Why Qualifiers Matter
A number copied from a publication can look precise while losing the information that gives it meaning. A tissue-to-plasma ratio of 2.4, a range of 1.1–4.8, and a result reported as below 0.2 are not interchangeable descriptions of a parameter. If a qualifier is dropped, the resulting PBPK input may imply an exact measurement where there was only a bound, or may treat variation among individuals as if it were measurement uncertainty.
The goal of extraction is therefore not simply to capture a numeric value. It is to preserve what the source says the value represents: its form, units, population or sample, and any qualifier attached to it. The earlier material on anatomy of a PBPK parameter record and assay metadata provides the context for recording these details. Here the focus is the faithful transcription of estimates and qualifiers, and the consequences for using them as model inputs.
Represent the Result Before Choosing an Input
First identify the form of the result. A point estimate is one reported value, such as a mean or a fitted parameter estimate. A range gives endpoints, but the word “range” alone does not say whether those endpoints are the minimum and maximum observations, a plausible interval, or the limits of an assay. A limit of quantification (LOQ) is an assay threshold: it marks a concentration or amount that the method can quantify under specified conditions. A censored result says that the actual value is not reported exactly, but is known to lie on one side of a threshold.
Population summaries describe a group, not necessarily a single individual. A mean and standard deviation (SD), a median and interquartile range (IQR), and a geometric mean with a stated interval summarize data in different ways. Preserve the statistic’s name and the group size when reported. Do not rename a standard deviation as a standard error, an observed range as a confidence interval, or a confidence interval as an individual-level range.
| Source wording | What it establishes | What it does not establish by itself |
|---|---|---|
| “Mean 3.2” | A reported mean of 3.2 in the stated units and population | The spread, sample size, or suitability as an individual value |
| “Range 1.4–5.8” | Endpoints of a reported range | Whether the range is observed, a confidence interval, or an assay interval |
| “Below 0.10” | The result is less than 0.10 in the stated units | An exact value, including zero or 0.10 |
| “95% CI: 2.1–4.0” | An interval estimate for a parameter, under the method used | A range containing 95% of individual measurements |
When the source’s wording is ambiguous, do not resolve the ambiguity by silently choosing an interpretation. Record the wording and the uncertainty about what it means. This is especially important when a model input is intended to represent an individual, a population typical value, or a distribution of values.
Worked Example: Keeping a Reported Range Intact
In a hypothetical study, a paper reports a tissue-to-plasma concentration ratio of “2.6 (range 1.2–5.1)” for eight samples. The methods describe these as the smallest and largest observed sample values. What should be extracted, and what could be entered as a PBPK input?
The faithful transcription is a reported value of 2.6, with a reported observed range of 1.2–5.1 across eight samples. The range is explicitly an observed minimum-to-maximum range, not a confidence interval. All three values are dimensionless ratios.
If the model requires one representative ratio, 2.6 is a candidate only if it is clear what that central value represents. The paper’s quoted wording does not identify 2.6 as a mean or median, so it must not be relabeled as either. The observed endpoints can be retained as descriptive bounds, but they do not define a probability distribution. Entering a uniform distribution from 1.2 to 5.1 would add an assumption that the report did not make.
The extraction therefore records the central number as “2.6, statistic unspecified,” the observed range as 1.2–5.1, and the sample count as eight. If the intended model input requires a named population summary, the report alone may not supply it.
Limits and Censored Results
A value reported as less than a threshold is not the threshold and is not zero. For example, “concentration < 0.05 mg/L” means the reported result is below 0.05 mg/L, subject to the assay and reporting rules. A result may be described as below the limit of detection (LOD) or below the LOQ; these terms should be retained as reported because they do not necessarily refer to the same analytical threshold. “Not detected” also does not automatically mean zero: the source’s method is needed to understand what detection limit applies.
The direction of the inequality matters. “< 0.05” and “≤ 0.05” do not state the same bound. Likewise, “> 10” indicates a value above 10, not an estimate of 10. When the source gives a numeric threshold, transcribe the threshold, the inequality, the units, and the stated limit type. If the limit type or units are absent, record that they are not stated rather than supplying them from assumption.
Worked Example: A Result Below the Quantification Limit
In a hypothetical assay, an unbound plasma fraction is reported as “<0.020,” with no exact value, and the methods identify 0.020 as the LOQ. The fraction is dimensionless. How should this result be represented in an input dossier?
The result should be recorded as \(f_u < 0.020\), with the qualifier “below LOQ.” It establishes an upper bound, not an exact \(f_u\) of 0.020. It also does not establish \(f_u=0\).
