On April 10, Amit Malviya, who heads the Bharatiya Janata Party’s publicity wing, wrote on Twitter that a study by the Indian Council of Medical Research had concluded that the number of Covid-19 cases in India would have crossed 8.20 lakh had there not been a lockdown.

Malviya attached an ABP News video clip as source of the information.

R-naught factor

According to the ABP News anchor, this information had been revealed to foreign journalists by Vikas Swarup, an additional secretary at the external affairs ministry. The reporter of the story went on to offer more details: this estimate, he explained to viewers, was the result of “research” by the ICMR.

The research, he continued, was based on the assumption that the virus’s basic reproductive number or R-naught was 2.5. This means that one person could infect 2.5 others on average. Thus, in the absence of social distancing measures or a lockdown, one coronavirus positive person could infect 406 others in 30 days, he added.

Three days ago, in the daily press briefing on April 7, joint health secretary Lav Agarwal had also cited the 406 figure – but not the 8.20 lakh number – attributing it to an unidentified study. His explanation, centred around virus’s R-naught being 2.5, was identical to the ABP news anchor’s.

Simultaneously, Agarwal also spoke of a study by the ICMR which estimated the R-naught of coronavirus to be between 1.5 and 4. This lead to confusion among journalists with many attributing the 406 number to the ICMR, forcing the ministry to later clarify that it was not the council that had arrived upon the 406 number.

On April 10, presumably as a consequence of Malviya tweet’s, reporters quizzed Agarwal about the 8.20 lakh figure. The joint secretary rejected the existence of any such report by the ICMR.

A flip-flop

But in a somersault of sorts, Agarwal, on April 11, validated the number. “If we hadn’t taken any action, the cumulative growth rate may have been 41% growth,” he said. “By April 15, we would have reported 8.2 lakh cases.”

He added: “Prior to the lockdown, we witnessed 28.9% growth rate and at that rate we would have reached 1.5 lakh cases by April 15.”

Agarwal even furnished a chart bearing these projections.

However, he clarified that this was not a projection by the ICMR. The health ministry, he said, had done its own “statistical growth rate-based analysis”.

joint health secretary Lav Agarwal addresses a press conference. Credit: PIB via Twitter

Confusion galore

Agarwal’s statements surprised many experts. Apart from the chart that he showed at the press conference, he revealed few other details about the projection model.

On what basis were the two growth rates computed? The chart itself has few details. It states that the 28.9% growth rate, estimated to be the pre-lockdown rate of the virus’s spread, was “projected with the peak growth rate before lockdown”. But there is no information on the rationale behind the 41% growth rate that yielded the contentious 8.20 lakh figure.

‘Extrapolating data’

Scroll.in spoke to several experts who expressed surprise over the opaque nature of the projections, which the joint secretary had initially refuted but subsequently validated.

Karthik Shashidhar, a quantitative analyst and a Mint columnist who lives in Bengaluru, said they looked like a “retrofit, trying to justify the policies so far”. “These numbers seem completely pulled out of thin air,” he said. “My guess is that they just took a handful of data points, fit a curve on it and then extrapolated it to get these graphs.”

Gautam Menon, a professor of physics and biology at Ashoka University in Sonepat, also cautioned against taking these projections seriously. “They have just assumed an exponential growth and plotted it for two different values of the growth rate,” said Menon, whose interests include modelling infectious diseases. “It is not a serious calculation of anything.”

Sitabhra Sinha, a scientist at the Institute of Mathematical Sciences in Chennai and the co-author of a study that estimates the R-naught for Covid-19 in India at 1.7, said: “To be very frank, I don’t know how these growth rates have been obtained.”

He added: “In epidemiology, we use either R0 [the basic reproduction number] or beta [the infection transmission rate] when talking about how fast the disease is growing. The figure doesn’t use either of these parameters, but something called CGR...which is normally used in actuarial calculations used in the insurance industry, suggesting that the projections have been done by people trained in such an area rather than epidemiology as such. I don’t know what to think of this.”

