Longitudinal, Spatial, and Spatio-temporal Modeling of Clinical and Epidemiological Data

Hierarchical data, with correlation in space and/or time, occur in a variety of areas. In clinical and epidemiological studies, such as in renal transplant studies, this is the case when a number of longitudinal markers are jointly observed, often in conjunction with (recurrent) event times as well. In the context of infectious diseases, such as SARS-CoV-2 induced COVID-19, the search for correlates of protection for vaccine efficacy implies the joint modeling of a number of markers (e.g., based on humoral and cellular immunity) and time to infection, embedded in a multi-centric study or multi-trial meta-analysis. Still in the area of SARS-CoV-2, the joint modeling of key epidemiological indicators (e.g., total and confirmed cases, positivity, hospitalizations, ICU occupancy, mortality)  is of interest. Such time series, when replicated at the level of sufficiently small geographical units (provinces, town, or statistical sector) allow for a refined analysis using multivariate longitudinal, spatial, or spatio-temporal methods. While some modeling efforts have been made, considerable work is needed to formulate models that do full justice to the data structure and hence allow for properly answering the research questions that come with it. In addition, work is needed to make these models computationally stable and efficient, and hence practically useful.