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

Abstract

In the recent COVID-19 pandemic, a wide range of epidemiological modelling approaches have been used topredict 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 spatialor 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 understandthe variation of these outcome measures to help inform decision making. In this paper, we combine these estimatesfor specific UK nations and regions using random effects meta analyses techniques, utilising the restricted maximumlikelihood (REML) method to estimate the heterogeneity variance parameter, and two approaches to calculate theconfidence interval for the combined estimate: the standard Wald-type intervals; 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 more standard inverse-variance weighting in order avoid potential up-weighting of models providing estimates with lower levels of uncertainty that are not fully accounting for inherent uncertain ties. 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 wider, and therefore more conservative, confidence intervals around the combined estimate compared to the standard inverse-variance weighting approach. Utilising these meta-analysis techniques has allowed for statistically robust combined estimates to be calculated for key COVID-19outcome measures. This in turn allows timely and informed decision making based on all of the available information.

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ORCID for David Woods: orcid.org/0000-0001-7648-429X

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