Re-interpreting conventional interval estimates taking into account bias and extra-variation

We propose the following way of re-interpreting conventional results. Given a specified focal value for a target parameter (typically the null value, but possibly a non-null value like that representing a twofold risk), the difference between the focal value and the nearest boundary of the confidence interval for the parameter is calculated. This represents the maximum correction of the interval boundary, for bias and extra-variation, that would still leave the focal value outside the interval, so that the focal value remained "incompatible" with the data. We describe a short example application concerning a meta analysis of air versus pure oxygen resuscitation treatment in newborn infants. Some general guidelines are provided for how to assess the probability that the appropriate correction for a particular study would be greater than this maximum (e.g. using knowledge of the general effects of bias and extra-variation from published bias-adjusted results).Although this approach does not yet provide a method, because the latter probability can not be objectively assessed, this paper aims to stimulate the re-interpretation of conventional confidence intervals, and more and better studies of the effects of different biases.Conventional causal estimates from observational data involve many assumptions, e.g. assumptions about random exposure assignment, selection and participation, ignorable missing data and absence of measurement error [[1], ch. 12–17; [2,3]]. Although causal systems in epidemiology are commonly assumed to be so complex that one cannot expect to understand or correct for all biases, one can hope to adjust for the major ones and estimate uncertainty more accurately [2].Conventional frequentist analyses often yield biased point estimates because they implicitly set all bias parameters (e.g. misclassification probabilities) to zero. Bias also arises from misspecation of models, e.g. the ignoring of covariates or of heterogeneity in individual effects [4,