What a BQL Record Tells You
In concentration-time data, an assay may be unable to quantify a sample reliably below its lower limit of quantification (LLOQ). A result reported as below the LLOQ still carries information: the concentration was not quantified, but it is known to be below a specified threshold. The record is therefore different from both a measured concentration and an observation that was never obtained.
The distinction matters when organizing data for an NLME analysis. A dataset that stores every result in one numeric column can obscure whether a value was measured, censored by the assay, or missing. An explicit status and the applicable limit preserve what the laboratory reported without pretending to know a concentration that was not quantified.
Here \(i\) indexes a subject and \(j\) indexes a record for that subject. \(Y_{ij}\) denotes the concentration that would be represented on the assay’s concentration scale, \(L_{ij}\) is the LLOQ applicable to that record, and the record status indicates what was actually reported. The status should come from the assay result or validated data-processing rules, not be inferred solely by comparing a stored number with a threshold.
Represent Status and Limit Explicitly
A practical record includes the subject, nominal or actual sampling time, analyte, result status, a numeric concentration when one is quantified, and the applicable LLOQ with its units. If a value is not quantified, the numeric concentration field should be blank or otherwise marked as unavailable—not filled with a convenient substitute. A separate status field preserves the reason that no exact concentration appears.
For a simple dataset, statuses might be labelled Q for quantified, B for BQL, and M for missing. These labels are examples of an encoding convention, not universal software keywords. The data dictionary must state their meanings and indicate how blank values are stored.
| Status | What the record says | Concentration field | Limit field |
|---|---|---|---|
| Q: quantified | An exact assay result was reported. | Store the reported concentration and units. | Retain if needed for assay traceability; it does not replace the measured value. |
| B: BQL | The result was below the applicable LLOQ. | Leave the exact concentration unfilled. | Store the applicable LLOQ and units. |
| M: missing | No usable concentration observation is available. | Leave the concentration unfilled. | Do not treat a limit alone as evidence of a BQL observation. |
A BQL result and a missing result can both have an empty numeric concentration field, but they do not carry the same information. The BQL status reports an assay outcome and a threshold; missingness says no usable result is available. Reasons for missingness—such as a missed sample, a sample-handling problem, or a failed assay—can be recorded separately when known.
Worked Example: Three Records, Three Different Meanings
Suppose a hypothetical subject has three scheduled plasma samples. The assay LLOQ is \(0.50\) mg/L for all three. The laboratory reports \(4.20\) mg/L at 1 hour, “<0.50 mg/L” at 4 hours, and no usable result at 8 hours because the sample was not collected.
| Time (h) | Status | Concentration (mg/L) | LLOQ (mg/L) | Interpretation |
|---|---|---|---|---|
| 1 | Q | 4.20 | 0.50 | Quantified concentration of 4.20 mg/L |
| 4 | B | Blank | 0.50 | Concentration reported below 0.50 mg/L |
| 8 | M | Blank | 0.50 | No concentration result because no sample was collected |
The 4-hour record is left-censored: it supplies the inequality \(Y_{ij} < 0.50\) mg/L, not a point measurement. The 8-hour record supplies no such inequality. Even though both concentration cells are blank, marking both as BQL would falsely claim that the 8-hour sample was tested and found below the assay limit.
Use the Limit That Applies to That Record
An LLOQ is not necessarily one universal constant for every record in an analysis. It can differ by assay, analyte, laboratory, sample dilution, or a documented assay change. The record must therefore be linked to the limit that applied to its own result. If the limit changes, the data should preserve that change rather than silently assigning one study-wide value.
Units are part of the limit. A number such as 25 is not an interpretable threshold unless its units and analyte are known. When records are converted to common units, convert the concentration and its limit consistently, retain sufficient precision, and document the conversion. Do not compare or combine a concentration in one unit with a limit in another.
Worked Example: Keeping Assay Limits and Units Aligned
In a hypothetical dataset, an early sample is reported BQL with an LLOQ of \(0.020\) mg/L. After a documented assay change, a later sample is reported BQL with an LLOQ of \(25\) ng/mL. For comparison, convert the second limit to mg/L. Since \(1\) mg \(=1{,}000{,}000\) ng and \(1\) L \(=1{,}000\) mL, \(1\) mg/L \(=1{,}000\) ng/mL. Therefore,
The early record means the result was below \(0.020\) mg/L; the later record means it was below \(0.025\) mg/L. They are both BQL, but they do not share the same numerical threshold. A consistent data representation could store the original limit and units alongside a converted limit of \(0.025\) mg/L for the later record. The conversion does not turn either BQL result into an exact concentration.
