Validity of comparing two hazard ratios from different models

[rakelren]

Hi Forum.

I am wondering if it is possible to compare two separate hazard ratios obtained from Cox models i.e. not a nested model, and obtain a p-value for comparison.

I came across a recent high impact journal publication where the authors state in their statistical methods: "Relative risks were expressed as hazard ratios with 95% confidence intervals derived from Cox models; hazard ratios for a positive FFRCT versus positive CTA were compared with the chi-square test." Link to paper: http://www.massgeneral.org/imaging/assets/pdfs/cardiac-mrpetct/lu-promise-ffrct-jacc-cvi-2017.pdf

How could this be done? My understanding is that chi-squared test is a global test, like the log-rank test; My take is that authors have done a 2x2 contingency table and obtained a p-value, but can you then extrapolate from this a comparison of hazard ratios? I did not think so because this is missing the time-to-event component.

Is this a valid method to perform?

[Chengyiw]

Hi rakelren,

I've come across the same situation where I would like to compare HRs from two cox models. Except p value, I am also thinking of 95% CI. I did a lot of research but still don't know what to do. I am wondering if you have figured out?