I have a cross-sectional study in which my dependent variable is a binary outcome measure (yes/no). At univariate level, chi-square test and simple logistic regression was performed to yield the unadjusted odds ratios, 95% CI and p-values. This was followed by multiple logistic regression analysis. While multiple logistic regression gives adjusted odds ratios, are the 95% CI yielded corrected for multiplicity? How do we adjust for multiplicity of 95% CIs - can it be checked using SPSS and will the Hochberg step-up procedure be appropriate?
No, CIs are usually not adjusted for multple testing. If you want to do this, a simple approach is to apply the Bonferroni-correction:
Instead of the (1-α)-CI you calculate the (1-α/k)-CI, where k is the number of coefficients. For a 95%-CI, α=0.05. If you have 5 coefficients, the "family-wise 95%-CIs" are obtained as individual 99%-CIs (α/k = 0.05/5 = 0.01; 1-0.01 = 0.99).