Generalized Dynamic Coefficient Models for Longitudinal Data Analysis in Health: An Application in HIV/AIDS and COVID-19

Longitudinal data analysis is essential when the response variable is measured repeatedly on the same observational unit over time. Traditionally, parametric methods have been employed to estimate coefficients that define the relationship between the linear predictor and the response variable. However, these methods fail when the assumptions regarding the response variable and the model's random components are violated, or when the expected value of the response variable (or its transformation via a link function) cannot be expressed as a known function of the fixed and random effects. In such cases, parametric models may yield conclusions that deviate significantly from the dataset's average trends. Non-parametric regression techniques, which replace fixed parameters with time-dependent smoothed local functions, offer a powerful alternative for longitudinal data analysis. These methods, known as dynamic coefficients or parameters, allow us to establish a more flexible functional relationship between the response variable and the covariates. In this study, we propose estimation and inference techniques for generalized non-parametric dynamic coefficient models, particularly for count response variables. We illustrate our approach through its application in analyzing the effect of viral load on CD4 cell count in HIV/AIDS patients undergoing antiretroviral therapy, as well as in predicting COVID-19 cases.