ABSTRACT
Associations are distinguished from causal effects. Three sources of bias are described: confounding, selection bias, and measurement error. Relationships between risk ratios, rate ratios, and odds ratios in a closed population are described. When the risk ratio is >1, then usually 1 < risk ratio < rate ratio < odds ratio. A data example illustrating these relationships is given and the role of person-time in producing these relationships is described. A counter-example is shown which violates these relationships. When outcomes are sufficiently rare, the odds ratio from a case-control study estimates the risk ratio. The odds ratio from a case-control study that uses density sampling estimates the rate ratio. Some history regarding the use of rate ratios and rate differences is given and reasons for choosing one or the other of these measures is described. Effect modification (variation in association, heterogeneity, subgroup analysis) may be present on the multiplicative scale but not the additive scale and vice versa.
