Fig 1.
Proportion of eventually-reported cases that were reported in each week1.
1 Estimates of πts(d) − πts(d − 1), obtained using Eq 6 and stratified by season/year.
Fig 2.
Summary of methods for handling reporting delay.
Fig 3.
Performance of nowcasts and forecasts in the Puerto Rico dengue fever and national US influenza-like illness data across all weeks 1.
1 Results for dengue fever are aggregated across each of 50 weeks in 18 seasons (1992–2009). Results for US national influenza are aggregated across 35 weeks in 7 seasons. The ensemble method corresponds to an equal-weight linear combination of all methods except validation data analysis. “Model” indicates that reporting factors were estimated via regression and allowed to vary by t and s. “Lag” indicates that reporting factors were estimated via Eq 6. “Local” indicates that reporting factors were estimated via Eq 8. Relative absolute biases are calculated relative to the largest value in each column.
Fig 4.
Proportion of weeks in which each of 4 methods performs best in terms of 1-week forecast weighted interval scores.
1 Results for Dengue fever in Puerto Rico are aggregated across all 50 weeks in 18 calendar years (1992–2009). Results for US national influenza are aggregated across 35 weeks in 7 seasons (2012–2013 through 2018–2019). Results for US state-level influenza are aggregated across 35 weeks in 49 states (excluding Florida) for the 2018–2019 season.
Fig 5.
Performance of proposed methods for handling reporting delay in 2009 across 100 simulated datasets using ARMA models1.
1 Results are aggregated across all 50 weeks in 100 replicate seasons. Each result, therefore, represents aggregates 5000 nowcasts or forecasts. When reporting factors varied across seasons, π2007 = π2008 = (0.01, 0.05, 0.55, 0.85, 0.95, 0.98, 1) and π2009 = (0.04, 0.54, 0.84, 0.0.94, 0.97, 0.99, 1). The ensemble method corresponds to an equal-weight linear combination of all methods except validation data analysis and exclusions of 4 and 5 weeks’ data. “Model” indicates that reporting factors were estimated via regression and allowed to vary by t and s. “Lag” indicates that reporting factors were estimated via Eq 6. “Local” indicates that reporting factors were estimated via Eq 8. Relative absolute biases are calculated relative to the largest value in each column. Model-based πts(d) estimation assumes reporting factors vary across weeks but incorrectly models how reporting factors vary across weeks.
Fig 6.
Coverage of 95% prediction intervals for 1 week forecasts across various assumed reporting profiles in 2008 and 2009 simulated datasets1.
1 Circled coverages correspond to correctly-specified reporting factors.