# [R-meta] Meta-Analisys whit events numbers, RR, OR and HR. It's possibe?

Guido Schwarzer @c @end|ng |rom |mb|@un|-|re|burg@de
Fri Jan 29 17:32:57 CET 2021

```Am 29.01.21 um 16:29 schrieb Martin Lobo:
> [...] I have six studies that report HR and its 95% CI. 2 studies that report number of events in the two branches. 3 studies that report OR and its 95% CI.
Dear Martin,

Tierney et al. (2007) describe why using event numbers or odds ratios /
risk ratios for time-to-event data can be problematic. Accordingly, I
would recommend to base the main analysis on studies providing hazard
ratios and to consider the meta-analysis of hazard and odds ratios as a
sensitivity analysis (with subgroups defined by effect measure).

> [...] Now, I could add the data of the papers that report OR for example:
>
> OR (0,47 , 0.77, 072)
> IC95% L (0.24, 0.52, 0.55)
> IC95% U (0.91, 0.81, 0.89)
>
> HR <- c(log(1.05),log(0.44), log(0.31), log(0.77), 0.47,0.77,0.72)
> lower.HR <- c(log(0.65), log(0.16), log(0.09), log(0.68),0.24, 0.52, 0.55)
> upper.HR <- (log(1.69), log(1.22), log(1.01),log( 0.87),0.91, 0.81, 0.89)
>
>
> metagen(log(HR), lower = log(lower.HR), upper = log(upper.HR),
>          studlab = study, sm = "HR")
>
> Is this correct or should I analyze the HR on the one hand and the OR on the other?
First, you are taking double logs for hazard ratios. Second, as
mentioned above, I would conduct a subgroup analysis:

HR       <- c(1.05, 0.44, 0.31, 0.77, 0.47, 0.77, 0.72)
lower.HR <- c(0.65, 0.16, 0.09, 0.68, 0.24, 0.52, 0.55)
upper.HR <- c(1.69, 1.22, 1.01, 0.87, 0.91, 0.81, 0.89)
##
effect.measure <- rep(c("HR", "OR"), c(4, 3))
##
metagen(log(HR), lower = log(lower.HR), upper = log(upper.HR),
sm = "HR", byvar = effect.measure)

> [...] all studies report HR of statin patients. HR 0.78 patients taking statins had 22% fewer events than those not taking it.
>
> One study reports the HR of patients not taking statins. HR2.17 (95% CI 1.04-4.54). In other words, those who did not take statins had twice the number of events.

If the hazard ratio for group B vs A is 'x' than the hazard ratio for A
vs B is '1 / x'. Accordingly, you can calculate the hazard ratio for
statins vs no statins as 1 / 2.17. The lower confidence limit is 1 /
4.54 and the upper limit is 1 / 1.04.

Best wishes,
Guido

Reference:

Tierney JF, Stewart LA, Ghersi D, Burdett S, Sydes MR. Practical methods
for incorporating summary time-to-event data into meta-analysis. Trials.
2007;8:16.

```