Regression-based reference limits and their reliability: example on hemoglobin during the first year of life

Calculation of reference limits by regression analysis makes it unnecessary to partition the reference data into subgroups, and age-dependent limits can be estimated within as narrow age intervals as necessary. However, the reliability of the regression-based reference limits has not been considered before. To get valid regression-based confidence intervals (CIs) for reference limits, one must evaluate the convolution of two distributions. In this study, age-dependent reference limits with corresponding CIs were produced for blood hemoglobin concentrations over the age interval from newborns to 12 months. We describe how the variance associated with the reference limits can be estimated, and present a Table from which appropriate values can be chosen for the calculation of regression-based reference limits and exact CIs. Also, an equation for the calculation of approximate CIs is given. The data were modeled by linear regression in several cumulative age groups to find the transition zone where the slope changed. After defining this cutoff point, piecewise linear regression was applied. Reference limits and their CIs calculated by conventional and piecewise linear regression methods were almost the same in older age groups but differed significantly during the period of most rapid age-dependent changes, i.e., during the 2 months after birth.