Linear regression estimation of minimal detectable concentration. Thyrotropin as an example

Minimal detectable concentration is an important analytic feature of certain clinical immunoassays. We believe that accuracy is an important component of the minimal detectable concentration; for a given observed concentration to be meaningful, it should reflect a consistent linear relationship with the amount of analyte actually present.

To evaluate the minimal detectable concentration, we developed a linearity regression protocol based on accuracy and also accounting for between-run variability. Using serial twofold dilutions of serum samples, we regressed the log of concentration (x) and of dilution (y) with linear, second-, and third-order polynomials. Initially, we evaluated two elements to find the linear region of the dataset, establishing the statistical significance of the beta coefficients with a t test and the reduction of the sum of square of the residuals between the linear regression and the higher-order regressions by means of an F test. As needed, we successively eliminated the lowest point until the linear regression was the best fit. Once we found the best fit, we added the most recently removed point back and calculated the difference between the value predicted by the first-order regression and the observed value. If the difference was not analytically significant, then we considered the point to be part of the linear set; otherwise, it was not included. In either case, the lowest included point was considered to be the minimal detectable concentration.

We applied the technique in evaluating two automated systems for serum thyrotropin. One system appeared linear and accurate down to 0.02 mU/L, or better, approximately 77% of the time, and to 0.01 mU/L 68% of the time. The second system was linear infrequently and appeared to be useful down to 0.02 mU/L, or better, only about 20% of the time.

This accuracy-based approach to determining the minimal detectable concentration is an attractive alternative to current empiric approaches, which are based only on interassay variability.