McGough 2020 - Delay Dynamics, Moving Windows and Limitations

Summary

Nowcast quality depends on (i) how much is reported at delay 0 and (ii) whether the delay distribution drifts. NobBS is robust to drift because the random walk anchors estimates to recent cases, but it still assumes one $\beta$ per window, and short windows trade better delay tracking for a volatile random-walk variance.

Overview

Sections covered: “Reporting delays impact nowcast performance”, “NobBS improves nowcasting with varying reporting delays”, moving-window experiments, Simulated ILI data, and the Discussion.

Main Content

Delay-0 share. Only ~4% of dengue cases were processed in the week of onset, versus >80% for ILI. Point accuracy was higher for ILI, since a large fraction already observed leaves less to predict. Sudden jumps in initial reports from low values (e.g. +16 and +17 cases on 3 Aug 1998 and 16 Aug 2010 after weeks averaging changes of 2.6 and 1.8) caused overestimates corrected the next week.

Simulated time-varying delay (ILI)

Keep the true final ILI counts but draw $\mathrm{Pr}(d=0)\sim U(0.2,0.9)$ in weeks above the mean (14,000 cases) and $U(0,0.65)$ in weeks at or below it (“faster reporting during outbreaks”); remaining cases spread over delays 1-52 with NB(0.9, 0.4). Results (S2/S3 Tables, text): NobBS average score 0.06 vs HH $\approx 0$, rRMSE 0.302 vs 0.621. Swapping the uniforms would simulate slower reporting in busy weeks (backfill).

Moving-window trade-off (empirical finding)

A window of $W$ weeks fits $\beta$ and ${\tau }_{\alpha }$ on recent data only. Dengue with $W=5$ gave rRMSE 7.381 (steep overestimates in 2007-08, 2010); windows of 12, 27 and 104 weeks gave rRMSE 0.6-0.655 and average score 0.35-0.37. Short windows track $\beta$ better (S8A) but make ${\tau }_{\alpha }$ highly variable (S8B), which hurts under extreme time-varying delays.

Why NobBS beats HH under drift. HH can model a time-varying delay only through pre-specified change points, which are unknown in real time; its smooth-epidemic option is bundled with that change-point model. NobBS instead conditions on previous weeks’ cases. It does not model temporal change in $\beta$ itself; extensions: P-spline time-varying delays (ref. 21), covariates in the log-linear predictor (Bastos et al., ref. 16), or the delay-hazard with weekday and drift effects of the PyMC examples (see Nowcasting Concepts - Delay Hazard Models and the Renewal Equation).

Limitations. Delay distribution fixed within window; smoothing prior can lag genuine abrupt change; log-score floor of $-10$ and binning make scores bin-width dependent; only two diseases; ILI delays >6 months excluded; coverage conservative (100%) for ILI at 95%.

Examples

Practical guidance: prior on ${\tau }_{\alpha }$ controls smoothness (Ga(10,0.1) = smoother); Dirichlet $\theta$ strength = pseudo-case count; choose $W$ from data length and desired reactivity; feed nowcasts rather than first-release counts to forecasters (e.g. CDC FluSight).

Connections

Marketing: attribution windows behave like ${\beta }_d$; a model that learns ${\beta }_d$ from fully matured cohorts and corrects the latest weeks avoids reading dashboards that “decline” only because data are immature.

See Also

McGough 2020 - Nowcasting by Bayesian Smoothing - Overview · McGough 2020 - Evaluation Design and Results