ABSTRACT
CONTENTS 7.1 Statistical Issues in Modeling HIV Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 7.2 Mixed-Effects Models for Censored HIV-1 RNA Data . . . . . . . . . . . . . . . 190
7.2.1 EM Algorithm for N/LME with Censored Response . . . . . . . . 191 7.2.1.1 The Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 7.2.1.2 Nonlinear Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
7.2.2 HIV-1 Viral Load Setpoint for Acutely Infected Subjects . . . . 194 7.3 Random Changepoint Modeling of CD4 Cells Rebound . . . . . . . . . . . . . 198
7.3.1 A Hierarchical Bayesian Changepoint Model . . . . . . . . . . . . . . . . . 199 7.3.2 Model Selection Using Deviance Information Criterion . . . . . 200 7.3.3 Analysis of ACTG 398 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
More than 20 years after its initial outburst, HIV/AIDS pandemic continues to be one of the most important threats of global public health, with an estimated 39 million people infected world wide and 4million new infections each year (UNAIDS, 2006). Modeling HIV data proved to be a challenging area of research and has led to numerous developments in the design and analysis of clinical trials andobservational studies. The introductionof highly active antiretroviral treatment in the mid-1990s led to a dramatic reduction in the rates of death or development of AIDS. The severity of infection has subsequently been measured by immunological and virological markers, especially concentration of CD4 cells and HIV-1 viral RNA (viral load, VL) in the plasma. Challenges to modeling these markers are (1) the measurements are longitudinal; (2) the models are in general complex and rarely can be reduced to
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are affected by several factors, development of viral resistance, start or stopping of treatment, nonadherence to treatment, choice of treatment, and treatment toxicity. These factors, alone or in combination, affect the validity of simple statistical models, may induce informative dropout, errors in variables, censored observations, and so forth. Furthermore, in contrast to randomized clinical trials, observational studies data are subject to confounding, such as the decision when to start or change treatment, and dropout. Recent work dealing with some of these issues includes Brown et al.
