Évaluation des interventions non-pharmaceutiques contre le COVID-19 en Allemagne : comparaison de cadres d’inférence statistique et analyse de robustesse

Details

Supervisors

Jungers, Raphaël M.

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enPublic health policies implemented during the COVID-19 pandemic have been the subject of numerous statistical analyses. However, accurately assessing their effectiveness remains challenging, as the epidemic evolved very differently across regions and exhibited a strong temporal dependence. This thesis therefore investigates the extent to which conclusions regarding the effectiveness of these measures depend on the statistical framework used to model the data. The analysis is based on epidemiological data from thirteen German regional groupings during the year 2020. Three approaches are compared: a classical frequentist mixed-effects model (lme4), a Bayesian hierarchical model (brms/Stan), and a frequentist model incorporating an explicit AR(1) autoregressive correction (glmmTMB). This analysis is complemented by simulations on synthetic data designed to assess the robustness of these models to the problem of reverse causality. The results first show that the frequentist and Bayesian approaches produce almost identical estimates ($r \approx 0.9998$). In other words, using a more sophisticated Bayesian framework does not compensate for an inadequate representation of the temporal dynamics. More importantly, the study demonstrates that when day-to-day dependence is not properly accounted for, statistical models tend to attribute part of the epidemic’s natural evolution to the effects of public health interventions. The simulations confirm this issue: without a temporal correction, conventional models can generate up to 100% false positives. Once autocorrelation is accounted for through an AR(1) filter, the effects previously attributed to public health measures are no longer statistically significant. However, the simulations also show that this correction does not reduce the model’s ability to detect a genuine effect when one exists, with a statistical power close to 99%. The loss of statistical significance observed in the real-world data should therefore not be interpreted as evidence that public health policies were ineffective. Rather, it highlights the limitations of regression models when applied to observational data. Overall, this work emphasizes the importance of properly modelling temporal dynamics in order to avoid misleading conclusions about the true impact of public health interventions.