Why These Three States Must Stay Separate
A concentration field may contain an empty cell, the number 0, or a result such as “BLQ.” These are not three ways to write the same observation. An empty cell says that a usable concentration result is not available in that record. A zero is a numeric result that may be valid under the source’s measurement and reporting conventions. “BLQ” indicates that a sample was assessed but the concentration was below the assay’s quantification limit. Each state carries different information about the sample and the measurement.
Keeping the states distinct is essential when building population pharmacokinetic data. Replacing a missing value with zero invents a concentration. Replacing a below-quantification result with zero discards the fact that the assay constrained the result to a range. Treating a valid zero as missing discards a reported result. The dataset should preserve what is known without claiming more than the source supports.
Represent the Result and Its Status
A robust record keeps the numeric concentration separate from the interpretation of the result. The exact dataset design can vary, but a useful conceptual structure has a concentration value, a result status, and enough source information to resolve or audit the record. For example, the status could distinguish “quantified,” “zero reported,” “below quantification,” and “missing.” If the source distinguishes why a result is missing, such as a sample not collected versus an assay result not available, retain that reason where possible.
For a quantified result, enter the numeric concentration in the agreed units and mark it as quantified. For an explicit, valid zero, enter 0 as the numeric value and retain a status that makes its origin clear. For a below-quantification result, preserve the result as below quantification and do not place 0 or the limit in the concentration field as though either were a measured value. For a missing result, leave the numeric concentration unavailable and record the status as missing rather than inserting a numerical substitute.
| Source meaning | Numeric concentration field | Result status | What the record tells you |
|---|---|---|---|
| Quantified concentration, such as 3.2 mg/L | 3.2 | Quantified | A numeric concentration was reported. |
| Valid concentration explicitly reported as zero | 0 | Zero reported (or an equivalent defined status) | The source reports a numeric zero under its stated conventions. |
| Below the assay’s quantification limit | Unavailable, not zero | Below quantification | The result is constrained by the assay but was not quantified as a numeric concentration. |
| No usable result available | Unavailable | Missing, with a reason if known | The record does not provide a concentration result. |
A below-quantification result is informative, but it is not a precise concentration. If an assay reports a result below a limit \(L\), the record generally indicates that the concentration is below \(L\), according to that assay’s reporting convention. It does not identify where below \(L\) the concentration lies. The exact inequality and interpretation should follow the source’s notation and assay documentation.
Likewise, “zero reported” should not be interpreted as proof that no drug molecules were present. It means the source provides a zero as a valid numeric result under its measurement and reporting conventions. In many analytical settings, an apparent zero may instead be an instrument response, a rounded value, or a database code for an unquantifiable result. Those possibilities must not be silently treated as a true numeric concentration.
Worked Example: Mapping Laboratory Text to Dataset States
Consider this hypothetical set of laboratory outputs. The assay documentation states that “<0.50” means below quantification, and the source system identifies “0.00” as a valid reported concentration for this example. A blank result means that no result was supplied.
| Sample | Source result | Numeric concentration | Result status |
|---|---|---|---|
| A | 2.40 mg/L | 2.40 | Quantified |
| B | 0.00 mg/L | 0.00 | Zero reported |
| C | <0.50 mg/L | Unavailable | Below quantification |
| D | Blank | Unavailable | Missing |
For sample A, record the measured numeric concentration in mg/L and identify it as quantified. For sample B, retain the zero because the hypothetical source explicitly defines it as a valid reported concentration. For sample C, retain the below-quantification meaning rather than entering 0 or 0.50 as a concentration. For sample D, do not invent a result; record it as missing. The same blank entry could arise for different reasons, so a known reason should be retained separately rather than inferred from the blank alone.
Why Collapsing the States Changes the Data
The distinction can be written as a simple record structure. Let \(Y_i\) denote the numeric concentration field for sample \(i\), and let \(R_i\) denote its result status. A quantified result provides a numeric \(Y_i\); a valid zero provides \(Y_i=0\) with the appropriate status. A below-quantification or missing result has no numeric \(Y_i\) in this representation, but its \(R_i\) distinguishes the two cases.
This structure avoids forcing different observations into one numeric code. If all non-numeric states are converted to 0, missing and below-quantification records become indistinguishable from valid zeroes. If all are left blank without a status, a downstream user cannot tell whether the assay found a result below its limit or whether no result was available.
A small hypothetical calculation shows the effect. Suppose four sample records are: a quantified concentration of 8 mg/L, a valid reported zero, a result below 2 mg/L, and a missing result. The mean of the two numeric results is:
This is only the mean of those two numeric results; it is not automatically an appropriate estimate of a broader population quantity. If the below-quantification result is incorrectly replaced by zero and the missing result is still excluded, the arithmetic mean becomes:
The change is not a harmless formatting choice. It changes the values being averaged and treats a result known only to be below 2 mg/L as if it were exactly zero. If the missing result were also replaced by zero, the mean would instead be \((8+0+0+0)/4=2.000\) mg/L, additionally treating the unavailable result as a measured concentration. Neither substitution follows from the recorded information.
