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

Author

Listed:
  • Amani Almohaimeed

    (Department of Statistics, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
    These authors contributed equally to this work.)

  • Jochen Einbeck

    (Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK
    These authors contributed equally to this work.)

  • Najla Qarmalah

    (Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia)

  • Hanan Alkhidhr

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51482, Saudi Arabia)

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.

Suggested Citation

  • Amani Almohaimeed & Jochen Einbeck & Najla Qarmalah & Hanan Alkhidhr, 2022. "Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data," IJERPH, MDPI, vol. 19(22), pages 1-13, November.
    • Handle: RePEc:gam:jijerp:v:19:y:2022:i:22:p:14960-:d:971739
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    References listed on IDEAS

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    1. Christel Faes & Steven Abrams & Dominique Van Beckhoven & Geert Meyfroidt & Erika Vlieghe & Niel Hens & Belgian Collaborative Group on COVID-19 Hospital Surveillance, 2020. "Time between Symptom Onset, Hospitalisation and Recovery or Death: Statistical Analysis of Belgian COVID-19 Patients," IJERPH, MDPI, vol. 17(20), pages 1-18, October.
    2. Holt, Charles C., 2004. "Forecasting seasonals and trends by exponentially weighted moving averages," International Journal of Forecasting, Elsevier, vol. 20(1), pages 5-10.
    3. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Holt, Charles C., 2004. "Author's retrospective on 'Forecasting seasonals and trends by exponentially weighted moving averages'," International Journal of Forecasting, Elsevier, vol. 20(1), pages 11-13.
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    Cited by:

    1. Ramalingam Shanmugam & Lawrence Fulton & Jose Betancourt & Gerardo J. Pacheco & Keya Sen, 2023. "Indexing of US Counties with Overdispersed Incidences of COVID-19 Deaths," Mathematics, MDPI, vol. 11(14), pages 1-11, July.

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