Bayesian inference and impact of parameter prior specification in flexible multilevel nonlinear models in the context of infectious disease modeling

Bayesian flexible multilevel nonlinear models (FMNLMs) are powerful tools to analyze infectious disease data with asymmetric and unbalanced structures, such as varying epidemic stages across countries. However, the robustness of these models can be undermined by poorly designed estimation methods, particularly due to uncertainties in prior distributions and initial values. This study investigates how varying levels of prior informativeness can influence the model convergence, parameter estimation, and computation time in a Bayesian flexible multilevel nonlinear model (FMNLM). A simulation study was conducted to evaluate the impact of modifying prior assumptions on posterior estimates and their subsequent effects on the interpretations. The framework was applied to COVID-19 data from Francophone West Africa. The results indicate that accurate, informative priors enhance the prediction performance with minimal impact on the computation time. Conversely, non-informative or inaccurate priors for nonlinear parameters led to lower convergence rates and a reduced recovery accuracy, although they may remain viable in standard multilevel nonlinear models.