Calculation of lifetime relative risks from summary cohort data and application to calculation of attributable fractions

In cohort studies, relative risks are estimated by comparing eventual disease risk in individuals exposed to the risk factor at baseline with similar unexposed individuals. However, such relative risk estimates intrinsically depend on how many of the unexposed individuals develop exposure after baseline and on the ages at which the exposed individuals developed exposure prior to baseline. These factors pertain to the distribution of risk factor incidence in the population, rather than to the causal effect the risk factor has on disease. As such, these cohort relative risk estimates have no straightforward causal interpretation, even after adjustment for confounding. Here, we instead consider initial exposure to the risk factor at differing ages as differing treatments, with corresponding potential outcomes. Subsequently, we define lifetime relative risk as the relative probability of eventual disease comparing initial exposure to the risk factor at differing ages to lifetime non-exposure. We describe a procedure to approximate lifetime relative risks using summary data from published cohort studies, and detail conditions under which such estimation is valid. In addition to being of independent interest, lifetime relative risks are useful in estimating population attributable fractions (PAF)s. In our applied example, we illustrate this connection via application of estimated lifetime relative risks to assess the PAF for incident vascular dementia due to hypertension in the United Kingdom.