Variable Selection in Multistate Models for Correlated Data With Application in a COVID ‐19 Vaccination Study

Depicting patient transitions among multiple clinical states is a common objective in health services and epidemiological research. Multistate models (MSM) are the primary analytical approach used in such studies. Although the structure of an MSM is typically determined by the research questions of a specific application, models are typically complex, with multiple transition paths and a large number of parameters. This complexity introduces computational and numerical challenges in parameter estimation and scientific difficulties in model interpretation. Compounding these issues is the inherent within-subject correlation. For example, in studies of care transitions among patients receiving coronavirus disease 2019 (COVID-19) vaccines, the transition times among different states within the same subject tend to be correlated. Failing to accommodate these correlations may lead to inefficient estimation and questionable inference. In this paper, we propose a method for variable selection in MSM with correlated data by reparameterizing the likelihood function and approximating the penalty term with a smooth hyperbolic tangent function. This approach enforces sparsity in the MSM. We conducted an extensive simulation study to evaluate the accuracy of variable selection and parameter estimation. Finally, we applied the method to analyze data from an observational study of care transitions among individuals receiving COVID-19 vaccines, focusing on four health states: healthy, infection, emergency department or hospital admission, and death.