Probability-based construction of reference ranges for ratios of log-gaussian analytes: an example from automated...

Reference ranges (RRs) are frequently used for interpreting laboratory values in clinical trials, assessing abnormality of laboratory results, and combining results from different laboratories. When a clinical laboratory measure must be derived from other tests, eg, the WBC differential percentage from the WBC count and WBC differential absolute count, a derivation of the RR may also be required. A naive method for determining RRs calculates the upper and lower limits of the derived test from the upper and lower limits of the measured values using the same algebraic formula used for the derived measure. This naive method and any others that do not use probability-based transformations do not maintain the distributional characteristics of the RRs. RRs derived in such a manner are deemed uninterpretable because they do not contain a specific proportion of the distribution. We propose a probability-based approach for the interconversion of RRs for ratios of 2 log-gaussian analytes. The proposed method gives a simple algebraic formula for calculating the RRs of the derived measures while preserving the probability relationships. The nonparametric method and a parametric method that takes the log transformation, estimates an RR, and then exponentiates are provided as comparators. An example that compares the commonly used naive method and the proposed method is provided on automated leukocyte count data. This provides evidence that the proposed method maintains the distributional characteristics of the transformed RR measures while the naive method does not.