Optimising Renewal Models for Real-Time Epidemic Prediction and Estimation

KV Parag; CA Donnelly

When k is too small, we infer rapidly and randomly fluctuatingR τ (s) values, 203 which sometimes can deceptively underlie reasonably looking incidence predic-204 tions. Consequently, optimal k-selection is integral for trustworthy inference 205 6 . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/835181 doi: bioRxiv preprint The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/835181 doi: bioRxiv preprint Figure 3 : APE prediction accuracy. We compare the APE metric (solid blue, left y axis) to the percentage of true incidence values, I s+1 that fall outside the 95% prediction intervals of x | I s s−k+1 (dotted red, right y axis) over the window search space k. The dashed line is k * and panels correspond to those of Fig. 2. and prediction. Observe that small k, which implies a more complex renewal 206 model (i.e. there are more parameters to be inferred), does not generally result 207 in better causally predictive one-step-ahead incidence predictions. Had we in-208 stead naively picked the k that best fits the existing epi-curve, then the smallest 209 k would always be favoured (overfitting) [9]. 210 We emphasize and validate the predictive performance of APE in Fig. 3 . The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/835181 doi: bioRxiv preprint tify our results over 10 3 simulated epi-curves with t = 150 days. We focus on 228 step-changes in R s and examine how the successively optimal window length, 229 k * (s), computed with data up to time s, responds. If k * (s) is sensitive to these 230 changes then it is likely a dependable means of diagnosing control efficacy. Note 231 that until now, the optimal window length was k * = k * (t). 232 We consider four possible models: (a) an epidemic that is increasing and [19] and apply the APE metric over 2 ≤ k ≤ t /2 with t as the last available 266 incidence time point. We compare the one-step-ahead I s+1 prediction fidelity 267 and the R τ (s) estimation accuracy obtained from the renewal model under the 268 APE-selected k * to that from the model used in [8] , which recommended weekly 269 windows (i.e. k = 7) after visually examining several window lengths. Our main 270 results are given in Fig. 6 and Fig. 7 . We benchmarked our estimates against The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/835181 doi: bioRxiv preprint Figure 4 : APE sensitivity to real-time transmission changes. We simulate 10 3 independent incidence curves under renewal models with reproduction numbers indicating (a) increasing, (b) controlled, (c) recovering and (d) cumulatively controlled epidemics. In each panel the top graphs give the true (green) and predicted (cyan) incidence ranges curves, the middle ones provide the estimate of R s under the final k * (t) and the bottom graphs illustrate how the successive k * (s) choices of the APE metric vary across time. We find that k * (s) responds rapidly to significant changes in the shape of the incidence curves. This makes it sensitive to important fluctuations in R s , especially those that force R s < 1. The APE metric is suitable for real-time applications and particularly useful for diagnosing the efficacy of control measur