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Abstract:
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Mechanistic models are able to capture the dynamics of the interaction between HIV and the immune system. Efficient treatments exist, but they have a cost, both financial and in terms of side-effects. Consider the situation where a treatment U can take M modalities and at times $t_j$, j=1,...,J, the modality given to subjects can be changed. If we knew the trajectory of $X^i_t$ (a state including CD4 counts) between $t_j$ and $t_{j+1}$, we could choose the modality of U which minimizes a loss function depending on this trajectory and of a cost $c_U$ of treatment. We propose the use of a mechanistic model with fixed and random parameters to estimate the trajectories. Observations of $X^i_t$ for i=1,...n, allow to up-date estimates of fixed and random parameters, from which the trajectories $X^i_t$ between $t_j$ and $t_{j+1}$ can be estimated, and thus, the loss functions.
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