Louisa H. Smith (Harvard TH Chan School of Public Health)
, Tyler VanderWeele

2019-07-01

# Abstract

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
exposureâ€“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.

### Citation

For attribution, please cite this work as

Smith & VanderWeele, "Bounding bias due to selection". Epidemiology, 2019.

BibTeX citation

@article{smith2019bounding,
author = {Smith, Louisa H. and VanderWeele, Tyler},
title = {Bounding bias due to selection},
journal = {Epidemiology},
year = {2019},
note = {https://doi.org/10.1097/EDE.0000000000001032},
doi = {10.1097/EDE.0000000000001032},
volume = {30},
issue = {4}
}