# How to combine two hazard ratios from the study for a meta-analysis?

I've been searching for a way to combine two hazard ratios from the same study for a meta-analysis, but found nothing. Does anyone know how to do this?

Any thoughts would be great.

Good Day,

Simon

• Hi everybody, I've been searching for a way to combine two hazard ratios from the same study for a meta-analysis, but found nothing. Does anyone know how to do so ? Any thoughts would be grate. Good Day, Simon Commented Aug 31, 2011 at 14:51

Hazard ratios can be combined if you have their 95% confidence intervals.

For instance, in Stata, using the user command metan (type findit metan from within Stata if you don't already have it), you can use the following code in a do file to check out how the HRs can be combined:

clear all

input str6 trialname hr ll ul
Trial1 0.7 .46 1.08
Trial2 1.05 .82 1.34
end

metan hr ll ul, effect(Hazard Ratio) null(1) xlabel(0, .5, 1, 1.5) ///
lcols(trialname) texts(200) force


Which gives the following output as well as a forest plot:

               Study     |     ES    [95% Conf. Interval]     % Weight
---------------------+---------------------------------------------------
Trial1               |  0.700       0.460     1.080         41.30
Trial2               |  1.050       0.820     1.340         58.70
---------------------+---------------------------------------------------
I-V pooled ES        |  0.905       0.706     1.105        100.00
---------------------+---------------------------------------------------
Heterogeneity calculated by formula
Q = SIGMA_i{ (1/variance_i)*(effect_i - effect_pooled)^2 }
where variance_i = ((upper limit - lower limit)/(2*z))^2

Heterogeneity chi-squared =   2.87 (d.f. = 1) p = 0.090
I-squared (variation in ES attributable to heterogeneity) =  65.2%

Test of ES=0 : z=   8.91 p = 0.000


I hope this helps. If you don't use Stata, I'm sure any stats package can do a similar thing if you adapt the code.

• Nice answer, but one caveat: The OP said that the two hazard ratios came from the same study. If that means that the two HRs were calculated based on the same sample of subjects (or at least overlapping groups to some extent), then the two HRs cannot be assumed to be independent (which the method described above assumes). Commented Aug 31, 2011 at 16:45
• That is true, but if they're from the same study, he's got all the data and presumably could calculate an overall HR primarily. To the OP: why do you need to combine HRs from the same study? Commented Aug 31, 2011 at 17:27
• (OP) it's for a meta-analysis. Let's say I have 10 hazard ratio. 8 of them are global HR from 8 differents studies. The last 2 are from the same study. I can't use the global HR because there's one category of more comparatively of the others studies. Commented Aug 31, 2011 at 18:36
• (I don't have the raw data) Commented Aug 31, 2011 at 18:36
• It's not safe to assume you can just calculate an overall HR. Sub-group or stratified reporting is pretty common. @user6101 Do the authors of the study give any information about how the HRs were obtained? Did they stratify the analysis, or is this the output of a regression model. If they literally split their population, it's pretty common to treat them as two separate studies. Commented Aug 31, 2011 at 22:34