Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data

Abstract

Tracking the progress of an infectious disease is critical during a pandemic. However, the incubation period, diagnosis, and treatment most often cause uncertainties in the reporting of both cases and deaths, leading in turn to unreliable death rates. Moreover, even if the reported counts were accurate, the “crude” estimates of death rates which simply divide country-wise reported deaths by case numbers may still be poor or even non-computable in the presence of small (or zero) counts. We present a novel methodological contribution which describes the problem of analyzing COVID-19 data by two nested Poisson models: (i) an “upper model” for the cases infected by COVID-19 with an offset of population size, and (ii) a “lower” model for deaths of COVID-19 with the cases infected by COVID-19 as an offset, each equipped with their own random effect. This approach generates robustness in both the numerator as well as the denominator of the estimated death rates to the presence of small or zero counts, by “borrowing” information from other countries in the overall dataset, and guarantees positivity of both the numerator and denominator. The estimation will be carried out through non-parametric maximum likelihood which approximates the random effect distribution through a discrete mixture. An added advantage of this approach is that it allows for the detection of latent subpopulations or subgroups of countries sharing similar behavior in terms of their death rates.

A Sequential Cross-Sectional Analysis Producing Robust Weekly COVID-19 Rates for South East Asian Countries

“…We applied the methodology recently proposed in [ 25 ] and adapted it to the setting of weekly counts. Therefore, in a given (for the moment, fixed) calendar week, denotes the observed total number of cases in regions (countries) , denotes the total number of deaths in that week in that region, and , denotes the population size of that region.…”

“…However, as explained in detail by [ 25 ], there are several potential problems with this approach. Firstly, it could be that the observed case rate was 0, making Equation ( 1 ) undefined.…”

“…This may lead to highly volatile values of the . Thirdly, the observed death count may be 0 which would result, if defined, in , which may constitute an implausible estimate of the true death rate (referred to as the “latent death rate” in [ 25 ]). Finally, there is a time lag between infection and death that certainly causes interpretational problems if the death-out-of-cases rates are considered to reflect any sort of causality.…”

“…Finally, there is a time lag between infection and death that certainly causes interpretational problems if the death-out-of-cases rates are considered to reflect any sort of causality. Therefore, one can include a time lag in the computation which has been performed and discussed in detail in [ 25 ]. We will not follow this idea here, but only consider un-lagged rates.…”

Indexing of US Counties with Overdispersed Incidences of COVID-19 Deaths

“…Castro et al [12] warned that the COVID-19 virus had had overwhelming global impacts on health, and consequently, the deaths were not solely due to COVID-19. Almohaimeed et al [13] explained the random effect to produce robust estimates of death rates in COVID-19 data, after including the incubation period, diagnosis, and appropriate treatment for the cases.…”