Why a BQL Record Is Not a Concentration
In a pharmacokinetic data set, a concentration reported as below the lower limit of quantification (BQL) is not an exact numerical measurement. It tells us that the assay did not provide a reportable concentration at or above its quantification threshold. Replacing that information with zero, the threshold itself, or another single number adds information that the assay did not provide.
The distinction matters because concentration-time data are used to describe exposure and estimate model parameters. A fabricated point value can change the apparent shape of a profile, especially when several late or early samples are BQL. The first task is therefore to record precisely what was observed: a quantified concentration, a below-threshold result, a missing sample, or an assay failure.
The LLOQ is a property of an analytical method in a defined setting, not a universal biological boundary. It depends on such things as the analyte, sample matrix, method, and validation criteria. A result from a plasma assay with one LLOQ cannot automatically be interpreted using a threshold from a different method or matrix.
The limit of detection (LOD) is a related but different concept: it concerns whether an analyte can be distinguished from background, whereas the LLOQ concerns whether its concentration can be quantified with acceptable performance. A signal can be detectable yet too imprecise or inaccurate to report as a reliable concentration. Thus, “not quantifiable” does not necessarily mean “not detected.”
Representing the Result as an Interval
Suppose the assay reports a concentration only when its processed result \(Y\) reaches the LLOQ, denoted by \(L\). Under a reporting rule that labels results below \(L\) as BQL, the information conveyed by that label is an inequality, not a point value:
If the result is represented on a nonnegative concentration scale, the corresponding interval is ordinarily written \([0,L)\). The square bracket includes zero and the parenthesis excludes \(L\): a value exactly equal to \(L\) is not below the limit. This interval describes the range compatible with the recorded BQL status; it does not say that every value within the interval is equally plausible.
This notation needs one qualification. Some analytical workflows can produce processed values below zero, for example after background correction. If the assay’s actual BQL rule is applied to that scale, the information may be \(Y<L\), with no nonnegative lower endpoint. Use the interval implied by the method’s reporting rule and data definition; do not impose a zero lower bound on a processed scale that can contain negative values. For ordinary concentration records constrained to be nonnegative, \([0,L)\) is a clear representation.
The interval is a description of the observation, not a replacement for a quantified result. A reported value such as \(0.42\) mg/L is a point measurement, subject to assay error. A BQL result with an LLOQ of \(0.10\) mg/L is instead recorded as an observation known to be below \(0.10\) mg/L under the assay’s reporting rule. It is not a measurement of \(0.05\) mg/L, even though that number lies in the interval.
Worked Example: Converting an LLOQ and Recording the Interval
A hypothetical plasma assay has an LLOQ of 40 ng/mL. A sample is reported BQL. Express the threshold in mg/L and state the interval represented on a nonnegative concentration scale.
Convert the units. Since \(1\) mg equals \(1{,}000{,}000\) ng and \(1\) L equals \(1{,}000\) mL:
Therefore, \(1\) mg/L equals \(1{,}000\) ng/mL, and the LLOQ converts as follows:
The BQL record is represented as a result below \(40\) ng/mL, or below \(0.040\) mg/L. On a nonnegative concentration scale, its interval is \([0,40)\) ng/mL, equivalently \([0,0.040)\) mg/L. The record does not identify a single concentration within that range.
Censoring, Missing Samples, and Assay Failures
These three record types must not be conflated. A censored observation occurs when a sample was collected and analyzed, but the reported result only locates the assay result on one side of a threshold. A missing sample provides no assay result because, for example, the sample was not collected or was unavailable for analysis. An assay failure means the intended measurement could not be considered valid, perhaps because of a failed run, a processing problem, or an unacceptable quality-control result.
Only the first case provides the threshold information needed for a BQL interval. For a missed sample, there is no measured result known to be below the LLOQ. For a failed assay, the available record does not establish a valid concentration or a valid BQL status. Those cases should be coded according to their reason and handled according to the data and analysis plan, not silently converted into BQL values.
Worked Example: Classifying Records Correctly
In a hypothetical study, the assay LLOQ is \(0.050\) mg/L. At four scheduled times for one participant, the records are: (1) \(0.083\) mg/L, (2) “BQL,” (3) “sample not collected,” and (4) “run invalid.” Classify each record and state what concentration information it supplies.
Record 1: \(0.083\) mg/L. This is a quantified concentration, above the \(0.050\) mg/L LLOQ. It supplies a reported point value of \(0.083\) mg/L, subject to measurement error.
Record 2: BQL. This is a censored result. On a nonnegative concentration scale, it supplies the interval \([0,0.050)\) mg/L. It does not supply a point estimate within that interval.
Record 3: sample not collected. This is missing, not censored. There is no assay result and therefore no interval implied by the LLOQ.
