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

[cpanderson]

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





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