Abstract
The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models. This approach allows incorporating biological knowledge naturally, and a continuum can be established between descriptive and mechanistic modeling. The mechanistic models involve distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results. Because of the difficulty of inference in models based on stochastic differential equations, most models that have been developed are based on ordinary differential equations. The different approaches are illustrated by estimating the effect of highly active antiretroviral treatment (HAART) on CD4+ lymphocytes counts in an observational study of HIV infected subjects. In this context, mechanistic models are available: they are much more challenging numerically than marginal structural models but they give much more precise results.