Determination of the Variance of Complex Calculated Clinical Chemistry Tests; Application in Calculated Low Density Lipoprotein and Atherogenic Index of Plasma

Abstract

Introduction: Measurement uncertainty is the random error component of the measurement and is an interval around the measured value, into which the true value lies with some probability. Aim: To determine the uncertainty in the calculation of Low Density Lipoprotein Cholesterol (LDL) cholesterol and the Atherogenic Index of the Plasma (AIP). Materials and Methods: A total of four samples with varying levels of total cholesterol, HDL and triglycerides were measured 34 times in a row to get repeated measurements. The variance of LDL and AIP were determined and compared using three different methods: the empirical distribution, error propagation (using first order Taylor approximation and for AIP second order too) and bootstrapping. Results: The empirical and error propagation variances were essentially identical but the bootstrap variance was lower for both calculated parameters for all samples. Distributions of cholesterol, HDL and triglycerides with constant mean and increasing variance were used to determine the measurement uncertainty using all methods mentioned above. The bootstrap variance was lower than the error propagation variance, for AIP the second order error propagation variance was very near the first order one and all the variances fluctuated in tandem. Conclusion: For complex calculated tests it would be more appropriate to use the bootstrap approach, especially in nonlinear functions, since the error propagation approach may overestimate or in other cases underestimate the measurement uncertainty.

Keywords

• bootstrap
• error propagation
• empirical and error propagation variances
• ldl cholesterol