# An Explanation of Sensitivity and the LLD, LLOQ, and ULOQ of a Multiplex ELISA

Assay sensitivity refers to the ability of a method or instrument to detect an analyte at a specified concentration and is often defined by a detection limit. There are several different “detection limits” that are commonly used in scientific literature, but even when the same terminology is used, there can be differences according to what type of noise contributes to the measurement, calibration methods, instrument precision, etc.

At Quansys Biosciences, we often use three terms to define the range and sensitivity of our multiplex ELISA assays: Lower Limit of Quantification (LLOQ), Lower Limit of Detection (LLD), and Upper Limit of Quantification (ULOQ). The definitions of these terms as used at Quansys Biosciences and in science are discussed below:

## Upper and Lower Limit of Quantification (ULOQ and LLOQ)

The ULOQ and LLOQ are the highest and lowest standard curve points that can still be used for quantification; they are the values below and above which, respectively, quantitative results may be obtained with a specified degree of confidence. In other words, they are the highest/lowest concentration of an analyte that can be accurately measured. Together, the ULOQ and LLOQ define the range of quantification for the assay. Limits of quantitation are matrix, method, and analyte-specific, and can be calculated as follows:

### Equation 1.

*(Calculation used in Q-View)*: ULOQ = Highest standard with a %backfit of 80%-120%, a %CV of < 30%, and a positive mean pixel intensity difference between it and the negative control.

LLOQ = Lowest standard with a %backfit of 75%-125% and %CV for the concentration and a positive mean pixel intensity difference between it and the negative control.

### Equation 2.

*(Commonly used in science to estimate the LLOQ)*: LLOQ = (Mean negative control pixel intensity) + 10 * (StDev of negative control pixel intensities).

## Lower Limit of Detection (LLD)

The LLD is the lowest concentration level that can be determined to be statistically different from a blank at a 99% confidence level. In other words, it is the lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) within a stated confidence limit, generally 1%. The Limit of detection is matrix, method, and analyte-specific, and can be calculated as follows:

### Equation 1.

*(Calculation used in Q-View)*: LLD = 2 * (StDev of negative control pixel intensities before ‘Negative Well Subtraction’) * LLOQ / (Difference between pixel intensity of lowest standard and negative control)

### Equation 2.

*(Commonly used in science to estimate the LLD, which estimate is typically deemed acceptable if it falls within a region where the signal to noise ratio is greater than 5)*: LLD = (Mean negative control pixel intensity) + 2 * (StDev of negative control pixel intensities).

To minimize variability between multiple plates in a single study, we recommend using the lot defined ULOQ / LLOQ, which are selected in “Assay Limits” in the “Data Analysis” tab in Q-View™.

## Reporting

When reporting assay data, it is conventional to include values such as the ULOQ, LLOQ, and LLD. Data that falls outside the limits should be reported as > ULOQ, < LLOQ, or < LLD. Data extrapolated beyond the limits are typically not included in published results.