Table 1.
Default parameter values used when simulating data, unless otherwise stated.
These values are chosen to reflect estimates from fitting each model to the REACT-1 study. Prevalence and incidence are as a proportion of the population.
Fig 1.
Simulated epidemic trajectories from the SIMPLE, Eales, and Abbott approaches.
Default parameter values as described in Table 1 were used for these simulations. A total of 20 simulations are shown per approach, reflecting the range of possible outcomes. The top row shows the simulated growth rate rt, the middle row shows the simulated prevalence Pt, and the bottom row shows the simulated number of positive swabs .
Fig 2.
Daily SARS-CoV-2 swab positivity in England from the REACT-1 survey (upper) and corresponding daily sample sizes (lower).
Daily 95% confidence intervals (vertical lines) for prevalence were calculated using the Agresti-Coull method [14] in the binconf function of the Hmisc package in R [39].
Fig 3.
Coverage and average width of 95% credible intervals for prevalence Pt (%) from fitting all three observation models (purple: basic, blue: extra-binomial, green: weighted) to simulated data from each model (column A: basic, column B: extra-binomial, column C: weighted).
Results from individual simulations are shown as semi-transparent crosses, with averages over 10 simulations shown as points connected by solid lines (for assumed ) and dashed lines (for assumed
). A range of assumed daily sample sizes nt are considered (x-axis). The horizontal black dashed line indicates the target coverage of 0.95. The y-axis for coverage is truncated to (0.5,1.0), although the coverage in some cases falls outside this range: reaching a minimum average of 0.33 for the basic model fit to the extra-binomial simulations and a minimum average of 0 for the basic and extra-binomial models fit to the weighted simulations (all when
).
Fig 4.
Coverage and average width of 95% credible intervals for the growth rate and prevalence, and coverage and average width of 95% predictive credible intervals for swab positivity.
Each approach (SIMPLE, Eales, and Abbott) is fit to 10 simulated datasets from each model. The horizontal black dashed line indicates the target coverage of 0.95. Boxes present the interquartile range of the results with the median shown as a horizontal line. Whiskers extend to the most extreme data point within 1.5 times the interquartile range from the box. Outliers are shown as points.
Fig 5.
Estimates of the growth rate rt, prevalence Pt, and predictive swab positivity , for SARS-CoV-2 in England between 1 May 2020 and 31 March 2022 using data from the REACT-1 study.
All three approaches are fit assuming a beta-binomial observation distribution. Solid coloured lines show the posterior means while shading and dashed lines show 95% credible intervals (of the posterior distribution for rt and Pt, and of the posterior predictive distribution for ). Independent daily confidence intervals from the Agresti-Coull method [14] for Pt are shown in vertical grey lines. The data, daily observed swab positivity
, are shown in black points. Grey shading indicates the periods in which sampling was conducted. The predictive distribution for swab positivity depends on the number of swabs taken each day nt, which tends to be lower in the early and late periods of each sampling round, hence the wider credible intervals at the boundaries of each study round.
Table 2.
Results from fitting the three approaches to data from the REACT-1 prevalence study.
Runtimes were measured once for each dataset considered and can vary considerably. Convergence diagnostics of maximum and minimum ESS are reported, although these are not directly comparable between the SIMPLE and Eales/Abbott approaches. Measures of fit are reported as coverage of the posterior predictive distribution and average width of 95% credible intervals on Pt (in terms of percentage points). Parameter estimates are shown as posterior means with 95% credible intervals in parentheses. Note that
depends on the knot spacing, which varies slightly between study rounds, so these estimates are not directly comparable even within the same model.
Fig 6.
Estimates of the instantaneous reproduction number Rt for SARS-CoV-2 in England between 1 May 2020 and 31 March 2022 using data from the REACT-1 study.
All approaches are fit assuming a beta-binomial observation distribution. Solid coloured lines show central estimates while shading and dashed lines show 95% credible intervals. Grey shading indicates the periods in which sampling was conducted. The second panel shows the same estimates for a shorter period (9 September 2021 to 31 March 2022), emphasising the differences between the three approaches. The third panel shows the same estimates, with estimates from the Eales approach shifted by days to partially account for bias induced by the trailing-window smoothing assumption.