ABSTRACT
Exposed and unexposed subjects are exchangeable if, aside from exposure, they are alike regarding their distribution of risk factors for an outcome. Whichever group is exposed, the estimate of association will not change. The crude (collapsed, unadjusted, or marginal) comparison of exchangeable groups is an unbiased estimate of causal effect. Data are said to be collapsible if the crude (collapsed) association is equal to the stratified (adjusted or conditional) association. If the association is measured by the risk ratio or difference, then adjusting for l (conditioning or stratifying on) some other factor related to the outcome, such as age, will not change the estimated effect when the compared groups are exchangeable. But if the association is expressed as an odds, rate, or hazard ratio, or a rate difference, the adjusted (standardized or conditional) association will be further from 1 than the unadjusted (collapsed or marginal) estimate. This means a rate ratio or difference is usually not an estimate of average effect. Rate ratios and differences are collapsible (the adjusted and unadjusted comparison of exchangeable populations are equal) if person-time is not influenced by the outcomes; for example, in a study of recurrent events in which all events are used and subjects are followed until the study ends. Rate ratios and differences are also collapsible if outcomes are uncommon.
