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We consider the problem of defining the effect of an intervention on atime-varying risk factor or treatment for a disease or a physiological marker;we develop here the latter case. So, the system considered is $(Y,A,C)$, where$Y=(Y_t)$, is the marker process of interest, $A=A_t$ the treatment. Arealistic case is that the treatment can be changed only at discrete times. Inan observational study the treatment attribution law is unknown; however, thephysical law can be estimated without knowing the treatment attribution law,provided a well-specified model is available. An intervention is specified bythe treatment attribution law, which is thus known. Simple interventions willsimply randomize the attribution of the treatment; interventions that take intoaccount the past history will be called "strategies". The effect ofinterventions can be defined by a risk function $R^{\intr}=\Ee_{\intr}[L(\barY_{t_J}, \bar A_{t_{J}},C)]$, where $L(\bar Y_{t_J}, \bar A_{t_{J}},C)$ is aloss function, and contrasts between risk functions for different strategiescan be formed. Once we can compute effects for any strategy, we can search foroptimal or sub-optimal strategies; in particular we can find optimal parametricstrategies. We present several ways for designing strategies. As anillustration, we consider the choice of a strategy for containing the HIV loadbelow a certain level while limiting the treatment burden. A simulation studydemonstrates the possibility of finding optimal parametric strategies.

Effects of interventions and optimal strategies in the stochastic system approach to causality