[R] Comparing summary hazard ratios in meta-analysis

Mario Petretta petretta at unina.it
Sun Nov 23 11:46:09 CET 2014

Many thanks again for your suggestions.


Sorry. Effectvely there was a mistake in the HR I previously submitted.


As suggested, I started from scratch and the correct HR are:


HR 3,12 (2,24-4.35)

HR 1,25 (1,03-1,52)





On 23/11/2014 09:23, Viechtbauer Wolfgang (STAT) wrote:

I actually don't see Michael suggesting that you should work with the
individual studies. My interpretation of his reply is that he is suggesting
the same thing that I have done. But in the end, you should get similar
results whether you test those two summary (log) HRs against each other or
if you work with the individual studies and test whether the summary (log)
HRs of the first set is different from the second.

I have cc-ed Michael in case I am misinterpreting his suggestion.

I had originally thought of using the individual studies as Mario
interpreted but I do not have strong feelings either way. I suppose I was
thinking of cases I have seen where either injudicious rounding or typos has
meant that it was better to start from scratch.

[Show Quoted Text - 122 lines][Nascondi Testo quotato] 


-----Original Message-----
From: Mario Petretta [mailto:
petretta a unina.it]
Sent: Friday, November 21, 2014 18:19
r-help a r-project.org
Cc: Viechtbauer Wolfgang (STAT)
Subject: R: [R] Comparing summary hazard ratios in meta-analysis

Many many thanks to Michael Dewey and to Viechtbauer Wolfgang for the
kindly and useful replay !!

I only ask to Wolfgang if I should log-transform hazard ratios and
compute standard error only for the summary hazard ratio estimates or, as
suggested by Michael, for each single study, combining them in a single
data frame and thereafter performing the meta-regression incorporating
the moderator.


-----Messaggio originale-----
Da: Viechtbauer Wolfgang (STAT)
wolfgang.viechtbauer a maastrichtuniversity.nl]
Inviato: venerdì 21 novembre 2014 15:37
A: Michael Dewey; Mario Petretta;
r-help a r-project.org
Oggetto: RE: [R] Comparing summary hazard ratios in meta-analysis

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)

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

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


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/> http://www.wvbauer.com

-----Original Message-----
r-help-bounces a r-project.org
r-help-bounces a r-project.org]
On Behalf Of Michael Dewey
Sent: Friday, November 21, 2014 13:25
To: Mario Petretta;
r-help a 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


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



The effects size is hazard ratio and its standard error (ln units)



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


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

 <http://www.dewey.myzen.co.uk/> http://www.dewey.myzen.co.uk

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