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Nowcasting Temporal Trends Using Indirect Surveys
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Proposes a latent-graph model showing indirect (network-based) survey responses track a hidden population's temporal trend better than direct surveys, and that weighted moving averages over time improve nowcasting, validated by simulation and CMU-CTIS COVID-19 data.
Problem
Nowcasting the temporal trend of a hidden population's size from continuously collected indirect survey (aggregated relational data) responses, without needing personal network sizes as NSUM requires.
Approach
A latent directed graph formulation where expected indirect response is proportional to the hidden population fraction (regardless of in-degree distribution), with analytic variance bounds showing indirect surveys beat direct ones under bounded degree variance, and smoothing over time windows via weighted moving averages reduces error when the underlying signal is smooth.
Key results
- On CMU-CTIS for California (accum=7, w=1), the indirect survey (Indirect2) achieves MAE 0.0292 vs 0.0703 for direct and 0.0443 for NSUM.
- In synthetic simulations, indirect methods with moving average produce lower median errors than NSUM and direct methods, with the advantage largest for small respondent counts n.
- On UMD-CTIS country data, the indirect approach gives lower MAE than NSUM and DirectCLI in most countries (e.g., Japan 0.08 vs 0.23 NSUM).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use indirect CLI responses instead of the strongest direct or NSUM baseline | Indirect nowcasting · UMD-CTIS, Brazil, Canada, France, Germany, Israel, Italy, Japan, Spain, Turkey, and UK | MAE: Brazil: 0.14 -> 0.15; Canada: 0.14 -> 0.12; France: 0.17 -> 0.13; Germany: 0.1 -> 0.12; Israel: 0.17 -> 0.12; Italy: 0.1 | Mixed |
| Use local-community indirect responses instead of NSUM | Indirect2 nowcasting · CMU-CTIS, California, Texas, New York, and Pennsylvania (accum=7, w=1) | MAE: California: 0.0443 -> 0.0292; Texas: 0.0379 -> 0.0270; New York: 0.0315 -> 0.0299; Pennsylvania: 0.0368 -> 0.0263 | Helped |
| Use local-community rather than household indirect responses | Indirect nowcasting · CMU-CTIS, generally across the reported states and parameter settings | MAE | Helped |
| Increase the smoothing window from w=1 to w=3 (ablation) | Indirect moving-average estimates · CMU-CTIS, California, Texas, New York, and Pennsylvania (accum=7) | MAE: California: 0.0292 -> 0.0811; Texas: 0.0270 -> 0.0782; New York: 0.0299 -> 0.0886; Pennsylvania: 0.0263 -> 0.0691 | Hurt |
| Increase accumulation from accum=7 to accum=14 (ablation) | Indirect2 nowcasting · CMU-CTIS, California, Texas, New York, and Pennsylvania (w=1) | MAE: California: 0.0292 -> 0.0477; Texas: 0.0270 -> 0.0336; New York: 0.0299 -> 0.0500; Pennsylvania: 0.0263 -> 0.0429 | Hurt |
| Apply weighted or unweighted moving-average smoothing rather than no smoothing (ablation) | Indirect survey estimates · Synthetic epidemic simulations | MAE | Helped |
| Increase the smoothing window excessively (ablation) | Moving-average survey estimates · Synthetic epidemic simulations | MAE | Hurt |
| Increase the accumulation width (ablation) | Survey estimates · Synthetic epidemic simulations | MAE | Mixed |
| Use weighted rather than unweighted moving-average smoothing (ablation) | Survey estimates · Synthetic epidemic simulations | MAE | No clear effect |
| Vary average degree d (ablation) | Survey methods · Synthetic epidemic simulations | MAE | No clear effect |
| Vary covered subpopulation size n_d (ablation) | Survey methods · Synthetic epidemic simulations | MAE | No clear effect |
| Replace indirect survey responses with direct survey responses | Survey estimation methods · Synthetic epidemic simulations | MAE | Hurt |
Surprising findings
- Indirect CLI estimates in UMD-CTIS were in most countries better than directly asking about positive tests (DirectTPR).
- NSUM outperformed the indirect approach in some configurations (e.g., NY and PN at accum=14, w=1 in the CTIS table).
Limitations
- Microdata of CTIS cannot be shared; only aggregated data released.
- Theory assumes honest responses; biased or malicious reporting is not analyzed in the main text.
- Variance condition on degree distribution and smoothness assumptions may not hold in all settings.
Experimental setup
Datasets: CMU-CTIS (US COVID-19 Trends and Impact Survey) Johns Hopkins COVID-19 data UMD-CTIS surveys Our World in Data COVID-19 cases
Benchmarks: CMU-CTIS COVID-19 incidence (CA, TX, NY, PA) UMD-CTIS country-level COVID-19 incidence synthetic SIR epidemic simulations
Metrics: MAE error distribution
Baselines: NSUM Direct survey
Builds on: Network Scale-Up Method SIR model CMU COVID-19 Trends and Impact Survey
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