Discussion of Estimating time-varying causal excursion effect in mobile health with binary outcomes by T. Qian et al

We discuss the recent paper on excursion effect by T. Qian et al. (2020). We show that the methods presented have close relationships to others in the literature, in particular to a series of papers by Robins, Hern{a}n and collaborators on analyzing observational studies as a series of randomized trials. There is also a close relationship to the history-restricted and the history-adjusted marginal structural models (MSM). Important differences and their methodological implications are clarified. We also demonstrate that the excursion effect can depend on the design and discuss its suitability for modifying the treatment protocol.