Approximations and heuristics for the "cause-modified" life table

Abstract

Life-table analysis can help to gauge the lifetime impacts that accrue from modifications to (age-specific) baseline mortality. Modifications of interest include those stemming from risk-factor-related exposures or from interventions. The specific algorithm used in these analyses can be called a cause-modified life table (a generalization of the cause-deleted life table). The author presents an approach for approximating that algorithm and uses it to obtain remarkably simplified expressions for approximating three indices of common interest: life-years lost (LYL), excess lifetime risk ratio (ELRR), and risk of exposure-induced death (REID). These efforts are restricted to the special case of multiplicative increases to baseline mortality (modeled as an excess rate ratio, ERR). The simplified expressions effectively "break open" what is often treated as a "black-box" calculation. Several insights result. For a practical range of risk factor impacts (ERRs), each index can be related to the ERR as a function of a baseline summary statistic and a "characteristic number" specific to the population and cause of interest. Conveniently, those numbers help form "rules of thumb" for translating among the three indices and suggest heuristics for extrapolating indices across populations and causes of death. © 2005 Society for Risk Analysis.