The impact of the second Covid wave in India has been investigated at many levels. After the initial reports — mostly images of packed crematoria and burials — many assessments have emerged about the undercounting of deaths. Analyses of death registrations show that “excess deaths” till May 2021 in some states compared to 2018 and 2019 were 30-40 times (x) the reported Covid deaths. A recent study estimated this undercount of excess deaths to be about 10x for the entire pandemic.
We have developed a patient-flow model to understand the drivers of fatality and to determine whether an undercount of 30x is possible. The model’s calibration explains that only under certain circumstances — when healthcare facilities are overwhelmed — such an undercount is possible. It is not a country-wide and pandemic-wide phenomenon.
There has been much discussion on “flattening the curve” at the onset of the pandemic in 2020. The curve to be “flattened” is the curve of rising infections such that hospitalisations of the infected remain within the capacity of the healthcare system. Once this capacity is breached, the infection turns fatal for individuals who would ordinarily be saved. The number of deaths can rise rapidly in such an overwhelmed health system.
Many countries faced this challenge at different timepoints during the pandemic indicating the difficulties in controlling the infection. In India, the second wave lasted for several weeks in April and May of 2021. As infections rose at an exponential rate driven by the then-new Delta variant, the number of individuals needing oxygen and ICU support increased. In situations wherein the oxygen-supported and ICU beds reached capacity occupancy, many additional patients needing this support likely succumbed to the disease.
The schematic illustrates this impact of exceeding healthcare capacity (the horizontal blue line). Each day, certain number of patients need oxygen and ICU beds and they stay in the hospital for, say, six days. Every day, a number of beds become available due to patient discharge or death. Once capacity is reached, there are new patients daily that cannot be admitted (shown in red) and contribute to overall deaths because of lack of care. This overflow number leads to the excessive death toll and high death undercounts (if the counting cannot keep up with out-of-hospital deaths).
The model estimates the daily numbers that need oxygen and ICU beds and the overflow number — ones that cannot avail these facilities. The following parameters are used — one, percentage of daily new cases that need such beds: This is estimated at 12 per cent in a pre-surge situation for cases caused by the delta variant. During the surge, since testing is constrained and a higher portion of positive cases are symptomatic, the percentage of cases needing assistance is higher. In our analysis, 15 per cent is taken as the baseline with 12 per cent and 18 per cent forming the bounds. Two, the number of hospital days on such care: This is taken as 14 days. Three, the total number of such beds (capacity data): This data is sourced district-wise from the latest (June 27–July 5th) district or municipal dashboards.
In addition to deaths due to overflow, there are deaths of patients succumbing to the disease even with the required care. The Infection Fatality Rate (IFR) of the disease is used for this calculation. The second serosurvey estimated a national IFR between 0.084–0.121 per cent (including the confidence intervals). We use an IFR of 0.1 per cent for all districts to estimate these deaths from the total estimated infections in the district (after subtracting the overflow cases calculated above). Details of these calculations are explained at the end of this article.
So, is 30x undercount in Covid deaths possible?
The charts below show the analysis for three example districts: Gwalior, Indore, and SPS Nellore. These districts are from states that had the highest estimated excess deaths till May 2021. (Total reported Covid deaths in the three districts as of May 31, were 583, 1,341 and 818 respectively.) The picture is the same in all three districts. As the second wave unfolded with increasing daily cases (the blue line in the top plot on the left-hand scale), the daily death undercount (as a seven-day average) relative to the reported numbers (red line on the right-hand scale) spikes up — going close to 30x — for a short period during March-May 2021 and subsides as the wave recedes.
The charts show the impact of breaching healthcare capacity on the death undercount. For Indore, especially, the impact of the change in hospitalisation rate from 12 per cent (lower bound of the red shaded curve) to 15 per cent (solid red line) and higher leads to overflow and a spike in deaths and undercount.
The cumulative death undercount (black line in the bottom plot on the right-hand scale) is around 5-9x depending upon the district as it averages the actual and reported deaths over a longer time period. An important consequence of overflow is that the calculated IFR (purple line on the left-hand scale) loses its property of being only disease-specific at 0.1 per cent and gets driven by healthcare capacity constraints to 0.15-0.37 per cent depending on the district.
Note that the calculated IFR and undercount need not be correlated because undercounts depend upon the actual reported Covid deaths and the calculated IFR reflects the deaths due to overwhelmed capacity. As an example, Indore has a similar undercount but a lower IFR as compared to SPS Nellore. Presumably, Nellore infrastructure was overwhelmed to a larger extent as compared to Indore, but both districts were similar in the manner the deaths were counted.
In addition to sensitivity to model parameters, the accuracy of output from this model depends upon the granularity of data used. The first aspect is geographic granularity. A state-level model will add up the healthcare capacity of districts that cope with hospitalisations with those that are overwhelmed. It’s likely that the total capacity that comes out of this calculation is sufficient to manage the combined patient load. In this situation, the model will erroneously under-predict the overflow whereas overwhelmed districts will report overflow and increased deaths.
Similarly, a granular time-scale is important. Every day, the overflow is determined by the total number of patients needing breathing assistance and the bed capacity of such equipment. Ideally, daily data, wherever available, should be used. Using averages (or other fixed numbers) across the entire wave causes inaccuracies because of differences in the average value and the daily value. Adequate oxygen flow is another confounding factor. Any limitation in oxygen supplies will reduce the effective bed capacity. We believe this dependence on multiple factors is precisely the reason for the wide range of death and undercount estimates.
Despite its dependence on several parameters, the patient-overflow approach to assessing Covid fatalities highlights the criticality of limiting overflow in the healthcare system and can provide insights into important factors to control. An overwhelmed system leads to a steep ramp-up in deaths. This model shows that high death undercounts, however, are limited to short time spans when the capacity is overwhelmed. Therefore, an underreporting bias of 30x over the entire pandemic for the full country is unlikely. For the eight districts we analysed (three shown here) using the described parameters, it is roughly between 3-9x.
Percent of cases that need hospitalization: Government updates at the Press Information Bureau (PIB) briefings prior to the second wave indicated that about 6% of active cases needed some breathing assistance. Estimates from UK suggest that the delta variant is twice as likely to cause hospitalizations; therefore, we estimate 12 percent of cases caused by the delta variant need such assistance in a normal (pre-wave) situation. During a wave this number is higher and the three scenarios used for our analysis are mentioned above.
Total infections (District-wise): The serosurveys tracked the infection prevalence in the different districts. We have used the population estimate from the Census data and the prevalence from the second survey to estimate the total infections at the end of the second serosurvey (Sep 2020) and calculate the infections-to-cases ratio for each analyzed district. Nationally, this ratio stayed stable around 26 between the second serosurvey in September and the third serosurvey in December 2020 and we assume that this ratio stays the same for each district till May end. (The results of the recent fourth national serosurvey support this assumption.) This ratio is used to calculate total infections from total detected cases. In some districts, this ratio does lead to total infections by May-end becoming greater than the total population. Only districts that had infections not exceeding 115% of the population by May-end were considered for analysis.
This column first appeared in the print edition on July 24, 2021 under the title ‘Covid death count, a reality check’. Gore’s focus area is pharmaceuticals. He has worked at McKinsey and Novo Nordisk. Acharya, former Deputy Governor of RBI, is the C.V. Starr Professor of Economics in the Department of Finance at New York University Stern School of Business.