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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?

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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.

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