[R] metafor- interpretation of moderators test for raw proportions

[Viechtbauer Wolfgang (STAT)]

Are you sure that output was produced by: rma(yi, vi, data=dat, mods=cbind(LateralWedge,Dome,Complex))?

Because your model does not have an intercept, which suggests that you actually used:

rma(yi, vi, data=dat, mods=cbind(LateralWedge,Dome,Complex), intercept=FALSE)

In that case, the coefficients are the estimated (average) proportions for each level of that moderator. If you want to actually see whether levels differ from each other, you make one of the levels your reference level, leave out the corresponding dummy, and include the model intercept:

rma(yi, vi, data=dat, mods=cbind(Dome,Complex))

Now the coefficients estimate the (average) difference between the proportions for the Dome vs. LateralWedge levels and the Complex vs. LateralWedge levels. If you want to estimate the difference between Dome and Complex, you can use:

rma(yi, vi, data=dat, mods=cbind(LateralWedge,Complex))

Those are all pairwise comparisons. The QM test will tell you whether that factor is significant overall.

Note that you do not need to dummy code those levels manually. You could just use:

rma(yi, vi, data=dat, mods = ~ Technique)

With the relevel() function, you can change which level is used as the reference level. For example:

rma(yi, vi, data=dat, mods = ~ relevel(Technique, ref="LateralWedge"))

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 cpanderson
> Sent: Friday, August 03, 2012 00:43
> To: r-help at r-project.org
> Subject: [R] metafor- interpretation of moderators test for raw
> proportions
> 
> Hello metafor users,
> I'm using metafor to perform a single-effect summary estimate of the raw
> proportion of patients experiencing a post-operative complication, and I'm
> interested in seeing if this proportion differs between the three most
> commonly used surgical techniques.  The software is working as expected,
> but
> I would like to double check on the interpretation of my mixed-effect
> model
> summary.
> 
> The levels of my moderator variable surgery.type are LateralWedge, Dome,
> and
> Complex, which I've dummy coded like this:
> 
> dat$LateralWedge<-ifelse(dat$Technique=="LateralWedge",1,0)
> datDome<-ifelse(dat$Technique=="Dome",1,0)
> dat$Complex<-ifelse(dat$Technique=="Complex",1,0)
> 
> When i fit this random effect model:
> rma(yi,vi,data=dat, mods=cbind(LateralWedge,Dome,Complex))
> 
> I get this output:
> /Mixed-Effects Model (k = 33; tau^2 estimator: REML)
> 
>   logLik  Deviance       AIC       BIC
> -11.2426   22.4852   30.4852   36.0900
> 
> tau^2 (estimate of residual amount of heterogeneity): 0.0925 (SE = 0.0269)
> tau (sqrt of the estimate of residual heterogeneity): 0.3041
> 
> Test for Residual Heterogeneity:
> QE(df = 30) = 654.3038, p-val < .0001
> 
> *Test of Moderators (coefficient(s) 1,2,3):
> QM(df = 3) = 128.7528, p-val < .0001*
> Model Results:
> 
>               estimate      se    zval    pval   ci.lb   ci.ub
> LateralWedge    *0.6462*  0.0722  8.9450  <.0001  *0.5046  0.7878*  ***
> Dome            *0.6659 * 0.1471  4.5283  <.0001  *0.3777  0.9541 * ***
> Complex         *0.6938*  0.1306  5.3136  <.0001 * 0.4379  0.9498*  ***/
> 
> My suspicion is that the test of moderators is addressing the hypothesis
> that the proportion of my outcome is not zero in any of the three groups,
> because all the estimated proportions appear to be well within the
> confidence bounds of the other two groups.  Is this correct?  If it is, I
> would appreciate any suggestions on how I would change that hypothesis
> test,
> so that I am testing whether the proportion in group 1 = the proportion in
> group 2 = the proportion in group 3?
> 
> Thanks for your input,
> Christopher Anderson