propensity score matching by disease and cox PH regression.. am I right? Normally I understood propensity score matching is the way to match the treated group and untreated group.
But I noticed some studies that used propensity score matching to match disease and non-disease group. And then check the ratio of exposure group and non-exposure group.
I wonder, if these cases, can we also use cox PH regression to find the relationship between exposure and disease? 
(like the analysis using propensity score matching after the matching by exposure variable and then use cox PH reg)
I’m really confused
 A: Your understanding of propensity matching is correct: the goal is to obtain matched sets of exposed to unexposed. I'd be curious about the studies where the diseased subset is matched to a healthy subset balancing risk of exposure. Technically, this approach should provide unbiased inference in a case control study where the log odds of disease given exposure is equal to the log odds of exposure given disease. 
The problem with analyzing outcome-dependent samples with a Cox model is that the effect measure is not a rate ratio. If controls are matched to cases, then the person-time among the cases is much smaller than expected, and the hazard ratio does not approximate the relative risk in an unconditional sample. A similar issue arises when you analyze matched pairs in a Cox model. 
There really is no satisfactory way of analyzing paired survival data. You might consider a Poisson GLM with a random intercept for each pair and a flexible adjustment for the log of the exposure time to estimate a rate ratio to mimic the trait of a proportional hazard and an arbitrary baseline hazard function, although the reduced degrees of freedom are of note.
