  When epidemiologic studies are conducted in a subset of the population,
selection bias can threaten the validity of causal inference. This bias can
occur whether or not that selected population is the target population, and can
occur even in the absence of exposure-outcome confounding. However, it is often
difficult to quantify the extent of selection bias, and sensitivity analysis
can be challenging to undertake and to understand. In this article we
demonstrate that the magnitude of the bias due to selection can be bounded by
simple expressions defined by parameters characterizing the relationships
between unmeasured factor(s) responsible for the bias and the measured
variables. No functional form assumptions are necessary about those unmeasured
factors. Using knowledge about the selection mechanism, researchers can account
for the possible extent of selection bias by specifying the size of the
parameters in the bounds. We also show that the bounds, which differ depending
on the target population, result in summary measures that can be used to
calculate the minimum magnitude of the parameters required to shift a risk
ratio to the null. The summary measure can be used to determine the overall
strength of selection that would be necessary to explain away a result. We then
show that the bounds and summary measures can be simplified in certain contexts
or with certain assumptions. Using examples with varying selection mechanisms,
we also demonstrate how researchers can implement these simple sensitivity
analyses.