Record 4: run invalid. This is an assay failure. It is not a valid quantified or BQL result, so the interval \([0,0.050)\) mg/L cannot be assigned on the basis of this record.
Only one of the four records is BQL. Treating all three non-numeric entries as “concentration below \(0.050\) mg/L” would incorrectly claim threshold information for the missed sample and the invalid run.
Checking and Documenting BQL Data
A defensible BQL record requires a known and applicable threshold. Before interpreting it, check the assay documentation and the data dictionary for the LLOQ, units, relevant matrix, and reporting convention. Confirm that the record came from a valid assay and that the BQL flag has not been confused with a blank field, a coded missing value, or a laboratory error code.
The concentration and the LLOQ must use compatible units. A mismatch can alter the interpretation by orders of magnitude. For example, \(25\) ng/mL is \(0.025\) mg/L, not \(25\) mg/L:
When building an analysis data set, retain the original BQL status and the applicable LLOQ rather than overwriting the status with a fabricated concentration. If a system requires a numeric field, keep the censoring indicator and threshold in separate, clearly defined fields. This preserves the distinction between what the assay reported and what a later analysis may assume or estimate.
Worked Example: Auditing a Small Concentration Record
A hypothetical profile has eight scheduled samples analyzed by one valid assay with an LLOQ of \(0.020\) mg/L. Five results are quantified: \(0.180\), \(0.091\), \(0.044\), \(0.028\), and \(0.022\) mg/L. Two records are BQL, and one sample was not collected. Summarize the record types and show how the BQL entries should be represented.
Check the quantified values. Each of the five reported concentrations exceeds \(0.020\) mg/L, including \(0.022\) mg/L. These are quantified observations. The difference between \(0.022\) and the LLOQ is small, but it does not change the stated classification.
Represent the two BQL records. Each is recorded as below \(0.020\) mg/L, or as \([0,0.020)\) mg/L on a nonnegative concentration scale. They are two censored observations, not measurements at \(0.010\) mg/L or at zero.
Keep the missing sample distinct. The uncollected sample has no concentration interval implied by the assay. It remains a missing record with its reason retained.
There are seven collected and assay-classified samples: five quantified and two BQL. Thus the fraction BQL among those seven is \(2/7=0.286\), or \(28.6\%\). Counting the uncollected sample as BQL would instead give \(3/8=37.5\%\), which answers a different and unjustified question because no BQL status was observed for that sample.
Common Mistakes and Practical Limits
The interval representation preserves what the assay tells us, but it does not recover the exact concentration. It also does not, on its own, specify how BQL observations should contribute to a population pharmacokinetic analysis. That requires assumptions about the observation process and the model; the appropriate statistical treatment depends on the analysis goal and is separate from correctly identifying the record.
Common errors include:
- Replacing BQL by zero. Zero is a specific value, while BQL says only that the result is below a threshold. The correction is to preserve the threshold information as an interval and retain the BQL flag.
- Replacing BQL by LLOQ/2. The midpoint is a chosen substitute, not an assay measurement. It may be used in some descriptive conventions, but it must not be mistaken for observed data or treated as though the assay reported it.
- Calling every blank or non-numeric record BQL. A blank may represent a missed sample, a data-processing issue, or an assay failure. Verify the reason before assigning censoring status.
- Assuming BQL proves the underlying concentration is below the LLOQ. The threshold applies to the assay result under its measurement process. Measurement error means the underlying concentration is not determined exactly by the BQL label.
- Ignoring units or the assay-specific threshold. A BQL label has no complete quantitative interpretation without its applicable LLOQ and units.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- An assay has an LLOQ of \(12\) ng/mL. What interval does a BQL result represent on a nonnegative concentration scale?
- Explain why an LLOQ is not the same as a limit of detection.
- A scheduled sample was never collected. Can it be recorded as BQL because the assay LLOQ is known? Why or why not?
- Convert \(30\) ng/mL to mg/L and state the interval for a BQL result at that LLOQ.
- A valid assay reports BQL. Does this establish that the underlying concentration is certainly below the LLOQ? Explain briefly.
Solutions. (1) The interval is \([0,12)\) ng/mL: zero is included and \(12\) ng/mL is excluded. (2) The LLOQ is the lowest concentration quantifiable with acceptable accuracy and precision under specified method conditions; the LOD concerns detection above background, so a detectable signal may still be unquantifiable. (3) No. There is no assay result for an uncollected sample, so the LLOQ supplies no censoring information about it; it is missing. (4) Since \(1\) ng/mL equals \(0.001\) mg/L, \(30\) ng/mL equals \(30\times0.001=0.030\) mg/L. The interval is \([0,0.030)\) mg/L. (5) No. BQL locates the assay result below its reporting threshold; measurement error means it does not determine the underlying concentration with certainty.