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Highly active antiretroviral therapy (HAART) has proved efficient inincreasing CD4 counts in many randomized clinical trials. Because randomizedtrials have some limitations (e.g., short duration, highly selected subjects),it is interesting to assess it using observational studies. This is challengingbecause treatment is started preferentially in subjects with severe conditions,in particular in subjects with low CD4 counts. This general problem had beentreated using Marginal Structural Models (MSM) relying on the counterfactualformulation. 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; thesecond has an equilibrium point; the third model is based on a system of twodifference equations which allows jointly modeling CD4 counts and viral load.Then we consider continuous time models based on ordinary differentialequations with random effects (ODE-NLME). These mechanistic models allowincorporating biological knowledge when available, which leads to increasedpower for detecting treatment effect. Inference in ODE-NLME models, however, ischallenging from a numerical point of view, and requires specific methods andsoftwares. LIMs are a valuable intermediary option in terms of consistency,precision and complexity. The different approaches are compared in simulationand applied to HIV cohorts (the ANRS CO3 Aquitaine Cohort and the Swiss HIVCohort Study).

Dynamic models for estimating the effect of HAART on CD4 in  observational studies: application to the Aquitaine Cohort study and the  Swiss HIV Cohort Study