A robust approach to reference interval estimation and evaluation

Abstract

We propose a new methodology for the estimation of reference intervals for data sets with small numbers of observations or for those with substantial numbers of outliers. We propose a prediction interval that uses robust estimates of location and scale. The SAS software can be readily modified to do these calculations. We compared four reference interval procedures (nonparametric, transformed, robust with a nonparametric lower limit, and transformed robust) for sample sizes of 20, 40, 60, 80, 100, and 120 from χ2 distributions of 1, 4, 7, and 10 df. χ2 distributions were chosen because they simulate the skewness of distributions often found in clinical chemistry populations. We used the root mean square error as the measure of performance and used computer simulation to calculate this measure. The robust estimator showed the best performance for small sample sizes. As the sample size increased, the performance values converged. The robust method for calculating upper reference interval values yields reasonable results. In two examples using real data for haptoglobin and glucose, the robust estimator provides slightly smaller upper reference limits than the other procedures. Lastly, the robust estimator was compared with the other procedures in a population where 5% of the values were multiplied by a factor of 5. The reference intervals were calculated with and without outlier detection. In this case, the robust approach consistently yielded upper reference interval values that were closer to those of the true underlying distributions. We propose that robust statistical analysis can be of great use for determinations of reference intervals from limited or possibly unreliable data.