Medical staff wearing protective gear wheel a patient to a ward at a government-run hospital in Mumbai on Saturday. Credit: Prashant Waydande/Reuters

Data inconsistency

But surely, there has to be some basis to the ministry’s calculations?

A 28.9% growth rate that the model assumed to be the pre-lockdown rate of spread in India – the “peak growth rate before lockdown”, according to the note on the graphic released by the ministry – would mean that the number of infections were doubling every three days.

That did indeed happen from March 20 to March 25. The lockdown began on March 25.

However, observers pointed out two other developments took place on March 20: the ICMR expanded India’s testing criteria to include hospitalised patients with severe acute respiratory infections.

Simultaneously, the health ministry aslo issued guidelines to hospitals stating that “all pneumonia patients must also be notified to NCDC [National Centre for Disease Control] or IDSP [Integrated Disease Surveillance Programme] so that they can be tested for Covid-19”.

Before that, the country was only testing symptomatic patients with international travel history and those who had come in contact with laboratory-confirmed Covid-19 cases.

This meant a significantly higher number of people were tested post-March 20. The testing numbers, experts said, were likely to have gone up gradually since – and, by extension, the number of positive cases.

“What the ministry seems to have done is literally counted the growth of test positives,” said a senior scientist with a government-affiliated institution, requesting anonymity. “But test positives are a function of rate of testing.”

Menon agreed. “The criteria for recording cases initially was so restrictive that it [the ministry] is bound to have missed lots of them,” he said.

What the scientists meant: it makes little sense to be comparing absolute number of test positives without accounting for the change in sample size.

Here is an example to understand this better:

On day 1, say 100 samples were tested and four were found positive.

On day 2, another 100 samples were tested. Out of them, eight turned out positive.

The growth rate in this case is 100%.

But if on day 3, if 200 samples are tested and 10 turn out positive, the growth rate cannot simply be considered 100%. It has to be normalised for the increase in sample size.

“It is the number of increased cases as a proportion of those tested that matters,” explained Joyojeet Pal, associate professor at the University of Michigan’s School of Information.

Scroll.in sent queries to the health ministry, seeking a clarification on whether the likely difference in sample sizes was taken into account. The ministry is yet to respond. The article will be updated if it responds.

Worst case scenario?

But what about the other growth rate that yielded the 8.20 lakh number that the BJP’s Malviya brandied: 41% in the case of no containment measures? A 41% growth rate would translate into cases doubling every two days – an ominous situation.

It is unclear where that has come from. The ministry did not clarify despite repeated requests.

Possibly from other countries where cases exploded because they reacted late? Data show that the peak growth in the UK and Italy was in that range before they clamped down.

A doctor wearing a protective suit takes a swab from a man who is under home quarantine, to test for coronavirus, in Ahmedabad on April 7. Credit: Amit Dave/Reuters

‘Two graphs without any context or explanation’

Bhramar Mukherjee, a professor of biostatistics and epidemiology at the school of public health at Michigan University, said it was “impossible to know where these numbers came from unless the assumptions are stated clearly”.

“Data and code transparency are critical to these discussions and should be made public,” said Mukherjee.

Besides, the results of any epidemiological models would be contingent on when data was last updated, said Mukherjee. “Every day as data come in, the projections change for the future,” she said. “So, it is important to say where did you stop to project the future and what reproduction number and transmission probabilities you used in this calculation.”

Yet again, it is not clear data up to what date was considered by the ministry. The health ministry’s analysis, Menon said, “just plots two graphs without any context or explanation.”

“You can think of it as comparing various extreme possibilities to the data, which is guaranteed not to be so extreme in real life,” he said.

However, experts noted that the ministry’s analysis, no matter how opaque, need not necessarily be a comment on the efficacy the lockdown itself. “As the famous statistician George Box had said, all models are wrong, but some are useful,” said Mukherjee. “Regardless of the exact numbers, it is true that with the interventions, there has been a profound drop in the expected number of cases in every country.”