A method to quantify deviations from assay linearity

We present a statistical method to quantify deviations from linearity for assays that veer from linear assay responses. Our procedure handles the common case of unequally spaced analyte levels and nonconstant variance and provides a least-squares estimate with a confidence interval for the amount of deviation from assay linearity at a specified analyte concentration. This estimate of assay bias due to nonlinearity goes beyond the NCCLS EP6 lack-of-fit test, which tests for only the presence of nonlinearity. Knowing that nonlinearity is present is insufficient; users need to know the magnitude of the bias caused by nonlinearity. Our method can also be used with multifactor designs that estimate other systematic assay effects such as drift and carryover, thus obviating the need for a separate protocol to assess linearity. The procedure is carried out by adding extra columns to the design matrix corresponding to the concentration level(s) of interest. The extra columns, which replace the quadratic column, are orthogonal to all other columns. We describe a general method of constructing the new columns, and illustrate the procedure with a manual ammonia assay example dataset from EP6.