Establishing upper reference limits for left-censored and contaminated data

When one establishes reference interval limits, measurements can sometimes be characterized by either A) being left-censored or B) being contaminated in the upper end. Although solutions to both characteristics have been described separately, no one to our knowledge has been handling the case when both characteristics are present. Left-censored data (A) are often wrongfully handled simply by using limit of detection (LOD), which leads to high mean estimates and too-low standard deviation estimates and hence incorrect cutoffs. Ignoring the characteristic (B), researchers often use transformations to handle the observed non-Gaussianity, which leads to too- high cutoffs and an increased proportion of false negatives (type 2 error). We propose a method based on normal quantile plots and OLS regressions to