[R-meta] Ratio of Means

[Viechtbauer Wolfgang (SP)]

Please keep r-sig-meta-analysis at r-project.org in cc.

Yes, the same formula hold regardless of the outcome measure.

The row/column names of the G matrix tell you what levels they refer to. In the example:

> res$G
         CON      EXP
CON 2.407333 1.757327
EXP 1.757327 1.431371

So, the variance in the log odds ratios (amount of heterogeneity) is:

> tau2 <- res$G[1,1] + res$G[2,2] - 2* res$G[1,2]
> tau2
[1] 0.3240504

The conditional variance in the log odds in the treatment (EXP) groups (and also of the log odds ratios) is:

> tau2.cond <- res$G[2,2] - res$G[1,2]^2 / res$G[1,1]
> tau2.cond
[1] 0.1485416

So, baseline risk explains:

> (tau2 - tau2.cond) / tau2
[1] 0.5416095

that is, 54% of the heterogeneity.

In your case, it would be about 2%.

Best,
Wolfgang

-- 
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and    
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD    
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com    

-----Original Message-----
From: Nathan Pace [mailto:n.l.pace at utah.edu] 
Sent: Thursday, July 27, 2017 20:45
To: Viechtbauer Wolfgang (SP)
Subject: Re: [R-meta] Ratio of Means

Hi,

I ended up using ggplot2 (see attached).

The slope is essentially 1 (0.9732  +/- 0.0407).

In van Houwelingen, page 605, there is an estimation of the per cent variance of the vaccination effect explained by the true log-odds of the not-vaccinated group.

I assume these formulas also would hold for the response ratio

The G matrix is used to calculate this. It appears that the G matrix is rotated on the minor axis compared to that reported by van Houwelingen. Correct?

If I assume that G matrix is not rotated, then I would use

var.mu <- G[1, 1] + G[2, 2] - 2 * G[1, 2]

cond.var.mu <- G[1, 1] - (G[1, 2]^2/G[2, 2])

explained.var.mu <- (var.mu - cond.var.mu)/var.mu

If I assume that G matrix is rotated, then I would use

var.mu <- G[1, 1] + G[2, 2] - 2 * G[1, 2]

cond.var.mu <- G[2, 2] - (G[1, 2]^2/G[1, 1])

explained.var.mu <- (var.mu - cond.var.mu)/var.mu

The G matrix for my data is 

         Exp      Ctl
Exp 1.245291 1.234160
Ctl 1.234160 1.268151

This gives an explained variance of either 0.02 (G matrix rotated) or 0.002 (G matrix not rotated).

Thanks always for your comments.

Nathan