Propensity score modelling in observational studies using dimension reduction methods

Conditional independence assumptions are very important in causal inference modelling as well as in dimension reduction methodologies. These are two very strikingly different statistical literatures, and we study links between the two in this article. The concept of covariate sufficiency plays an important role, and we provide theoretical justification when dimension reduction and partial least squares methods will allow for valid causal inference to be performed. The methods are illustrated with application to a medical study and to simulated data.