Negative values and variance functions: Implications for statistical analysis

When reporting concentrations of substances in biological specimens it has been virtually universal practice to suppress negative results, initially by left-censoring negative results to zero and more recently by left-censoring to values such as limit of blank, limit of detection or even limit of quantification. Negative concentrations are obviously nonsensical and current reporting practices place proper emphasis on assisting the clinician. However, it is easily overlooked that negative concentrations are merely artefacts of data reduction and while adjusting them is sensible clinical practice there are potentially adverse consequences for statistical analysis, in particular for those parametric summaries and analyses which rely on reliable estimates of low-end uncertainty. This article puts a case for the availability of negative results, describes complications with respect to estimating variance functions and discusses practical workarounds.