of tests down just to stretch the doubling time. We do need to test much more to identify infected cases, and isolate them. The more tests, the better; of course, within the feasibility limits of labs, kits, and personnel. Mildly symptomatic cases, or asymptomatic contacts would be uncovered by liberal testing, the purpose of which is not to peg down the doubling time in the short run, but to identify infected persons who need to be isolated to prevent their becoming spreaders. Breaking the chain of transmission is our highest priority.


The case-fatality rate (CFR) is estimated as the percentage of infected persons who have a fatal outcome. A range of numbers has been reported across the world, with comparisons being made not only between countries but also age, gender, and regional groups within each country. We have numbers ranging from less than 1% in Korea to over 12% in Italy. When CFRs vary widely, it is tempting to draw conclusions about health system inefficiencies, or ethnic differences. These do have a role, but the rates must first be ascertained in a comparable manner.

CFR is influenced by the age structure of the population. Since Covid-19 manifests with greater severity in the older age groups, the number of deaths per 100 infected persons will be higher in that age group. If we calculate CFR as a crude rate, a country with a younger population will have a lower CFR than a country with an older population. The Italian CFR appears much higher than that of China because Italy has an older demographic profile than China’s. If we adjust for age differences by comparing age-specific death rates across each decade of age, and calculate age standardised death rates for the whole population of each country, the differences will shrink. India has an even younger population than China. Our cases, too, will have a younger age profile. So, age standardisation of death rates should precede CFR comparisons with other countries.

The rate of testing also matters. When testing is restricted in numbers, usually the more severely ill persons get tested. Death rates among this group are high. If testing is liberal, mild, or even asymptomatic infections get picked up in large numbers. Death rates in these groups are very low. Thus, extensive testing results in a lower CFR than seen with restrictive testing. South Korea, which has done far more extensive testing than other countries, exemplifies this. More liberal clinical criteria for defining cases will also result in a lower CFR than stringent criteria that pick up only the sick cases. It is, therefore, necessary to ascertain the extent of testing done, and the clinical criteria used to define a case in a given country before we use the CFR as a population metric for comparison with other countries.

Summing Up

Doubling time is influenced by both rate of infection spread, and increased case detection by more testing. Mortality rates must be age standardised, and take into account case detection methods for comparison. Covid-19 has closed academic institutions, but may end up teaching us all some statistical principles of epidemiology before it exits.

(The author is President, Public Health Foundation of India. Views are personal)

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