Theories behind propensity score analysis assume that the covariates are fully observed (Rosenbaum & Rubin, 1983, 1984). However, in practice, observational analyses require large administrative databases or surveys, which inevitably will have missingness in the covariates. The response patterns of people with missing covariates may be different than those of people with observed data (Mohan, Pearl, & Tian, 2013). Therefore, ways to handle missing covariate data need to be examined.
In my qualifying exam, in the written part, I was asked about how to analyze the effect of continuous, not binary, treatment using propensity score analysis. I skipped it for the written but I spent a few days looking up how to analyze this in case I would be asked during my oral examination. Sadly, no one asked me even when I asked them to, so here is a blog detailing my explorations.