Why BQL Is Censoring, Not a Point Value
The record’s meaning follows directly from what the assay reported. A quantified result supplies a reported number. A BQL qualifier supplies a threshold statement. Replacing that threshold statement with a number adds information that was not observed.
For example, if the only reported result is “<0.50 mg/L,” assigning \(0.50\) mg/L asserts that the concentration equals the limit. Assigning zero asserts it equals zero. Assigning \(0.25\) mg/L asserts it equals half the limit. None of these equalities follows from the original report. The distinction is not a matter of numeric formatting: it changes the data being represented.
The exact treatment of a result at the boundary must follow the assay’s reporting convention. Some systems report a quantified result at the LLOQ; a BQL qualifier should not be overwritten merely because a software comparison uses a rule such as “less than or equal to” the limit. Store the laboratory qualifier and document the validated rule used to resolve any ambiguous boundary records.
Worked Example: A Value at the LLOQ Is Not Automatically BQL
Suppose a hypothetical assay has an LLOQ of \(0.10\) mg/L. For one sample, the validated laboratory report gives a quantified result of \(0.10\) mg/L. For another, the report gives “<0.10 mg/L.” How should the records be encoded?
For the first sample, store status Q and concentration \(0.10\) mg/L because the assay reported a quantified value at the boundary. For the second, store status B, leave the exact concentration blank, and store LLOQ \(0.10\) mg/L. The second record carries the threshold information, not an exact concentration.
The numeric values alone do not settle the classification. The status comes from the assay’s result qualifier and boundary convention. If raw data contain a numeric placeholder for the second result, verify the laboratory’s data dictionary before deciding what that field means; it may be a coding value rather than a measured concentration.
Checks Before Analysis
Before using a dataset, verify that its status and limit fields agree with the source assay records. These checks are data-quality checks, not a statistical method for analyzing censored observations.
- Check status against source qualifiers. Confirm that each BQL label represents a result reported below the limit, rather than a missed sample or an arbitrary numeric code.
- Check units and analyte. Ensure the concentration and applicable LLOQ refer to the same analyte and use compatible units.
- Check limits over time and across assays. Confirm documented changes, dilution rules, and sample-specific limits are represented on the correct records.
- Check numeric fields by status. Quantified records should have a reported value; BQL and missing records should not masquerade as exact measurements.
- Check boundary handling. Investigate records equal to the limit and use the assay’s stated reporting convention.
A common warning sign is a dataset in which every BQL record contains the LLOQ as its concentration and has no separate status field. That structure may indicate substitution occurred during data preparation. It loses the distinction between an assay result below the threshold and an exact value at the threshold, so the source records and transformation steps should be reviewed.
What This Encoding Does—and Does Not—Decide
Explicit status and limit fields preserve the observation before an analysis method is chosen. They do not, by themselves, specify how a statistical model should use a BQL record, nor do they determine the probability model, residual-error scale, or likelihood contribution. Those are modeling decisions that require their own assumptions.
The main alternatives often encountered in a data pipeline are to delete BQL records or replace them with a fixed number such as zero, half the LLOQ, or the LLOQ. Deletion discards the reported below-limit information. Substitution presents an unmeasured value as if it were an exact observation. Explicit censoring status instead retains the inequality information and applicable threshold for a method that can use it. None of these choices makes an assay limit irrelevant; the record must still carry its correct limit.
Censoring status is also not a cure for assay problems. If the wrong LLOQ was attached, the sample was mislabelled, or the assay qualifier was lost, the encoded inequality may be wrong. Moreover, a BQL result does not reveal how far below the limit the concentration lies. The record should preserve that uncertainty rather than imply more precision than the assay provides.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A sample is reported “<0.20 mg/L.” What status and limit should be stored, and what should go in the exact concentration field?
- A concentration field is blank, and the sample was not collected. Is this a BQL result? Explain.
- An assay reports a quantified concentration of \(0.30\) mg/L with an LLOQ of \(0.30\) mg/L. Should the record automatically be relabelled BQL?
- A BQL result has an LLOQ of \(40\) ng/mL. Express that limit in mg/L.
Solutions. (1) Store BQL status and an LLOQ of \(0.20\) mg/L; leave the exact concentration unfilled, because the report gives an inequality, not a point value. (2) No. It is missing because no sample was collected; there is no assay result establishing that its concentration was below a limit. (3) No. Keep the quantified status and reported concentration if that is what the validated assay report says; follow the assay’s boundary convention rather than classifying from a numeric comparison alone. (4) Since \(1\) mg/L \(=1000\) ng/mL, \(40\) ng/mL divided by \(1000\) is \(0.040\) mg/L. The BQL record remains censored at that limit, not equal to \(0.040\) mg/L.