Causal inference for longitudinal observationnal data - application to multinomial longitudinal data ; Approches causales pour l'analyse de données observationnelles - application aux données longitudinales avec traitements multiples

Obstructive Sleep Apnoea Syndrome (OSA) is a chronic condition with multi-organ consequences and significant economic and social costs. It is estimated that more than one billion adults aged between 30 and 69 (men and women) worldwide suffer from moderate to severe OSA. OSA is often accompanied by co-morbidities and has a major impact on quality of life. Continuous positive airway pressure (CPAP), the first-line treatment for OSA, is highly effective in improving symptoms, but no randomised clinical trial has demonstrated a clear effect on long-term cardiovascular prognosis.To demonstrate a causal effect of a treatment on the prognosis of patients with OSA, the reference method is the randomised controlled trial (RCT), despite their limitations. To compensate for the limitations of RCTs, observational databases derived from prospective cohorts or medico-administrative databases provide an alternative source of information for studying causality. However, these observational data also have their limitations, starting with the fact that, unlike an RCT, patients are not assigned to a treatment group at random. This limitation induces a selection bias which makes the evaluation of the effect of the treatment dependent on the characteristics of the patients: the confounding factors.Methods based on propensity scores are increasingly used for causal inference on observational data, and are recognised by the health authorities, to enhance the value of observational databases by correcting these limitations, thus enabling causal conclusions to be drawn from this type of data. These methods are based on a rigorous study design and assumptions: consistency, non-interference, conditional exchangeability and positivity, which must be respected in order to come as close as possible to the conditions of an RCT.Several methods exist for calculating propensity scores, such as regression or machine learning algorithms like Generalized Boosted Models, and can be used for binary or multi-level treatments. However, in the majority ...