Comparative evaluation of methodologies for estimating the effectiveness of non-pharmaceutical interventions in the context of COVID-19: a simulation study

Numerous studies assessing the effectiveness of non-pharmaceutical interventions (NPIs) against COVID-19 have produced conflicting results, partly due to methodological differences. This study aims to clarify these discrepancies by comparing two frequently used approaches in terms of parameter bias and confidence interval coverage of NPI effectiveness parameters. We compared two-step approaches, where NPI effects are regressed on by-products of a first analysis, such as the effective reproduction number ${\mathcal{R}}_t$, with more integrated models that jointly estimate NPI effects and transmission rates in a single-step approach. We simulated datasets with mechanistic and an agent-based models and analyzed them with both mechanistic models and a two-step regression procedure. In the latter, ${\mathcal{R}}_t$ was estimated first and then used as the outcome in a linear regression with NPI variables as predictors. Mechanistic models consistently outperformed two-step regressions, exhibiting minimal bias (0-5%) and accurate confidence interval coverage. Conversely, the two-step regression showed bias up to 25%, with significantly lower-than-nominal confidence interval coverage, reflecting challenges in uncertainty propagation. We identified additional challenges in the two-step regression method, such high depletion of susceptibles and time lags in observational data. Our findings suggest caution when using two-step regression methods for estimating NPI effectiveness.