Performance of principal scores to estimate the marginal compliers causal effect of an intervention.

We examine the properties of principal scores methods to estimate the causal marginal odds ratio of an intervention for compliers in the context of a randomized controlled trial with non-compliers. The two-stage estimation approach has been proposed for a linear model by Jo and Stuart (Statistics in Medicine 2009; 28:2857-2875) under a principal ignorability (PI) assumption. Using a Monte Carlo simulation study, we compared the performance of several strategies to build and use principal score models and the robustness of the method to violations of underlying assumptions, in particular PI. Results showed that the principal score approach yielded unbiased estimates of the causal marginal log odds ratio under PI but that the method was sensitive to violations of PI, which occurs in particular when confounders are omitted from the analysis. For principal score analysis, probability weighting performed slightly better than full matching or 1:1 matching. Concerning the variables to be included in principal score models, the lowest mean squared error was generally obtained when using the true confounders. Using variables associated with the outcome only but not compliance however yielded very similar performance.