Comparing frequentist and Bayesian methods to identify drivers of pathogen strain invasion: A temporal case study of pertussis in the United States

Since the 20th century, it has been widely recognized that the emergence of new pathogens is closely linked to human activities such as global travel and environmental exploitation. In addition, the widespread use of antibiotics and vaccines has contributed to the evolution and dissemination of new pathogen variants. However, the role of environmental and socio-demographic cofactors on the dynamics of pathogen spread remains insufficiently explored. In this study, we argue that such influences are best captured using mixed logistic regression models that incorporate temporally autocorrelated random effects, in order to reflect the complex and time-dependent nature of strain invasion processes. To address the statistical challenges of this framework, we compared two approaches: (i) a simplified model with independent random effects and frequentist inference, and (ii) a full model accounting for temporal autocorrelation, estimated using Bayesian inference. Our results show that the simplified model, although commonly used in longitudinal analyses, substantially underestimates the probability of detecting false-positive associations (i.e., it underestimates the Type I error rate), leading to potentially misleading conclusions. In contrast, the full Bayesian model avoids this bias and offers a more robust alternative. We applied this approach to a dataset monitoring the emergence of vaccine-escape <i>Bordetella pertussis</i> strains in the United States between 2007 and 2017. Among the eight cofactors tested, only temperature was significantly associated with the rate of strain invasion. Further simulation-based analyses revealed that the current dataset has limited statistical power to detect such associations. However, our results suggest that increasing the temporal resolution of data collection could substantially improve the model's ability to detect meaningful associations - without increasing surveillance costs.