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Statistical methods used to combine the effective reproduction number, R ( t ) , and other related measures of COVID-19 in the UK.

Maishman T, Schaap S, Silk DS, Nevitt SJ, Woods DC, Bowman VE

Statistical methods in medical research, 2022

Abstract

In the recent COVID-19 pandemic, a wide range of epidemiological modelling approaches were used to predict the effective reproduction number, R(t), and other COVID-19-related measures such as the daily rate of exponential growth, r(t). These candidate models use different modelling approaches or differing assumptions about spatial or age-mixing, and some capture genuine uncertainty in scientific understanding of disease dynamics. Combining estimates using appropriate statistical methodology from multiple candidate models is important to better understand the variation of these outcome measures to help inform decision-making. In this paper, we combine estimates for specific UK nations/regions using random-effects meta-analyses techniques, utilising the restricted maximum-likelihood (REML) method to estimate the heterogeneity variance parameter, and two approaches to calculate the confidence interval for the combined estimate: the standard Wald-type and the Knapp and Hartung (KNHA) method. As estimates in this setting are derived using model predictions, each with varying degrees of uncertainty, equal-weighting is favoured over the standard inverse-variance weighting to avoid potential up-weighting of models providing estimates with lower levels of uncertainty that are not fully accounting for inherent uncertainties. Both equally-weighted models using REML alone and REML+KNHA approaches were found to provide similar variation for R(t) and r(t), with both approaches providing…

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