[R] Mixed effects multinomial regression and meta-analysis

[Inman, Brant A. M.D.]

R Experts:

I am conducting a meta-analysis where the effect measures to be pooled
are simple proportions.  For example, consider this  data from
Fleiss/Levin/Paik's Statistical methods for rates and proportions (2003,
p189) on smokers:

Study	   N       Event P(Event)
 1       86       83    0.965
 2       93       90    0.968
 3       136     129    0.949
 4       82       70    0.854
Total    397     372    

A test of heterogeneity for a table like this could simply be Pearson'
chi-square test.  
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smoke.data <- matrix(c(83,90,129,70,3,3,7,12), ncol=2, byrow=F)
chisq.test(smoke.data, correct=T)

> X-squared = 12.6004, df = 3, p-value = 0.005585

------

Now this test implies that the data is heterogenous and that pooling
might be inappropriate. This type of analysis could be considered a
fixed effects analysis because it assumes that the 4 studies are all
coming from one underlying population.  But what if I wanted to do a
mixed effects (fixed + random) analysis of data like this, possibly
adjusting for an important covariate or two (assuming I had more
studies, of course)...how would I go about doing it? One thought that I
had would be to use a mixed effects multinomial logistic regression
model, such as that reported by Hedeker (Stat Med 2003, 22: 1433),
though I don't know if (or where) it is implemented in R.  I am certain
there are also other ways...

So, my questions to the R experts are:

1) What method would you use to estimate or account for the between
study variance in a dataset like the one above that would also allow you
to adjust for a variable that might explain the heterogeneity?

2) Is it implemented in R?


Brant Inman
Mayo Clinic