Computation of time-specified tolerance intervals for hybrid time series, illustrated for growth hormone

The ideal reference interval for a variable of clinical interest would be specific for all deterministic factors affecting that variable, including the time of sampling in relation to predictable variations. In particular, growth hormone (GH) is characterized in children by circadian and ultradian variability, with high peaks of secretion occurring mainly during sleep. For clinical applications, the use of tolerance intervals has been recommended as a substitution for prediction limits. In the case of hybrid data (time series collected from a group of subjects), a tolerance interval could be very difficult to determine following a parametric approach similar to the procedure used for the computation of prediction intervals, especially when consideration of both within-subject and between-subject variances is wanted. Accordingly, we have developed a nonparametric method for the computation of tolerance intervals. The method, based on bootstrap techniques, does not require the assumption of normality or symmetry in the data, and is also more appropriate when dealing with small samples. The method was used to establish time-qualified reference limits for several series of GH sampled around the clock in groups of prepubertal children differentiated according to stature. The provision of such tolerance limits introduces time-specification and time-structure evaluation into the prevention, diagnosis and treatment of growth disorders.