Bayesian inference in epidemiology--modelling and prediction on infectious and chronic diseases

Abstract

Bayesian inference is an effective statistical inference method, which could deal with some uncertain problems and update our beliefs about unknown parameters with the integration of new evidence. However, one disadvantage of Bayesian statistics is that the Bayesian formula is more complex than the frequentist parameter estimation, thus it has become an appealing issue that how to choose an appropriate prior distribution to make Bayesian statistics easier to calculate for specific data. The primary objective of the thesis is to explore the performance of Bayesian inference for different data types in the aspect of epidemiology in three parts. As the representatives of Bayesian inference methods, Markov chains Monte Carlo and integrated nested Laplace approximation are explored for different types of data to focus on some practical issues in epidemiology: 1.) access the common features and variations of infectiousness of infectious disease in different contact settings; 2.) evaluate the effect of immigration on chronic disease mortality in the past and future along with the effects of age, period and cohort; 3.) due to their merits and weaknesses, evaluate the performance of Markov chains Monte Carlo and integrated nested Laplace approximation to determine preferred simulation methodology for different types of data in epidemiology. The principle and application of one Bayesian inference method—Markov chain Monte Carlo (MCMC) with datasets of COVID-19 were emphasized to explore the estimated reproductive numbers and dispersion parameters, in order to 1) access the common features and variations of infectiousness in different settings, and 2) examine if there exist significant variation among individuals to investigate the association between community spread and superspreading events. MCMC performs satisfactory convergence and estimation as iterations increase for the short-term dataset of infectious disease. Methodology of Bayesian inference on the long-term and large sample-sized data of chronic disease was perform in this chapter. The mortality rates of lung, pancreatic, colon, liver, prostate and stomach cancers between locally born residents in Hong Kong and immigrants from mainland China were assessed, and we adopted a MCMC-free Bayesian age-period-cohort (APC) model based on integrated nested Laplace approximation (INLA) to explore the projection of mortality rates for the locally born population and immigrants in Hong Kong, taking into account age, period, and birth cohort effects as well. Compared to MCMC, INLA indicate higher computational efficiency, accuracy and flexibility for long-term data of chronic disease. With similar data of chronic disease, some criteria, such as Continuous Ranked Probability Score (CRPS) and a calibration test were applied to evaluate the performance of retrospective projections based on MCMC and INLA. Two methods expound approximately significant performance on retrospective projections, and the projections based on INLA indicate less dispersion with observations than those based on MCMC in most of immigrations groups. Some circumstances, such as prostate cancer and stomach cancer, against the conclusion result from lack of data since INLA requires large sample size. The findings underscore the significance for targeted interventions and strict control measures for vulnerable populations to curb the spread of infectious diseases effectively, and we could reach to equal opportunities of optimal healthcare of cancers and other chronic diseases for every individual regardless of culture or background. Furthermore, the research demonstrates that the findings and conclusions can be also applied to other countries and regions with similar methods.