Abstract
Abstract Unmeasured confounding is one of the most important threats to the validity of observational studies. In this paper we scrutinize a recently proposed sensitivity analysis for unmeasured confounding. The analysis requires specification of two parameters, loosely defined as the maximal strength of association that an unmeasured confounder may have with the exposure and with the outcome, respectively. The E-value is defined as the strength of association that the confounder must have with the exposure and the outcome, to fully explain away an observed exposure-outcome association. We derive the feasible region of the sensitivity analysis parameters, and we show that the bounds produced by the sensitivity analysis are not always sharp. We finally establish a region in which the bounds are guaranteed to be sharp, and we discuss the implications of this sharp region for the interpretation of the E-value. We illustrate the theory with a real data example and a simulation.
Highlights
Unmeasured confounding is one of the most important threats to the validity of observational studies
In line with Ding and VanderWeele [3] and VanderWeele and Ding [16] we focus on sensitivity analysis for the causal risk ratio, but we show in Section 6 that all our results carry over with no or little modification to the causal risk difference
When the feasible region of a parameter is not restricted by the observed data distribution, we say that the parameter is variation independent of the observed data distribution. This variation independence is a desirable feature of a sensitivity analysis parameter, since it means that the analyst is free, in any given scenario, to speculate about the plausible values of the parameter, as long as these values are within the a priori feasible region of the parameter
Summary
Unmeasured confounding is one of the most important threats to the validity of observational studies. In a recent publication, Ding and VanderWeele [3], hereafter DV, proposed a method to assess the sensitivity of observed associations to unmeasured confounding. The method requires the analyst to provide guesses of certain sensitivity analysis parameters, defined as the maximal strength of association that an unmeasured confounder may have with the exposure and with the outcome. Given these parameters, the method gives bounds for the causal risk ratio, i.e. a range of values that is guaranteed to include the true exposure effect. In this paper we complement DV’s work, by deriving and clarifying several important points regarding their sensitivity analysis and E-value.
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