BLQs (below limit of quantification) and LLOQ (Lower Limit of Quantification): how to handle them in analyses?

In data analyses of the clinical trial, one type of data is the laboratory data containing the results measured by the central laboratory or specialty laboratory on the specimen (blood sample, plasma or serum sample, urine sample, bronchoalveolar lavage,...) collected from clinical trial participants. The laboratory results are usually reported as quantitative measures in numeric format. However, sometimes, we will see the results reported as '<xxx' or 'BLQ'.

The laboratory measures rely on the assay and the assay has its limit and can only accurately measure the level or concentration to a certain degree - the limit is called the Lower Limit of Quantification (LLOQ) or the Limit of Quantification (LOQ) or the Limit of Detection (LOD). 

In FDA's guidance (2018) "Bioanalytical Method Validation", they defined the Quantification range, LLOQ and ULOQ: 

The quantification range is the range of concentrations, including the ULOQ and the LLOQ that can be reliably and reproducibly quantified with accuracy and precision with a concentration-response relationship.

Lower limit of quantification (LLOQ): The LLOQ is the lowest amount of an analyte that can be quantitatively determined with acceptable precision and accuracy.

Upper limit of quantification (ULOQ): The ULOQ is the highest amount of an analyte in a sample that can be quantitatively determined with precision and accuracy.

According to the article by Vashist and Luong "Bioanalytical Requirements and Regulatory Guidelines for Immunoassays". The LLOQ and LOQ are different. In practice, the LLOQ and LOQ may be used interchangeably. 

The LOQ is the lowest analyte concentration that can be quantitatively detected with a stated accuracy and precision [24]. However, the determination of LOQ depends on the predefined acceptance criteria and performance requirements set by the IA developers. Although such criteria and performances are not internationally adopted, it is of importance to consider the clinical utility of the IA to define such performance requirements.

The LLOQ is the lowest calibration standard on the calibration curve where the detection response for the analyte should be at least five times over the blank. The detection response should be discrete, identifiable, and reproducible. The precision of the determined concentration should be within 20% of the CV while its accuracy should be within 20% of the nominal concentration.

In FDA's guidance "Studies to Evaluate the Metabolism and ResidueKinetics of Veterinary Drugs in Food-ProducingAnimals: Validation of Analytical Methods Used in Residue Depletion Studies", the LOD and LOQ are differentiated a little bit. 

3.4. Limit of Detection

The limit of detection (LOD) is the smallest measured concentration of an analyte from which it is possible to deduce the presence of the analyte in the test sample with acceptable certainty. There are several scientifically valid ways to determine LOD and any of these could be used as long as a scientific justification is provided for their use. 

3.5. Limit of Quantitation

The LOQ is the smallest measured content of an analyte above which the determination can be made with the specified degree of accuracy and precision. As with the LOD, there are several scientifically valid ways to determine LOQ and any of these could be used as long as scientific justification is provided. 

If the level or concentration is below the range that the assay can detect, it will be reported as the BLQ (Below the Limit of Quantification), BQL (Below Quantification Level), BLOQ (Below the Limit Of Quantification), or <xxx where xxx is the LLOQ. The results are seldom reported as 0 or missing since the result is only undetectable using the corresponding assay. It is usually agreed that the BLQ values are not missing values - they are measured, but not measurable. 

In clinical laboratory data with the purpose of safety assessment, the BLQ or <xxx is reported in the character variable. When converting the character variable to the numerical variable, the BLQ or <xxx will be automatically treated as missing unless we do something. The following four approaches may be seen in handling the BLQ values (with an example assuming LLOQ 0.01 ng/mL). 

Reported Value	Converted Value	Explanation
< 0.01 ng/mL	missing	The specific measure will be set to missing and will not be included in summary and analysis.
< 0.01 ng/mL	0	The specific measure will be set to 0 in summary and analysis
< 0.01 ng/mL	0.005 ng/mL	Half of the LLOQ – commonly used in clinical pharmacology studies (Bioavailability and Bioequivalence studies)
<0.01 ng/mL	0.01 ng/mL	Ignore the less than the ‘<’ sign and take the LLOQ as the value for summary and analysis. This approach can also handle the values beyond the ULOQ (upper limit of quantification), for example, '>1000 ng/mL' by removing the greater than '>' sign.

