Computation of time-specified tolerance intervals for hybrid time series with nonequidistant sampling, illustrated...

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 biological rhythms. In particular, growth hormone 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, and they should substitute, whenever possible, for prediction limits. In the case of hybrid data (time series of data collected from a group of subjects), such 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-subjects and among-subjects variances is wanted. Accordingly, we have developed a nonparametric method for the computation of such tolerance intervals. Because the method is based on bootstrap techniques, it 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 a series of growth hormone sampled around the clock in groups of prepubertal children differentiated according to stature. The use of these tolerance intervals may eliminate many false-positive and false-negative diagnoses that might be obtained when relying on time-unspecified single samples. The provision of such tolerance limits introduces time-specification and time-structure evaluation into prevention, diagnosis, and treatment of growth disorders.