Methods of Dealing with Values Below the Limit of Detection using SAS

Due to limitations of chemical analysis procedures, small concentrations cannot be precisely measured. These concentrations are said to be below the limit of detection (LOD). In statistical analyses, these values are often censored and substituted with a constant value, such as half the LOD, the LOD divided by the square root of 2, or zero. These methods for handling below-detection values results in two distributions, a uniform distribution for those values below the LOD, and the true distribution. As a result, this can produce questionable descriptive statistics depending upon the percentage of values below the LOD. An alternative method uses the characteristics of the distribution of the values above the LOD to estimate the values below the LOD. This can be done with an extrapolation technique or maximum likelihood estimation. An example program using the same data is presented calculating the mean, standard deviation, t-test, and relative difference in the means for various methods and compares the results. The extrapolation and maximum likelihood estimate techniques have smaller error rates than all the standard replacement techniques. Although more computational, these methods produce more reliable descriptive statistics.