Handling of values below or above a threshold (Below the Low Limit of Quantification or Above the Upper Limit of Quantification)?

In clinical trials, the samples are often collected and sent to the central laboratory or specialty laboratory for measuring certain parameters (drug concentrations, metabolite concentrations, biomarkers,...). It is not uncommon that the results may be reported as "<xxx" or ">xxx" indicating that the measurement is below or above a threshold, outside the range, or the quality control curves. We call them below the low limit of quantification or above the upper limit of quantification.

How to handle them in the data set and in the analyses?

In the data set, the laboratory results should be reported as it is in character variable. The data listings should use the character variable so that the signs of '<' or '>' will be kept and displayed.

For the purpose of the statistical summaries and analyses, a separate numeric variable should be derived and appropriate rules will be applied to these values below the low limit of quantification or above the upper limit of quantification.

 
Most of the discussions were about the handling of the values below the low limit of quantification (BLQs). See a previous post "BLQs (below limit of quantification) and LLOQ (Lower Limit of Quantification): how to handle them in analyses?" and the researchgate.net discussion board "How should one treat data with <LOQ values during statistical analysis?".

The options for handling the BLQs are:

• Treat BLQs as missing
• Treat BLQs as 0
• Treat BLQs as 1/2 of the LLQ (lower limit of qualification). For example, if the result was reported as "<10" µg, take 5 µg as the measure - this approach is pretty common in handling pharmacokinetic concentration data. 
•  Simply remove the sign of  '<' and take the face value (i.e. LLQ value). For example, if the result was reported as "<10" µg, take 10 µg as the measure. 
• More complicated methods using statistical (regression, maximum likelihood,...) approaches 

There are fewer discussions about handling the values above the upper limit of quantification (ULQ). Usually, these values above the upper threshold will be handled by:

• Treat values above ULQ as missing
• Simply remove the sign of  '>' and take the face value (i.e. ULQ value). For example, if the result was reported as ">100" mg, take 100 mg as the numeric value

In an SAP developed by Astellas, the simple rule was specified for handling the values below or above a threshold:

"For continuous variables that are recorded as “< X” or “> X”, the value of “X” will be used in the calculation of summary statistics. The original values will be used for the listings."

In an SAP developed by Galapagos for their phase 3 study of GLPG1690 in subjects with idiopathic pulmonary fibrosis, the following rules were proposed to handle values below or above a threshold. Their approach of adding or deducting a small number from the face value is unconventional.

7.3. Handling of Values Below (or Above) a Threshold 

Values below (above) the detection limit will be imputed by the value one unit smaller or larger than the detection limit itself. In listings, the original value will be presented. Example: if the database contains the value “<0.04”, then for the descriptive statistics the value “0.03” will be used. The value “>1000” will be imputed by “1001”.