Comparing Deaths from COVID-19 among Uttarakhand Police in Two Periods

The Indian Express put up a write-up on incidences of COVID-19 and fatality among police personnel of Uttarakhand. It indicates that the police personnel of the state had started vaccination in January 2021 and more than 93% among them have been vaccinated. This is an impressive figure because for a disease with reproduction number or R₀ "R naught" around three (R₀=3), the proportions needed for herd immunity (including natural infection) should be around 67%.

Given this backdrop, it might be a matter of concern that in April and May of 2021 the number of police personnel inflicted by the disease in Uttarakhand were 2,382. However, it is comforting that from among these 2,204 have already recovered while five (5) of them, bless their souls, are no more with us. The proportion of death from those inflicted by the disease is 0.21% (which could increase if there are additional deaths from the remaining 173 who have not recovered). The write-up further points out that the severity of the disease and and the number of deaths were lower than previously observed.

For instance, the proportion of deaths from the start of the pandemic till March 2021 was 0.40% (that is, 08 deaths from among 1,982 inflicted by the disease). Even if one ignores the fact that we are comparing more than 13 months of data with two months and that there are 173 cases for which we still do not know the final outcome but consider them to have recovered, a proper comparison would be to estimate absolute risk reduction (ARR) and relative risk reduction (RRR) and their statistical significance for deaths among those inflicted by the disease in the two periods. 

The ARR and RRR estimates and their 95% confidence intervals are:

ARR%=0.19% (95% CI: -0.14%, 0.53%) and

RRR%=48.1% (95% CI: -58.7%, 83.0%). 

This indicates that when one compares the second period with the first, ARR in per cent is 0.19% and RRR in per cent is 48.1%, but more importantly both the estimates are not statistically significantly different from zero. This suggests that one should be cautious with the comparative statements between the two periods by using absolute numbers.

ARR is d1-d2 

95% Confidence Interval (CI) for ARR is ARR±1.96*Standard Error (SE) of ARR

SE of ARR is {[(d1*r1)/N1]+ [(d2*r2)/N2]}^(1/2)

RRR=1-RR; RR is d2/d1

95% CI for RRR is 1-95% CI of RR

95% CI of RR is {exp^[Ln(RR)±1.96 SE of RR]}; SE of RR is {[(r1/d1)/N1]+ [(r2/d2)/N2]}^(1/2)

In the above calculations, d  and r denote share of death and share of recovery from among those inflicted by the disease with subscripts 1 and 2 denoting periods 1 and 2, respectively, such that in each period their sums add up to unity, d1+r1=d2+r2=1. N1 and N2 denote number of people inflicted by the disease in periods 1 and 2 respectively.

The write-up also had mentioned that from among the family members of the police personnel 751 were inflicted by the disease and from among them there were 64 deaths. This is indeed an important sacrifice by their family members. The adverse effects, in terms of deaths, is much higher then that on the actual force and this should be an important concern.

One is also curious to know what would be the incidences and deaths by family members across the two time periods. Has that number increased in the second period then a question that comes to mind is the possibility of adverse impact having increased after a public health intervention among police personnel. A period wise break of the data will help us examine that.