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. 2021 Sep 1;32(5):617-624.
doi: 10.1097/EDE.0000000000001381.

The Importance of Making Assumptions in Bias Analysis

Richard F MacLehose  1 , Thomas P Ahern  2 , Timothy L Lash  3 , Charles Poole  4 , Sander Greenland  5   6
Affiliations

The Importance of Making Assumptions in Bias Analysis

Richard F MacLehose et al. Epidemiology. .

Abstract

Quantitative bias analyses allow researchers to adjust for uncontrolled confounding, given specification of certain bias parameters. When researchers are concerned about unknown confounders, plausible values for these bias parameters will be difficult to specify. Ding and VanderWeele developed bounding factor and E-value approaches that require the user to specify only some of the bias parameters. We describe the mathematical meaning of bounding factors and E-values and the plausibility of these methods in an applied context. We encourage researchers to pay particular attention to the assumption made, when using E-values, that the prevalence of the uncontrolled confounder among the exposed is 100% (or, equivalently, the prevalence of the exposure among those without the confounder is 0%). We contrast methods that attempt to bound biases or effects and alternative approaches such as quantitative bias analysis. We provide an example where failure to make this distinction led to erroneous statements. If the primary concern in an analysis is with known but unmeasured potential confounders, then E-values are not needed and may be misleading. In cases where the concern is with unknown confounders, the E-value assumption of an extreme possible prevalence of the confounder limits its practical utility.

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Figures

FIGURE 1.
FIGURE 1.
Bias factors for the extent of confounding when RREU = RRUD = 2 and RRobs > 1 over the range of possible values of the prevalence of the confounder in the exposed. Solid line is the Schlesselman bias factor, BFs, and dashed line is the bounding factor of Ding and VanderWeele, BFdvw.
FIGURE 2.
FIGURE 2.
Distribution of the Schlesselman bias factor BFs if prevalence is assumed to follow a triangular distribution with minimum = 0.255, maximum = 0.717, and mode = 0.55. Dark vertical line is the limit from the bounding factor, BFDVW.
FIGURE 3.
FIGURE 3.
G-value(p1) for the strength required for equal confounder-exposure and confounder-disease associations RREU = RRUD to reduce an observed RR = 2 to the null. The E-value of Ding and VanderWeele is obtained at G-value(1) = 3.41.
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