# Pharmacodynamics and patient drug compliance

This study is conducted in the frame of the *DIGITEO DIM* “ANIFRAC” project, which involves INRIA, ECP and Supelec. It is performed partly in collaboration with Pr. F. Nekka at the faculty of pharmacy at Montréal University.

Poor adherence to treatment is a worldwide problem that threatens efficacy of therapy, particularly in the case of chronic diseases. Compliance to pharmacotherapy can range from 5% to 90%. This fact renders clinical tested therapies less effective in ambulatory settings. Increasing the effectiveness of adherence interventions has been placed by the World Health Organization at the top list of the most urgent needs for the health system. A large number of studies have appeared on this new topic in recent years.

We consider the problem of compliance within the context of multiple dosing. Analysis of multiple dosing drug concentrations, with common deterministic models, is usually based on patient full compliance assumption, i.e., drugs are administered at a fixed dosage. However, the drug concentration-time curve is strongly influenced by the random drug input generated by patient poor adherence behaviour, inducing erratic therapeutic outcomes. Following work already started in Montréal, we consider stochastic processes generated by taking into account a random drug intake.

Such studies have been made possible by technological progress, such as the “medication event monitoring system”, which allows to obtain data describing the behaviour of patients.

The deterministic model describing the evolution of drug concentration can be considered as a “black box.” The efficiency of the drug is usually an output of this model, when the intake is realized as prescribed. To obtain a robust efficiency of the drug, we need to cope with fluctuations of the behaviour of patients. As in the generic approach which is studied in the EHPOC project, we will use different approaches: statistical methods where enough data are available, model-based ones in presence of a qualitative description of the patient behaviour.

In this latter case, piecewise deterministic Markov processes (PDP) seem a promising path. PDP are non-diffusion processes whose evolution follows a deterministic trajectory governed by a flow between random time instants, where it undergoes a jump according to some probability measure. There is a well-developed theory for PDP, which studies stochastic properties such as extended generator, Dynkin formula, long time behaviour (stability). It is easy to cast a simplified model of non-compliance in terms of PDP. This has allowed us to obtain certain properties of interest of the random concentration of drug. Crucial statistical aspects remain to be investigated.