[BioC] Overlap of 3 gene lists and the Mantel-Haenszel test

[Edwin Groot]

Hello all,
For calculating the significance of the overlap of 2 gene lists I use
either the Fisher exact test or the hypergeometric distribution.
When I tried this on the overlap of 3 gene lists I have to make a 2x2x2
contingency table of what is IN or NOT in a list. Unfortunately the
Fisher test cannot handle multidimensional contingency tables.
Can someone with statistics background check if the Mantel-Haenszel
test can be used to calculate the significance of the overlap of 3 gene
lists? My sample code is below.

# Here is a case that has an overlap close to that expected by chance.
The experiment has 2000 genes, and 3 lists of 50, 100 and 200 genes
each. In the overlap of all 3 lists, 5 genes are found.
> c.table <- c(5,15, 5,175,   0,80, 40,1680)
> dim(c.table) <- c(2,2,2)
> dimnames(c.table) <- list(List1=c("in1","not1"),
List2=c("in2","not2"), List3=c("in3","not3"))
> c.table
, , List3 = in3

      List2
List1  in2 not2
  in1    5    5
  not1  15  175

, , List3 = not3

      List2
List1  in2 not2
  in1    0   40
  not1  80 1680

> sum(c.table)
[1] 2000
> fisher.test(c.table)
Error in fisher.test(c.table) : if 'x' is not a matrix, 'y' must be
given
> mantelhaen.test(c.table)

        Mantel-Haenszel chi-squared test with continuity correction

data:  c.table 
Mantel-Haenszel X-squared = 1.1764, df = 1, p-value = 0.2781
alternative hypothesis: true common odds ratio is not equal to 1 
95 percent confidence interval:
 0.764363 5.403287 
sample estimates:
common odds ratio 
         2.032258 

The test tells me that the overlap is probably due to chance alone,
which is what I expected.
>From what I understand, the Mantel-Haenszel tells me that it is testing
that the overlap of List 1 and List 2 is independent from List 3. To
me, that seems like extending the Fisher test to a third dimension
(gene list).

Thanks for your insights,
Edwin
-- 
Dr. Edwin Groot, postdoctoral associate
AG Laux
Institut fuer Biologie III
Schaenzlestr. 1
79104 Freiburg, Deutschland
+49 761-2032948