LAUSR

Introduction Ding and VanderWeele, hereafter DV, proposed a method to assess the sensitivity of observed associations to uncontrolled confounding. Briefly, this method requires the analyst to provide guesses of two sensitivity parameters RRUD and RREU, loosely defined as the maximal strength of association that an uncontrolled (set of) confounder(s) may have with the outcome and with the exposure, respectively. DV derived a lower bound for the causal exposure–outcome risk ratio as a function of these sensitivity parameters and the observed exposure–outcome risk ratio. By setting the sensitivity parameters to values that are considered plausible for the study at hand, one obtains a lower bound for the causal risk ratio. In a subsequent paper, VanderWeele and Ding coined the term ‘E-value’ for the common value RRUD 1⁄4RREU of the sensitivity parameters that gives a lower bound equal to 1; i.e. the E-value shows the minimum size these sensitivity parameters must have if they are equal and the confounding that they produce is exactly the inverse of the observed association. For an observed risk ratio RR ED above 1, the Evalue turns out to be RR ED þ RR ED RR ED 1 1=2 ; it measures how strong an association the uncontrolled confounder must have with exposure and outcome to entirely explain away RR ED. The larger the E-value, the stronger the required uncontrolled confounding, and (presumably) the more trustworthy the result of the study. DV’s two papers have quickly become influential; as of 28 September 2021, they have 314 and 1431 citations, respectively, according to Google Scholar. In a systematic literature review up to the end of 2018, Blum et al. found 87 papers presenting 516 E-values, and E-values have now been recommended as a main basis for evaluating residual confounding. However, the E-value has also been subject to quite intense debate and criticism. The critics agree that the E-value is merely a transform of the observed risk ratio and thus can mislead because it uses ‘no background or data information on confounders or prevalences, and no expectations about unobserved confounders or correlations with controlled confounders’. We will elaborate on two important ensuing criticisms. Ioannidis et al. argued that a high E-value may not provide much assurance because ‘if dozens of unknown confounders exist, such a [large] composite effect [i.e. such large values of the sensitivity parameters] might not be totally implausible, even if each confounder’s strength of association [with the exposure and the outcome] is modest’. In contrast, Greenland argued that a low E-value may give an unnecessarily pessimistic impression of the study, since ‘confounding by unmeasured factors may be weakened considerably due to their associations with strong controlled confounders (e.g. age and sex)’, and MacLehose et al. argued that ‘the calculation of E-values for unknown and unsuspected confounders is an exercise in