Determination of the lower limit of detection.

In a recent Letter (1) a distinction was made between sensitivity and lower limit of detection (LID). The author stated that these parameters differ and can be determined from a linear calibration plot, with the sensitivity equaling the value of the slope and the LLD equaling the value of the x-intercept. Although correct in the assessment that the sensitivity is equal to the slope of the calibration plot, the author is not correct in stating that the LID is given by the xintercept. The author probably conceptualized the x-intercept as being a measure of a threshold response. However, the x-intercept is also affected by the method’s bias and for this reason cannot be used for the determination of the LLD. The incorrectness of using the x-intercept is apparent by noting that negative x-intercept values would be meaningless in regard to estimating the LID. The essential parameter in the LID determination is the precision of the data points (2). The LID is the lowest value for an analyte (usually expressed as concentration) that can be statistically distinguished from a blank. It can be calculated from either the precision of repeated measurements of a blank or from the scatter of data points about a calibration plot. Although many different means of determining LLD have been proposed, most are based on one of these two methods, differing only in the criteria used for distinguishing the blank from the sample (2, 3). Furthermore, the calculation of the LW by these two methods is based on the same basic principle (4). It is my purpose here to expound upon this principle, more fully to explain how the LLD is calculated from a calibration plot. The first method is currently the most widely used method of LU) determination, in which repeated measurements of analyte concentration are made for a blank. The theoretical basis for this approach is given below (4). Repeated measurements of a blank or of a sample give a distribution of values that is assumed to be gaussian. The standard deviation of this distribution is considered to be independent of the concentration, at least for a small range of analyte concentrations. Thus, the standard deviation of blank measurements equals the standard deviation of measurements on a sample at the LW. For the determination of the LLD, the critical consideration is the separation of the distribution of values for a blank from the distribution of values for a sample having an analyte concentration at the LLD. One criterion for distinctness of the distributions is whether the means are separated by 3.29 standard deviation (SD) units; in this case, there is only a 5% chance of classifying a result in the wrong population. At this separation, 95% of the blank determinations are below the concentration that is midway between the means (referred to as the limit of decision), while 95% of the LID sample determinations are above this midway concentration. In practice, repeated measurements of concentration are made on a blank and a standard deviation is calculated, with the value of the LID being 3.29 SD. Most investigators, however, round down to a 3 SD criterion, corresponding to a 7% chance of misclassification. Some investigators use a 2 SD criterion, which has a 16% chance of misclassification. The above analysis assumes a “wellknown blank” model (2). Note that, for determinations in which a result is obtained by subtracting a blank response from a sample response, there is increased variability in the result (because there is variability associated with both the sample and the blank). The “paired observations” model takes into account this variability (2). For this model there is a 5% chance of misclassification when the means of the distributions of the blank and the LLD sample are separated by 4.65 SD units (compared with 3.29 for the “well-known blank” model). See reference 2 for further information. The second method for the determination of the LLD is the calibration plot method (4). In this method the standard error of the y-estimate for the least-squares regression line, isused inplaceofthe standard deviation of the blank. Confidence limits of the regression line have also been used (3). s,,, is a measure of the average deviation of the experimental values from the regression line, as given by equation 1. Equation 1 defines s,, for a regression line fitted through the experimental points (Xi, Y), where X, is the concentration of analyte and Y, is the analytical signal measured by the technique. The parameters Y,. , and n are the analytical signal predicted by the regression line and the number ofdata points,respectively.