Variable selection for dynamic treatment regimes

Nowadays, many illnesses as for example HIV/AIDS, cancer or psychological diseases are seen by the medical community as being chronic-like diseases. For treating such diseases, physicians often adopt explicit, operationalized series of decision rules specifying how treatment level and type should vary overtime. These rules are referred to in the medical community as dynamic treatment regime or DTR in short. Designing DTR for such diseases is a challenging issue. Among the difficulties encountered, we can mention the poor compliance to treatments due to the side effects associated to some drugs (e.g., chemotherapies can decrease significantly the quality of life of some patients), the decrease of treatment efficiency with time (e.g., apparition of drugresistant HIV viruses after several years of treatment) and the enormous cost of administrating drugs to patients over periods ranging sometimes to tens of years. To a large extent DTR are nowadays based on clinical judgment and medical instinct rather than on a formal and systematic data-driven process that could reveal itself to be more efficient. These latter ten years, one has seen the emergence among the biostatistics community of a research field addressing specifically problems of inference of DTR from clinical data. While this research field is still young, encouraging results have already been published. We mention for example [1] where the authors propose such an approach for designing treatments for psychotic patients.