A new indirect estimation of reference intervals: truncated minimum chi-square (TMC) approach

All known direct and indirect approaches for the estimation of reference intervals (RIs) have difficulties in processing very skewed data with a high percentage of values at or below the detection limit. A new model for the indirect estimation of RIs is proposed, which can be applied even to extremely skewed data distributions with a relatively high percentage of data at or below the detection limit. Furthermore, it fits better to some simulated data files than other indirect methods. The approach starts with a quantile-quantile plot providing preliminary estimates for the parameters (λ, μ, σ) of the assumed power normal distribution. These are iteratively refined by a truncated minimum chi-square (TMC) estimation. The finally estimated parameters are used to calculate the 95% reference interval. Confidence intervals for the interval limits are calculated by the asymptotic formula for quantiles, and tolerance limits are determined via bootstrapping. If age intervals are given, the procedure is applied per age interval and a spline function describes the age dependency of the reference limits by a continuous function. The approach can be performed in the statistical package R and on the Excel platform.