  In the COVID-19 pandemic, a range of epidemiological models have been used to
predict the number of new daily infections, $I$, daily rate of exponential
growth, $r$, and effective reproduction number, $R(t)$. These models differ in
their approaches (e.g. mechanistic or empirical) and/or assumptions about
spatial or age mixing, and some capture uncertainty in scientific understanding
of disease dynamics, and/or have different simplifying assumptions. Combining
estimates from multiple models to better understand the variation of these
outcome measures is important to help inform decision making. We incorporate
estimates of these outcome measures from a number of candidate models for
specific UK nations/regions using meta analysis. Random effects models have
been implemented to accommodate differing modelling approaches and assumptions
between candidate models. Restricted maximum likelihood (REML) is used to
estimate the heterogeneity variance parameter, with two approaches to calculate
the confidence interval for the combined effect: standard Wald-type intervals
and the Knapp and Hartung (KNHA) method. Approaches using REML alone and
REML+KNHA provided similar ranges of variation for $R(t)$ and $r$. However,
differences were observed when combining estimates on $I$, with the REML+KNHA
approach providing more conservative confidence intervals. This is likely due
to the limited number of candidate models contributing estimates for this
outcome measure, coupled with the large variability observed between model
estimates. Utilising these meta-analysis techniques has allowed for
statistically robust combined estimates to be calculated for key COVID-19
outcome measures, allowing an overall assessment of the current response
measures with associated uncertainty. This in turn allows timely and informed
decision making based on all available information.
