  Mortality displacement is the concept that deaths are moved forward in time
(e.g., a few days, several months, and years) by exposure from when they would
occur without the exposure, which is common in environmental time-series
studies. Using concepts of a frail population and loss of life expectancy, it
is understood that mortality displacement may decrease rate ratio (RR). Such
decreases are thought to be minimal or substantial depending on study
populations. Environmental epidemiologists have interpreted RR considering
mortality displacement. This theoretical paper reveals that mortality
displacement can be formulated as a built-in selection bias of RR in Cox models
due to unmeasured risk factors independent from exposure of interest, and
mortality displacement can also be viewed as an effect modifier by integrating
the concepts of rate and loss of life expectancy. Thus, depending on the
framework through which we view bias, mortality displacement can be categorized
as selection bias in the bias taxonomy of epidemiology, and simultaneously
mortality displacement can be seen as an effect modifier. This dichotomy
provides useful implications regarding policy, effect modification, exposure
time-windows selection, and generalizability, specifically why research in
epidemiology may produce unexpected and heterogeneous RR over different studies
and sub-populations.
