Statistical methods for assays with limits of detection: Serum bile acid as a differentiator between patients with normal colons, adenomas, and colorectal cancer

In analytic chemistry a detection limit (DL) is the lowest measurable amount of an analyte that can be distinguished from a blank; many biomedical measurement technologies exhibit this property. From a statistical perspective, these data present inferential challenges because instead of precise measures, one only has information that the value is somewhere between 0 and the DL (below detection limit, BDL). Substitution of BDL values, with 0 or the DL can lead to biased parameter estimates and a loss of statistical power. Statistical methods that make adjustments when dealing with these types of data, often called left-censored data, are available in many commercial statistical packages. Despite this availability, the use of these methods is still not widespread in biomedical literature. We have reviewed the statistical approaches of dealing with BDL values, and used simulations to examine the performance of the commonly used substitution methods and the most widely available statistical methods. We have illustrated these methods using a study undertaken at the Vanderbilt-Ingram Cancer Center, to examine the serum bile acid levels in patients with colorectal cancer and adenoma. We have found that the modern methods for BDL values identify disease-related differences that are often missed, with statistically naive approaches.