Absence of confounding does not correspond to collapsibility of the rate ratio or rate difference

Miettinen and Cook (Am J Epidemiol 1981; 114:593-603) showed that absence of confounding does not imply collapsibility of the odds ratio; that is, the crude odds ratio need not equal a common stratum-specific odds ratio even if the exposed and unexposed study groups have the same distribution of risk factors. Less well known is that absence of confounding does not correspond to collapsibility of the person-time rate ratio or rate difference. For example, two study groups can have the same distribution of all risk factors and yet the crude rate ratio need not equal a common stratum-specific rate ratio. The present paper provides an example and explanation of this phenomenon. The discrepancy between nonconfounding and collapsibility in rate comparisons arises when person-time is a post-exposure variable whose distribution can be altered by the effects of exposure and other risk factors.