Plenty of organised data on daily counts of COVID-19 cases are available. Consequently, many statisticians, epidemiologists, data scientists are extrapolating existing data to predict the progression of the disease outbreak, and forecasting the trajectory of the disease over time. No wonder that the numbers are often contradictory in nature. And, no surprise that many of the forecasts have already been proved wrong.
Reliable ‘expertise’ may be an alien concept for a new and unknown disease. Consequently, although retrospective analysis is alright, the dynamics of any perspective analysis for uncertain and complex events like COVID-19 might be erroneous. Let me explain why.
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Various standard epidemiological models, and regression and time series models are generally attempted for modeling cumulative number of cases and deaths data for COVID-19. Can the models depict the complex and unknown trajectory of the disease in the long run? If so, which one? Certainly, I know the common aphorism “all models are wrong but some models are useful”. But, any such model relies on strong assumptions about aspects of the disease we haven’t thoroughly studied yet. Thus, some assumptions are bound to be violated, and some remain unverified. This is a new disease, at least three varieties have been detected so far, and we are learning new features of the virus everyday. With several blind spots, it is utterly difficult to choose a model.
The key parameters
Once a model is chosen, a few ‘parameters’ dictate its performance. These key numbers are ‘infections rate’, ‘incubation rate’, ‘recovery rate’, ‘birth’ and ‘death’ rates, and also the rate at which recovered individuals return to the susceptible state due to loss of immunity, if at all. Values of most of these parameters are unknown — they are to be estimated from the data of cumulative cases and deaths over time. However, often data quality is questionable — speculations of under-reporting of cases from different parts of the world persist. Sensitivity and specificity of the testing procedures are also known to be high. Again, some models need to assume how people will adhere to government instructions like lockdown.
Also, COVID-19 has 2-14 days of incubation period. And patients may infect others during the incubation period as well. What is more, there are a lot of asymptomatic patients who go on infecting others who, in turn, might not be asymptomatic. This, along with the fact that there is scarcity of test kits in most parts of the world, surely misses many asymptomatic patients in the count of cases. Iceland, for example, managed to test almost 50,000 people of its 3,60,000 population, and found that 0.6% of the population were “silent carriers” of the disease with no symptoms or only a mild cough and runny nose!
According to a survey conducted by the Public Health Authority of Sweden, about 2.5% of Stockholmers had an ongoing COVID-19 infection at the end of March, which was 30 times the number tested positive by then. It became 80 times the number of tested positive cases within three weeks — about 20% Stockholmers were already immune to COVID-19 by that time. Thus, it is clear that the proportion of asymptomatic cases increased at an accelerated rate via a convex path, at least in the case of Sweden. However, Sweden didn’t impose any lockdown measure. So, the volume and pattern of asymptomatic patients are likely to differ in countries where lockdown was imposed. But, without a good estimate of the asymptomatic patients — possibly through survey of antibody tests — it’s impossible to have a reliable estimate of different unknown parameters of a model.
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Testing asymptomatic patients
Again, when somebody is reporting a 3.3% fatality rate for a region, it is based on numbers of deaths and cases. However, there is a huge ‘selection bias’ in the data due to limited testing capacity — only those more likely to be positive are likely to be tested. If the actual number of undetected asymptomatic patients is 10x the observed cases, the actual fatality rate becomes just 0.3%. Similarly, the predicted trajectory might change significantly with the inclusion of the huge number of “asymptomatic cases” into calculations.
I understand that various policymakers would still need the help of such mathematical models fitted with available case data — to navigate the pandemic as much as possible for taking critical decisions dynamically. However, such contradicting and erroneous predictions from different experts would give rise to either horror or a false sense of relief in common people, both situations being very much undesirable.
Atanu Biswas is a Professor of Statistics at the Indian Statistical Institute, Kolkata
