Generalized time-varying coefficient models for the analysis of longitudinal data in health: an application in HIV / AIDS and COVID-19

Abstract

Longitudinal data analysis is necessary when the response variable is repeatedly measured on the same observation unit over time. The parametric methods have been traditionally used in the analysis of longitudinal data to estimate the coefficients that define the relationship between the linear predictor and the response variable, However, parametric techniques do not work when the assumptions about the response variable and the random component of the model are not fulfilled, or when the expected value of the response variable (or a function of this variable via a link function) is not be a known function of the fixed and random effects, reasons why parametric models can draw conclusions away from the average trend of the data set. In these cases, {non-parametric regression techniques, in which time-dependent smoothed local functions are used instead of parameters, called coefficients or dynamic parameters, constitute a very powerful modeling alternative in the analysis of longitudinal data, since they allow establish a more flexible functional dependence between the response variable and the covariates. In this work, it is proposed to develop estimation and inference techniques for generalized non-parametric dynamic coefficient models, particularly when the response variable is counting, illustrating its application in the effect of viral load on CD4 cell count, in patients with HIV / AIDS undergoing antiretroviral treatment, and also in the prediction of COVID-19 cases.