[R] Comparing summary hazard ratios in meta-analysis

[Viechtbauer Wolfgang (STAT)]

Those hazard ratios and CIs seem a bit strange. On the log-scale, they should be symmetric, but they are not. Could be due to heavy rounding though. At any rate, it comes down to this:

hr    <- c(3.12, 1.15)
ci.lb <- c(2.2, 1.03)
ci.ub <- c(4.1, 2.6)
meta  <- c(1,2)

### log-transform hazard ratios and compute standard error based on the CI bounds
yi  <- log(hr)
sei <- (log(ci.ub) - log(ci.lb)) / (2*1.96)

library(metafor)
res <- rma(yi ~ factor(meta), sei=sei, method="FE")
res

So, yes, the two hazard ratios are significantly different from each other.

Best,
Wolfgang

--   
Wolfgang Viechtbauer, Ph.D., Statistician   
Department of Psychiatry and Psychology   
School for Mental Health and Neuroscience   
Faculty of Health, Medicine, and Life Sciences   
Maastricht University, P.O. Box 616 (VIJV1)   
6200 MD Maastricht, The Netherlands   
+31 (43) 388-4170 | http://www.wvbauer.com   

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of Michael Dewey
> Sent: Friday, November 21, 2014 13:25
> To: Mario Petretta; r-help at r-project.org
> Subject: Re: [R] Comparing summary hazard ratios in meta-analysis
> 
> On 21/11/2014 08:51, Mario Petretta wrote:
> > Dear all,
> >
> > I use R 3.1.1 for Windows.
> >
> > I performed two different meta-analysis assessing the prognostic value
> of
> > two different tests in patients with coronary artery disease. The study
> > included in the two analysis are different.
> 
> That makes life simpler.
> 
> >
> > The variable of interest in dichotomous (normal/abnormal result) for
> both
> > tests.
> >
> > The effects size is hazard ratio and its standard error (ln units) for
> both
> > meta-analysis.
> 
> It sounds as though you might want to use meta-regression. You will need
> a single data frame containing at least log hr, se of log hr, an
> identifier for the test. I would use the metafor package for this, look
> in the documentation for how to incorporate a moderator (your test
> variable). The advantage of meta-regression is that you not only get a
> test but also a measure of how different the hr are with a confidence
> interval.
> 
> > I would like to statistically compare the two summary hazard ratios and
> 95%
> > CI (eform) obtained from the two meta-analysis.
> >
> > For one meta-analysis: HR 3.12 (95% CI 2.2 - 4.1)
> > For the other: HR 1.25 (95% CI 1.03 - 2.6)
> >
> > It is possible or I'm comparing apples with oranges?
> >
> > Any suggestion is welcome.
> >
> > -------------------------------------------------------
> > Mario Petretta
> > Associate Professor of Internal Medicine
> > Department of Translational Medical Sciences Naples
> > University Federico II Italy