Gostic 2020 - Observation Process, Smoothing Windows and Recommendations

Summary

Constant under-ascertainment leaves $R_t$ point estimates unbiased but intervals too narrow; changing ascertainment biases them. Smoothing windows trade noise for lag: report $R_t$ at the window midpoint and choose the width by leave-future-out log score. The paper recommends Cori for real time and stresses structured surveillance.

Overview

Covers the last sections: incomplete observation, day-of-week and stochastic reporting noise, window choice, overfitting, and conclusions with bullet recommendations.

Main Content

Ascertainment (qualitative result)

If the fraction of infections observed is constant in time and representative, the $R_t$ ratio estimators are unbiased because the fraction cancels in $I_t/{\Lambda }_t$; but credible intervals ignore ascertainment uncertainty (false precision). Time-varying testing effort, criteria or hospital capacity are read as changes in $R_t$. Mitigation: model testing effort, flag estimates after changes in data collection, prefer sentinel/structured data.

Smoothing window and lag

The Cori window of $w$ days pools data to estimate $R_t$. Reporting $R_t$ on the last date of the window (Cori’s convention) uses only past data and lags the true value; reporting at the midpoint is temporally accurate but sacrifices the final $w/2$ days. Short windows pick up noise; long windows over-smooth real changes (Fig 6). Choose $w$ by short-term predictive accuracy, e.g. leave-future-out validation minimising the one-step-ahead log score or a ranked probability score; time-varying windows possible.

Recommendations (Box-style bullets). Use Cori for the instantaneous $R_t$; Wallinga-Teunis only retrospectively or for individual covariates; avoid Bettencourt-Ribeiro as-is; specify the intrinsic generation interval carefully; infer infections by deconvolution or a joint forward model; adjust or drop right-truncated days; propagate delay, truncation and ascertainment uncertainty; require daily counts large enough for a small window. Future work: inferring infections under uncertain delays; EpiNow2 extensions; sentinel populations.

Examples

Window midpoint rule

A 7-day window ending at day 100 has midpoint 97. Reporting at 97 means the latest displayable day is $T-3$, so the estimate for the most recent three days is withheld, but a drop in transmission on day 90 is seen on about day 90-93 rather than 97-100.

Connections

Marketing: weekly smoothing of response curves and “report-at-end-of-window” dashboards share the lag artifact. Window selection by one-step-ahead log score is the same device as time-series cross-validation (Proper Scoring Rules (CRPS, Log Score, Pinball Loss)).

See Also

Gostic 2020 - Rt Estimation Pipeline and Right-Truncation Bias