Bayesian inference for infectious disease transmission models based on ordinary differential equations

摘要

Predicting the epidemiological effects of new vaccination programmes through mathematical-statistical transmission modelling is of increasing importance for the German Standing Committee on Vaccination. Such models commonly capture large populations utilizing a compartmental structure with its dynamics being governed by a system of ordinary differential equations (ODEs). Unfortunately, these ODE-based models are generally computationally expensive to solve, which poses a challenge for any statistical procedure inferring corresponding model parameters from disease surveillance data. Thus, in practice parameters are often fixed based on epidemiological knowledge hence ignoring uncertainty. A Bayesian inference framework incorporating this prior knowledge promises to be a more suitable approach allowing for additional parameter flexibility.ududThis thesis is concerned with statistical methods for performing Bayesian inference of ODE-based models. A posterior approximation approach based on a Gaussian distribution around the posterior mode through its respective observed Fisher information is presented. By employing a newly proposed method for adjusting the likelihood impact in terms of using a power posterior, the approximation procedure is able to account for the residual autocorrelation in the data given the model. As an alternative to this approximation approach, an adaptive Metropolis-Hastings algorithm is described which is geared towards an efficient posterior sampling in the case of a high-dimensional parameter space and considerable parameter collinearities. In order to identify relevant model components, Bayesian model selection criteria based on the marginal likelihood of the data are applied. The estimation of the marginal likelihood for each considered model is performed via a newly proposed approach which utilizes the available posterior sample obtained from the preceding Metropolis-Hastings algorithm.ududFurthermore, the thesis contains an application of the presented methods by predicting the epidemiological effects of introducing rotavirus childhood vaccination in Germany. Again, an ODE-based compartmental model accounting for the most relevant transmission aspects of rotavirus is presented. After extending the model with vaccination mechanisms, it becomes possible to estimate the rotavirus vaccine effectiveness through routinely collected surveillance data. By employing the Bayesian framework, model predictions on the future epidemiological development assuming a high vaccination coverage rate incorporate uncertainty regarding both model structure and parameters. The forecast suggests that routine vaccination may cause a rotavirus incidence increase among older children and elderly, but drastically reduces the disease burden among the target group of young children, even beyond the expected direct vaccination effect by means of herd protection.ududAltogether, this thesis provides a statistical perspective on the modelling of routine vaccination effects in order to assist decision making under uncertainty. The presented methodology is thereby easily applicable to other infectious diseases such as influenza.