Worked Example: A Numeric Zero With Unclear Meaning
In a hypothetical export, one sample has a concentration value of 0. The original laboratory report is not available, and the export contains no result status or qualifier. Decide whether to classify the record as a valid zero, below quantification, or missing.
Step 1: Do not infer a status from the number alone. A zero in an export might be a valid reported concentration, a database substitution for a below-quantification result, or a default entered when no result was available. The numeric field alone does not distinguish these possibilities.
Step 2: Preserve the received value and identify the ambiguity. Keep the raw exported value of 0 unchanged in the source record. In the analysis-ready representation, do not certify it as a valid zero until documentation or source review supports that meaning. Mark the record for resolution using the dataset’s defined workflow.
Step 3: Resolve using evidence. If the laboratory report confirms a valid numeric zero, represent it as zero reported. If it shows a below-quantification qualifier, represent it as below quantification with no numeric concentration. If it shows no result was available, represent it as missing. If the evidence cannot be obtained, retain the ambiguity rather than making an unsupported choice.
This example illustrates why a plausible-looking numeric value is not always sufficient evidence about the result state. The status should be supported by the source, not guessed from a common convention.
Quality Checks and Common Failure Modes
Basic checks can detect many coding problems before the data are used. They do not replace review of the source, but they help identify records whose numeric values and statuses disagree.
- Check for a numeric value with a missing status. A numeric zero, in particular, should not silently inherit the interpretation of a missing-value code or a below-quantification convention.
- Check for a below-quantification status paired with a numeric concentration. This may be valid only if the dataset design explicitly stores a separate bound or source value. Do not treat that number as a quantified concentration without a defined reason.
- Check for missing status paired with a numeric value, or a quantified status with no numeric value. These combinations may indicate a data-entry or transformation error.
- Check the raw source notation. A number such as 0 may have been generated during export, rounding, or data transformation. Retain the original text or source value when possible so the decision can be traced.
- Check units and recorded qualifiers together. A concentration and its qualifier must be interpreted in the same units and source context; otherwise a value may be misread.
A frequent mistake is to reason, “The result is below the quantification limit, so it is effectively zero.” The correction is that “below the limit” is a bound, not an exact measurement. Another mistake is to say, “The cell is empty, so the concentration must be zero.” The correction is that an empty cell carries no concentration result unless the source explicitly defines that coding. Conversely, a reported zero should not be discarded merely because zero concentrations are uncommon; first establish what the source means.
A useful alternative to a single numeric field is a representation that preserves both the numeric result where one exists and a separate status for the result state. This is more explicit than relying on special numeric codes such as 0, a negative number, or a chosen constant to stand for missing or below-quantification results. Special numeric codes can be mistaken for actual concentrations during summaries or modeling, and they obscure the distinction among the states.
This representation does not decide how below-quantification observations should be handled in a particular analysis. It ensures that the information needed to make that decision remains available. Nor does it explain an unknown result automatically: the status should be based on source documentation, and unresolved records should remain identifiable as unresolved rather than being forced into a convenient category.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A laboratory report says “<0.20 mg/L.” What should the numeric concentration field and result status represent?
- A data export contains a blank concentration and no explanation. What can you conclude, and what should you avoid concluding?
- A sample is explicitly reported as a valid concentration of 0 mg/L under the source’s conventions. How should it differ from a missing result?
- For values 6 mg/L, 0 mg/L (valid reported zero), “<1 mg/L,” and missing, calculate the mean of the numeric results only. Why is this not the mean of all four records?
- An export shows a numeric zero, but the laboratory qualifier is unavailable. What is the appropriate data-quality action?
Solutions. (1) Leave the numeric concentration unavailable and record the status as below quantification; preserve the reported limit or qualifier in the appropriate source or metadata field. Do not enter 0.20 as if it were measured. (2) Conclude only that the result is unavailable in the export. Do not conclude that the sample concentration was zero or that it was below quantification; seek a source or reason if possible and retain the missing status. (3) Store numeric concentration 0 with a status indicating a valid reported zero. A missing result has no numeric concentration and a missing status, so it does not contribute a reported value. (4) The numeric-result mean is \((6+0)/2=3\) mg/L. The below-quantification and missing records do not provide numeric concentrations for this calculation, so this is not a mean over all four records and does not by itself resolve how those records should be treated in an analysis. (5) Preserve the raw exported zero and flag the record for source review. Do not classify it as a valid zero, below quantification, or missing without supporting evidence.