The odds ratio is the most common way to model the association between a binary treatment and outcome. The popularity of this measure is driven in part by the ease with which logistic regression can be used to describe the way that the odds ratio varies with baseline variables. However, there are fundamental difficulties that arise when attempting to interpret odds ratios since they are non-linear measures that are not collapsible.
These results motivate the development of methods for modeling the relative risk (RR) and risk difference (RD), rather than the odds ratio, as a function of baseline covariates. Using a novel odds-product nuisance model, I will describe a simple parametrization under which models for the RR and RD may be estimated via maximum likelihood. The odds-product is used as a novel nuisance model. Further, this parametrization also permits doubly-robust estimation for the model of interest, given a correctly specified model for the propensity score.
Time permitting I will sketch how these ideas may be extend to the case of multiple treatments, via Structural Nested Mean Models (SNMMs).