  Unmeasured confounding, selection bias, and measurement error are well-known
sources of bias in epidemiologic research. Methods for assessing these biases
have their own limitations. Many quantitative sensitivity analysis approaches
consider each type of bias individually, while more complex approaches are
harder to implement or require numerous assumptions. By failing to consider
multiple biases at once, researchers can underestimate -- or overestimate --
their joint impact. We show that it is possible to bound the total composite
bias due to these three sources, and to use that bound to assess the
sensitivity of a risk ratio to any combination of these biases. We derive
bounds for the total composite bias under a variety of scenarios, providing
researchers with tools to assess their total potential impact. We apply this
technique to a study where unmeasured confounding and selection bias are both
concerns, and to another study in which possible differential exposure
misclassification and unmeasured confounding are concerns. We also show that a
"multi-bias E-value" can describe the minimal strength of joint bias-parameter
association necessary for an observed risk ratio to be compatible with a null
causal effect (or with other pre-specified effect sizes). This may provide
intuition about the relative impacts of each type of bias. The approach we
describe is easy to implement with minimal assumptions, and we provide R
functions to do so.
