Unifying theory of errors for the analytical methods of concentration-dependent distribution, immunoassay and substoichiometric and subsuperequivalence isotope dilution

Abstract

The statistical uncertainty of results for the concentration-dependent distribution of analyte A, which enters a bimolecular heterogeneous reaction with reagent B after which individual analytical responses S_A and S_AB are measured, has been expressed as the product of three factors, f₁, f₂, and f₃; and these have been tabulated and assessed in numerical form. The first factor f₁ depends on the ratio of variable amounts of analyte A to a constant added amount (e.g., the tracer). Ideally, f₁= 1 at large variable amounts, and at low amounts f₁=∞; the optimum practical ratio of analyte to additive lies in the interval 1:1 to 4:1. The second factor f₂ depends firstly on the yield of analyte binding; ideally, f₂= 1 for quantitative yields of the reaction with substoichiometric (subequivalent) amounts of reagent B; however, even at lower yields, the uncertainty of analysis does not increase seriously (f₂ < 2). The third factor f₃ depends on the mode of measurement of the analytical responses S_A and S_AB. The ideal ratio of signals (e.g., radioactivity or absorbance) used for quantifying free and bound analyte is I=S_A/S_AB= 1, for which f₃= 1. Under optimum performance, the statistical uncertainty for concentration-dependent distribution, radioimmunoassay, and subsuperequivalence isotope dilution analysis methods appears to be of the same order as the errors of analytical response measurements. Simplicity of evaluation of error propagation is demonstrated.