In clinical pharmacology studies (bioavailability and bioequivalence studies), series pharmacokinetic (PK) samples will be drawn and analyzed to get a PK profile for a specific compound or formulation. The series samples will include a pre-dose sample (the sample drawn before the dosing) and multiple time points after the dosing. It is entirely possible to have results reported as BLQ especially for the pre-dose sample and the late time points. BLQ values can also be possible for samples in the middle of the PK profile (i.e., between two samples with non-BLQ values). The rules for handling these BLQs are different depending on the samples at pre-dose, at the middle of the profile, and at the end of the PK profile (with an example assuming LLOQ 0.01 ng/mL)

Timepoint	Reported Value	Converted Value	Explanation
Pre-dose sample for a compound with no endogenous level	< 0.01 ng/mL	0	The BLQ(s) occurring before the first quantifiable concentration will be set to zero.
Pre-dose sample for a compound with endogenous level or pre-dose at the steady-state	< 0.01 ng/mL	0.005 ng/mL	The endogenous pre-dose level will be set to half of the LLOQ.  In multiple-dose situation, the pre-dose sample (trough or Cmin) is set to half of the LLOQ
At middle of the PK profile or between two non-BLQ time points	< 0.01 ng/mL	missing	The BLQ values between the two reported concentrations will be set to missing in the analysis – essentially the linear interpolation rule will be used in AUC calculation.
The last time point(s) of the PK profile	< 0.01 ng/mL	0  or 0.005 ng/mL	It is common to set the last BLQ(s) to 0 to be consistent with the rule for pre-dose BLQ handling. According to FDA's "Bioequivalence Guidance", "For a single dose bioequivalence study, AUC should be calculated from time 0 (predose) to the last sampling time associated with quantifiable drug concentration AUC(0-LOQ)." In some situations, the BLQ values after the last non-BLQ measure can also be set to half of the LLOQ.

There are some discussions that these single imputation methods will generate biased estimates. In a presentation by Helen Barnett et al "Non-compartmental methods for BelowLimit of Quantification (BLOQ)responses", they concluded:

It is clear that the method of kernel density imputation is the best performing out of all the methods considered and is hence is the preferred method for dealing with BLOQ responses in NCA. 

In a recent paper by Barnetta et al (2021 Statistics in Biopharmaceutical Research) "Methods for Non-Compartmental Pharmacokinetic AnalysisWith Observations Below the Limit of Quantification", eight different methods were discussed for handling the BLQs (or BLOQs). The authors conclude that the kernel-based method performs best for most situations.

• Method 1; replace BLOQ values with 0
• Method 2: replace BLOQ values with LOQ/2
• Method 3: regression on order statistics (ROS) imputation
• Method 4: maximum likelihood per timepoint (summary)
• Method 5: maximum likelihood per timepoint (imputation)
• Method 6: Full Likelihood
• Method 7: Kernel Density Imputation
• Method 8: Discarding BLOQ Values

For the specific study, rules for handling the BLQs may be different depending on the time point in the PK profile, the measured compound (with or without endogenous concentrations), the single dose or multiple doses, study design (single dose, parallel, crossover). No matter what the rules are, they need to be specified (preferably pre-specified before the study unblinding if it is pivotal study and the PK analysis results are the basis for regulatory approval) in the statistical analysis plan (SAP) or PK analysis plan (PKAP).   

Here are two examples with descriptions of the BLQ handling rules. In a phase I study by Shire, the BLQ handling rules are specified as the following: 

In a phase I study by Emergent Product Development, the BLQ rules are described as the following:

REFERENCES:

• ICH E10 BIOANALYTICAL METHOD VALIDATION
• EMA "Bioanalytical method validation"
• Limit of Quantitation
• Limit of Blank, Limit of Detection and Limit of Quantitation
• What to Do with Those BLQs!
• Use of Pharmacokinetic Data Below Lower Limit of Quantitation Values
• Beal 2001 "Ways to Fit a PK Model with Some Data Below the Quantification Limit"
• WinNonlin User's Guide