Propensity Score Matching with Cox Regression I am conducting a survival analysis with a Cox regression whereby the outcome variable (promotion to a senior role) is either 0 or 1. I am particulalry interested in the hazard rate (i.e., the 'hazard' of being promoted). My predictor of interest is extraversion (continuous), and my covariates are gender (binary), age (continuous), other personality variables (four continuous), and industry (for which there are 8 binary variables).
Rather than running a Cox regression with all of these covariates, I was wondering if it makes sense (from a statistical theory perspective) to apply propensity score matching to the covariates to thus match on the outcome variable and then run my Cox regression with extraversion as the only predictor on the resulting matched dataset?
 A: It is uncertain which statistical method should be used on the matched data, as you must respect the matched nature of the new artificial dataset.  An equally big problem is that the Cox coefficient for the exposure in the matched dataset has a different meaning and is usually smaller in absolute value than had you done a full conditional-on-covariates analysis, due to non-collapsibility of hazard ratios.  By using the propensity analysis you are not respecting outcome heterogeneity that would have been explainable by covariate adjustment.
Think of propensity scores as part of a data reduction strategy (unsupervised learning) that assists in the case where there are too many covariates to adjust for for the number of outcome events (you need at least, say, 4 events per covariate for stable adjustment).  I say part because you also need to adjust for the big predictors of outcome which a matched analysis doesn't allow you to do, so covariate adjustment using a spline of the logit of propensity would be preferred to matching if you really, really needed to do data reduction.
A: The propensity score method is to make the baseline covariates of the treatment and control groups are similar as possible. Because individuals who select one treatment or who exposed to some risk factor of interest likely different from those who don't in the non-randomized trail.
So, you could use the propensity score method to make the balance in the distribution of the baseline covariates, then run cox regression for the matched data set.  
