Differences in results between -metan- and -cc- for the Breslow-Day test

[Tiago Pereira]

Dear Statalisters,

I noticed major differences between -metan- and -cc- for the Breslow-Day test of homogeneity of odds ratio. Apparently, major differences appear when there are some cells from the 2x2 table with zero events. Please, see the code below:

a = events among exposed persons
b = non-events among exposed persons
c = events among non-exposed persons
d = non-events among non-exposed persons

clear
input a b c d
a b c d
2 43 4 40
2 35 0 37
3 36 0 39
4 34 2 36
5 40 3 42
3 45 2 46
end
metan a b c d, or breslow nograph
local bd1 = r(het)
rename a counts1
rename b counts2
rename c counts3
rename d counts4
gene strata = _n
qui reshape long counts, i(strata) j(j)
gene exposure = cond(j==1|j==2,1,0)
drop j
gene event = cond(mod(_n,2),1,0)
qui expand counts
cc event exposure, by(strata) bd woolf
local bd2 = r(chi2_bd)
*/"Breslow-Day's chi-square from -metan-"
dis `bd1'
*/ "Breslow-Day's chi-square from -cc-"
dis `bd2'

If I replace both 0's by any integer >=1, both -cc- and -metan- give nearly identical results. However, with zeros, results are greatly different. Hence, my question is: Which one should we trust for sparse data?

All the best,

Tiago

[Tiago Pereira]

Just realized that I've been missing a line in my code. Before expanding data, I forgot of adding
drop if counts==0
Really sorry for that. Both -cc- and -metan- agree in their results - with -metan- being a little more conservative.