# [R-meta] R: It is possible to calculate the Hazard Ratio and 95% CI on different reference groups from summary available data?

Mario Petretta petrett@ @end|ng |rom un|n@@|t
Wed Jul 3 11:49:17 CEST 2019

```Thank you so much for your kind, clear and complete answer.

Mario

-----Messaggio originale-----
Da: Gerta Ruecker [mailto:ruecker using imbi.uni-freiburg.de]
Inviato: martedì 2 luglio 2019 20:05
A: Prof. Mario Petretta; r-sig-meta-analysis using r-project.org
Oggetto: Re: [R-meta] It is possible to calculate the Hazzard Ratio and 95% CI on different reference groups from summary available data?

Dear Mario,

I think this is not possible without further assumptions. You have not
enough information. Even if we assume that all arms in the study are of
equal size, the only thing we roughly know is that the hazard ratio
between arm 3 and the arm mixed of 1 and 2 is something like

hr21 <- 1.89
hr31 <- 3.03
u21 <- 3.33
l21 <- 1.09
u31 <- 5.56
l31 <- 1.67

d21 <- log(hr21)
d31 <- log(hr31)
s21 <- (log(u21) - log(l21))/2/1.96
s31 <- (log(u31) - log(l31))/2/1.96

d12.3 <- d31 - d21/2 # assumes that arm 1 and arm 2 have equal
information size
hr12.3 <- exp(d12.3)

However, we do not know the covariance between the log hazard ratios
log(hr21) and log(hr31) which we would need to estimate the standard
error for this hazard ratio. This covariance is not zero because these
HRs are dependent, as both involve arm 1.

The problem is the same as when having a triangle with two side lengths
known, but we do not know the angle between the known sides. Then we
cannot make inference about the third side.

Best,

Gerta

Am 02.07.2019 um 17:55 schrieb Prof. Mario Petretta:
> Dear mailing list members
>
> I am doing a meta-analysis on the prognostic value of diastolic blood
> pressure (BP).
> A study reported the unadjusted hazard ratio (from Cox regression) for three
> categories:
>
> 1)	BP under 90 - hazard ratio 1 (reference)
> 2)	BP 90 - 99 - hazard ratio 1.89 (95% CI 1.09, 3.33)
> 3)	BP over 100 - hazard ratio 3.03 (95% 1.67, 5.56)
>
> It is possible to combine these hazard ratios and the 95% confidence
> intervals for three categories in two categories, considering together the
> reference category and the second category as a new reference vs the third
> category?
>
> A more general question is: It is possible to convert hazard ratios and 95%
> CI for 3 or more categories to a hazard ratio for 2 categories, changing the
> reference category?
>
>
>
> ___________________________________________
> Mario Petretta, MD, FAHA
> Associate Professor of Internal Medicine
> Department of Translational Medical Sciences
> Naples University "Federico II" - Italy
>
> _______________________________________________
> R-sig-meta-analysis mailing list
> R-sig-meta-analysis using r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis

--

Dr. rer. nat. Gerta Rücker, Dipl.-Math.

Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center - University of Freiburg

Stefan-Meier-Str. 26, D-79104 Freiburg, Germany

Phone:    +49/761/203-6673
Fax:      +49/761/203-6680
Mail:     ruecker using imbi.uni-freiburg.de
Homepage: https://www.imbi.uni-freiburg.de/persons/ruecker/person_view

```