Fitting Polyexponentials and Quasipolynomials to HIV Viral Load Data

Measurements of HIV1-RNA plasma concentrations are an important method of assessing patient response to anti-HIV1 treatments, and in most clinical trials of such treatments these plasma concentrations are assessed at regular intervals of time. HIV1-RNA plasma levels in successfully treated patients tend to follow a standard pattern, which shows a relatively rapid early decline in viral load, followed by a period of much slower continuing decline or a steady level ( see e.g. Havlir and Richman, 1996; Huang et. al. 2001; Hatzakis et. al., 2001; ) There is much theoretical work on the dynamics of HIV1 infections which may provide explanations of why the decline in HIV1-RNA plasma concentrations exhibits this type of pattern – often referred to as a “biphasic decline” (e.g. Perelson and Nelson, 1999; Wu and Ding, 1999; Ding and Wu, 1999). Fitting nonlinear regression models to these patterns of declining HIV1RNA levels can be of value in comparing different treatment regimes and in predicting treatment outcome. Simple exponential-decline models can give an adequate fit to the typical pattern of decreasing HIV1RNA plasma levels, but we have explored the extent to which curve-fitting can be improved by using some less commonly encountered nonlinear regression models. Specifically, we describe here the fitting of polyexponential, multiple polyexponential, and quasipolynomial regression models to longitudinal HIV1-RNA plasma data collected in two recent trials of the novel anti-HIV1 treatment Fuzeon.