Age‐dependent biochemical quantities: An approach for calculating reference intervals

Abstract

Objective. A parametric method is often preferred when calculating reference intervals for biochemical quantities, as non‐parametric methods are less efficient and require more observations/study subjects. Parametric methods are complicated, however, because of three commonly encountered features. First, biochemical quantities seldom display a Gaussian distribution, and there must either be a transformation procedure to obtain such a distribution or a more complex distribution has to be used. Second, biochemical quantities are often dependent on a continuous covariate, exemplified by rising serum concentrations of MUC1 (episialin, CA15.3) with increasing age. Third, outliers often exert substantial influence on parametric estimations and therefore need to be excluded before calculations are made. Material and methods. The International Federation of Clinical Chemistry (IFCC) currently recommends that confidence intervals be calculated for the reference centiles obtained. However, common statistical packages allowing for the adjustment of a continuous covariate do not make this calculation. Results. In the method described in the current study, Tukey's fence is used to eliminate outliers and two‐stage transformations (modulus‐exponential‐normal) in order to render Gaussian distributions. Fractional polynomials are employed to model functions for mean and standard deviations dependent on a covariate, and the model is selected by maximum likelihood. Confidence intervals are calculated for the fitted centiles by combining parameter estimation and sampling uncertainties. Finally, the elimination of outliers was made dependent on covariates by reiteration. Conclusions. Though a good knowledge of statistical theory is needed when performing the analysis, the current method is rewarding because the results are of practical use in patient care.

• Confidence intervals
• covariate
• exponential
• fractional polynomials
• Gaussian
• maximum likelihood
• reference intervals
• regression
• transformation

Acknowledgements

I thank Professor Lars Mørkrid, Department of Medical Biochemistry, Rikshospitalet, Oslo, Professor Odd Olai Aalen, Department of Biostatistics, University of Oslo, referees and editors for valuable comments.