  Highly active antiretroviral therapy (HAART) has proved efficient in
increasing CD4 counts in many randomized clinical trials. Because randomized
trials have some limitations (e.g., short duration, highly selected subjects),
it is interesting to assess it using observational studies. This is challenging
because treatment is started preferentially in subjects with severe conditions,
in particular in subjects with low CD4 counts. This general problem had been
treated using Marginal Structural Models (MSM) relying on the counterfactual
formulation. Another approach to causality is based on dynamical models. First,
we present three discrete-time dynamic models based on linear increments (LIM):
the simplest model is described by one difference equation for CD4 counts; the
second has an equilibrium point; the third model is based on a system of two
difference equations which allows jointly modeling CD4 counts and viral load.
Then we consider continuous time models based on ordinary differential
equations with random effects (ODE-NLME). These mechanistic models allow
incorporating biological knowledge when available, which leads to increased
power for detecting treatment effect. Inference in ODE-NLME models, however, is
challenging from a numerical point of view, and requires specific methods and
softwares. LIMs are a valuable intermediary option in terms of consistency,
precision and complexity. The different approaches are compared in simulation
and applied to HIV cohorts (the ANRS CO3 Aquitaine Cohort and the Swiss HIV
Cohort Study).
