Centile charts II: alternative nonparametric approach for establishing time-specific reference centiles and assessment of the sample size required.

BACKGROUND: Reference intervals, and more generally centile estimates, are used to characterize a reference population for the purposes of interpreting an individual patient's clinical measurement. We describe methods of calculating reference intervals where these centiles vary with a covariate, usually age or time. METHODS: The US Food and Drug Administration and the IFCC have made recommendations on two approaches: the parametric approach, which models the structural characteristics of the data set with a theoretical distribution, and the nonparametric approach, which makes no particular assumption about this structure. In this report we propose a nonparametric procedure that relies on the principles of regression and show how sample size determination can be assessed. We also show how the sample size calculation is influenced by the distribution of the times measured. RESULTS: We illustrated our method on three data sets and compared the results for our proposed nonparametric method with parametric estimates. We showed that the bias is reduced and that the nonparametric method is less likely to produce fluctuating profiles. CONCLUSIONS: To achieve adequate precision the sample size needs to be larger than 120, as has often been recommended. If there is doubt about the parametric model, then threshold sample sizes may need to be as high as 500.

Centile charts I: new method of assessment for univariate reference intervals.

BACKGROUND: We introduce a new criterion, the percentile inclusion probability, for comparing methods for calculating reference intervals. The criterion is compared with a previously published measure of reliability suggested by Linnet (Linnet K. Clin Chem 1987;33:381-6), the ratio of the width of the confidence interval for the percentile to that of the reference interval. METHODS: Data were simulated from a range of theoretical statistical distributions representing the shapes of data sets encountered in clinical investigations. The two-stage transformation of the data to a gaussian distribution recommended by the IFCC was compared with a nonparametric approach. RESULTS: The percentile inclusion probability criterion identified that the parametric approach is in some cases seriously affected by bias. Using different parametric models, we compared nonparametric and parametric methods for two sets of clinical data and showed that the parametric approach is susceptible to model choice. CONCLUSIONS: Sample sizes significantly greater than those currently recommended are required to establish reference intervals, regardless of whether parametric or nonparametric methods are used. Parametric methods are preferable when the data are truly gaussian, but are only marginally better than nonparametric methods when data transformation is needed to achieve a gaussian shape.