I'm aware of the issues regarding the use of relative risk in a case control study. But a colleague recently told me that odds ratios are inappropriate for cross-sectional and cohort studies but can't seem to elaborate further. I think he's just assuming that since relative risk is used in cohort studies rather than case controls, odds ratios must be used for case controls and not cross-sectional studies or cohorts. However, I can't find very much information of the appropriateness of odds ratios in these contexts. Can anyone point me in the right direction? Thanks!
Quick reference can be made to Bhopal's Concepts of Epidemiology 2nd edition (Ch. 9).
Odds ratios calculations are possible and valid in cohort, case-control and cross-sectional designs, but the OR is often not the estimate that is desired or is less efficient than alternatives.
1) Cross-sectional studies often want to estimate prevalence, so a relative measure such as OR wouldn't make sense if prevalence is your goal. It is certainly possible to estimate the OR though.
2) Cohort studies will have information about person-time at risk, and so the desired outcomes are often incidence rates, population attributable risk, or risk ratios. The odds ratio estimate for rare outcomes will approximately estimate the risk ratio in this design, but it makes more sense to compute the risk ratio directly.