Odds ratios multiple comparisons

Question

I have to assess for each product p, the odds ratio associated (success/failure). The data are in this table:

N_success   N_trials    p1    p2   p3    p4   p5
5          310         n     n     n     n    n
17         700         n     y     n     n    y
12         650         y     y     y     n    n
27         214         n     y     n     n    y
0          87          n     n     n     y    n

So I did that and I got the odds ratios for each plus the 95% asymptotic confidence intervals:

p1= (0.2558322 0.48442194 0.91725993)
p2= (1.1584454 2.9114056 7.316946)
p3= (0.2558322 0.48442194 0.91725993)
p4= nil
p5= (1.738197 3.0642326 5.4018736)

Now is this correct way to assess? There are at least two situations where the lower 95% CI of the OR is above 1 (p2 and p4) but should I not take into account multiple comparisons? What is the best way to do that with odds ratios (Bonferroni, others)? Is it better to use logistic regressions (and how)? Thanks

Answer 1

I believe you could use "simultaneous score confidence interval for OR" to analyze your question. The reference is Agresti et al. 2008 Simultaneous confidence intervals for comparing binomial parameters. Biometrics 64 1270-1275.

The R code is available in http://www.stat.ufl.edu/~aa/cda/software.html

Sincerely,