McGough 2020 - Nowcasting by Bayesian Smoothing - Overview
Summary
McGough, Johansson, Lipsitch & Menzies (2020, PLoS Comput Biol 16(4): e1007735) propose NobBS, a Bayesian log-linear chain-ladder nowcast whose weekly “true signal” follows a first-order (geometric) random walk and whose delay distribution has a Dirichlet prior. Linking cases across weeks makes nowcasts smoother and more robust than a pure delay-hazard model when the reporting delay drifts over time.
Overview
Research question. Reported counts are right-truncated: events that occurred recently are only partly reported. How should we estimate the eventual total for the current week, with honest uncertainty, in settings where the share reported at delay 0 ranges from 4% (dengue, Puerto Rico) to >80% (US influenza-like illness)?
Contribution. (1) A simple model with a random walk, i.e. an autocorrelated epidemic curve; (2) an R package (NobBS); (3) a benchmark against the Hoehle & an der Heiden (2014) reverse-time discrete hazard approach (“HH”), scored by the logarithmic score on 989 weeks of dengue and 170 weeks of ILI; (4) a simulation where the delay probability varies with incidence; (5) a moving-window sensitivity study.
Key result. Over the weeks both methods could predict, NobBS cut dengue rRMSE from 1.24 to 0.464 and roughly doubled the average log score (0.274 vs 0.161); for ILI the HH point estimate was slightly better (rRMSE 0.062 vs 0.074) but HH’s intervals were too narrow (0% coverage vs 100%), so the NobBS average score was 0.218 vs 0.017.
Motivating PyMC examples
The reporting-triangle nowcast in the PyMC example set is E38 (“Real-time epidemic tracking: is it growing right now? Nowcasting + a renewal-equation R”) and E90 (“Call it today or wait? Hospital thresholds, nowcasts and decision curves”), both German COVID-19 hospitalisation triangles. Their delay-hazard parameterisation is the HH-style alternative to NobBS’s multiplicative form; both are covered in McGough 2020 - Reporting Triangle and Chain-Ladder Setup and Nowcasting Concepts - Delay Hazard Models and the Renewal Equation (concept note, no raw source).
Source Map
| Paper section | Pages | Covered in |
|---|---|---|
| Abstract, Author summary, Introduction | 1-3 | this note; McGough 2020 - Reporting Triangle and Chain-Ladder Setup |
| Results: dengue and ILI performance (Figs 1-2, Tables 1-2) | 3-8 | McGough 2020 - Evaluation Design and Results |
| Results: reporting delays; time-varying delays; simulated ILI | 8-9 | McGough 2020 - Delay Dynamics, Moving Windows and Limitations |
| Results: performance by year (Table 3); moving windows | 9-10 | McGough 2020 - Evaluation Design and Results; McGough 2020 - Delay Dynamics, Moving Windows and Limitations |
| Discussion | 10-13 | McGough 2020 - Delay Dynamics, Moving Windows and Limitations |
| Methods: surveillance data, reporting triangle | 13 | McGough 2020 - Reporting Triangle and Chain-Ladder Setup |
| Methods: Bayesian nowcast model, priors, package | 13-16 | McGough 2020 - NobBS Model and Priors |
| Methods: HH comparator, metrics, log score, simulation | 16-18 | McGough 2020 - Evaluation Design and Results |
| Supporting information (S1-S6 tables, S1-S8 figs) | 18 | listed only; not reproduced |
Connections
State-space view: the random-walk is a local-level model observed through delay-thinned counts; see Linear-Gaussian State-Space Models and Bayesian Structural Time-Series Model. The log score is covered in Proper Scoring Rules (CRPS, Log Score, Pinball Loss). Right truncation is a survival-analysis idea (Survival Analysis). Downstream use of nowcasts to estimate : Gostic 2020 - Rt Estimation Pipeline and Right-Truncation Bias.
Relevance to marketing measurement
Conversions, offline sales and survey responses also arrive with reporting lag (attribution windows, delayed store feeds). The same reporting-triangle thinking applies to “latest-week” dashboards in MMM and incrementality monitoring: the most recent weeks are systematically under-counted and should be nowcast, not read at face value.