Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment. These models, introduced by Robins (e.g. Robins (2000a), Robins (2000b), van der Laan and Robins (2002)), model the marginal distributions of treatment-specific counterfactual outcomes,...

The term multi-valued treatment effects refers to a collection of population parameters capturing the impact of a treatment variable on an outcome variable when the treatment takes multiple values. For example, in labour training programmes participants receive different hours of training or in...