The relationship between virologic and immunologic responses in AIDS clinical research using mixed-effects varying-coefficient models with measurement error

In this article we study the relationship between virologic and immunologic responses in AIDS clinical trials. Since plasma HIV RNA copies (viral load) and CD4+ cell counts are crucial virologic and immunologic markers for HIV infection, it is important to study their relationship during HIV/AIDS treatment. We propose a mixed-effects varying-coefficient model based on an exploratory analysis of data from a clinical trial. Since both viral load and CD4+ cell counts are subject to measurement error, we also consider the measurement error problem in covariates in our model. The regression spline method is proposed for inference for parameters in the proposed model. The regression spline method transforms the unknown nonparametric components into parametric functions. It is relatively simple to implement using readily available software, and parameter inference can be developed from standard parametric models. We apply the proposed models and methods to an AIDS clinical study. From this study, we find an interesting relationship between viral load and CD4+ cell counts during antiviral treatments. Biological interpretations and clinical implications are discussed.