Cox regression hazard ratio interpretation

[Josh Wang]

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* Example generated by -dataex-. For more info, type help dataex
clear
input str4 Var double HazardRatio byte pvalue
"X1"   2.24 0
"X2"   1.45 0
"X3=1"  .88 0
"X3=2"  .21 0
end

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Hello,
I posted a segment of my Cox regression results. and I have two questions.
Q1: X1 and X2 are continuous variables with hazard ratios of 2.24 and 1.45. I saw many results from papers that the hazard ratios are generally less than 2, so is my result reasonable? I have a ratio of 2.24 after all.
Q2: X3 is a categorical variable, X3=1 with a hazard ratio of 0.88, which means X3=1 can decrease the rate of hazard by 12% (1-0.88), X3=2 with a hazard ratio of 0.21 means X3=2 can decrease the rate of hazard by 79% (1-0.21), can I also say X3=2 could reduce higher degree of hazard than X3=1? I'm not sure if I could compare them directly.

Thank you in advance!

[Clyde Schechter]

Q1: X1 and X2 are continuous variables with hazard ratios of 2.24 and 1.45. I saw many results from papers that the hazard ratios are generally less than 2, so is my result reasonable? I have a ratio of 2.24 after all.

For continuous variables, there is no guideline on the size of hazard ratios because it depends on the scale of the variable. If X1 were, say, a weight measured in pounds, redoing the analysis changing X1 to kilograms would multiply the coefficient by 2.2, and the hazard ratio would be raised to the 2.2 power. So you really have to look at this in terms of the implied hazard rates over the range of values of X1 itself. This is different from simple dichotomous variables where it is appropriate to be skeptical of hazard ratios greater than 2 and be very skeptical of hazard ratios greater than 4 because very few discrete things have that much effect on most time-to-event outcomes that large.

can I also say X3=2 could reduce higher degree of hazard than X3=1? I'm not sure if I could compare them directly.

Well, you can't really say that without doing a direct comparison using -lincom-.

[Josh Wang]

For continuous variables, there is no guideline on the size of hazard ratios because it depends on the scale of the variable. If X1 were, say, a weight measured in pounds, redoing the analysis changing X1 to kilograms would multiply the coefficient by 2.2, and the hazard ratio would be raised to the 2.2 power. So you really have to look at this in terms of the implied hazard rates over the range of values of X1 itself. This is different from simple dichotomous variables where it is appropriate to be skeptical of hazard ratios greater than 2 and be very skeptical of hazard ratios greater than 4 because very few discrete things have that much effect on most time-to-event outcomes that large.


Well, you can't really say that without doing a direct comparison using -lincom-.

Thank you for your detailed explanation!