If the PBPK model requires a single numeric value for \(f_u\), the report does not provide one. Substituting the LOQ, half the LOQ, or zero would create a value not measured in the study. Each substitution would need a separate, justified decision and must not be presented as the reported result. If the model can accept a bounded or censored input, retain the bound; otherwise, the limitation should be explicit before the value is used.
Why Replacing Censored Values Can Mislead
The problem with replacing a censored value is not merely documentary. It changes the data being summarized or modeled. Suppose a measured random quantity \(Y\) is normally distributed with mean \(\mu\) and standard deviation \(\sigma\), and a result is reported only as \(Y<L\). Under this illustrative model, that observation contributes the probability of falling below the limit, not a probability density evaluated at \(L/2\).
Here \(\Phi\) is the standard normal cumulative distribution function. The expression uses the information that the value lies below \(L\), while preserving uncertainty about its exact location. Replacing the result by \(L/2\) instead treats one arbitrary value as if it had been observed. The normal model is only an illustration; an analysis should use a distribution appropriate to the data and assay. The general point is that a bound contains less information than an exact measurement, and should not be transcribed as one.
For a PBPK model, the practical consequence depends on where the parameter enters. A low binding fraction, for example, can affect predicted unbound concentrations. But a censored assay result alone does not tell the modeler which value below the limit to use. It is a constraint on the possible value, not a ready-made point estimate.
Population Summaries and Model Inputs
A population summary should be carried forward with its statistic, spread measure, units, and sample size when available. A mean summarizes the arithmetic center; a median identifies the middle of the ordered observations. An SD describes variability among observations in the summarized group, whereas a standard error describes precision of an estimated mean under a sampling model. These quantities answer different questions. The number \(n\) is also important: a mean based on four samples and one based on forty do not have the same evidential basis, even if their numerical values match.
A reported group summary is not automatically an appropriate value for every simulated individual. A model may need a typical value, an individual-level parameter, or a representation of between-subject variation. A mean and SD might help characterize the group, but do not alone specify an appropriate distribution or justify assigning independent parameter values. Nor is a median interchangeable with a mean. When a model’s intended parameter differs from what the study summarized, record the mismatch rather than disguising it through a copied number.
Worked Example: Preserving a Population Summary
A hypothetical publication reports a hepatic blood flow value of “mean 1.42 L/min, SD 0.18 L/min, \(n=16\)” in a specified adult sample. A PBPK model requires a representative flow value for a typical adult. What can be transcribed, and what should not be inferred automatically?
Transcribe the reported mean as 1.42 L/min, the SD as 0.18 L/min, and the sample size as 16. The reported summary is explicitly a mean with an SD, so neither statistic should be relabeled. The mean is a candidate representative value if the modeled population and measurement definition are sufficiently aligned with the study sample.
For clarity, the standard error of the sample mean would be \(s/\sqrt{n}\) if the 16 observations are independent and the reported SD is their sample SD:
This derived standard error describes the estimated mean’s sampling precision under those conditions; it is not the reported SD and does not describe the spread of individual flows. The source reports no distributional form, so the mean and SD alone do not justify assuming normally distributed individual values. For a single typical-adult input, the mean may be considered, while the SD remains a description of sample variability rather than an automatic input range.
A Reliable Extraction and Use Sequence
Preserve the number, units, inequality sign, statistic name, endpoints, and any phrases such as “below LOQ.”
Determine whether it refers to individual observations, uncertainty in an estimated parameter, an assay threshold, or a population summary.
Check whether the model needs a point value, a typical population value, or information about variation, and whether the source actually provides that form.
Say what can be used as a candidate input and what remains unknown. Do not turn a bound or descriptive range into an exact value or distribution without an explicit rationale.
This sequence also helps distinguish extraction from later decisions. A transcription records what the source reported. Selecting a model input may require considering applicability and other evidence, but that decision should not rewrite the transcription. Keep the reported result and any chosen model value distinguishable.
Diagnostics, Alternatives, and Common Pitfalls
Several checks can reveal that a qualifier has been lost. Ask whether an inequality sign is missing, whether a range’s type is stated, whether a summary statistic has been named, and whether the number of observations and units are available. Compare the extracted wording with the source table or methods: a value in a table footnote may be a geometric mean, an assay limit, or a confidence interval rather than an unqualified point estimate. Also check that the qualifier still makes sense for the model quantity; an assay LOQ is a property of a measurement procedure, not a biological lower bound.
The main alternatives are not interchangeable data-handling choices. A reported point estimate can be carried as a candidate single value. A reported range can be kept as endpoints with its stated meaning. A censored result can be retained as a bound, or handled with a method that accounts for censoring when an analysis requires it. A population summary can be used as a group summary, with its statistic and spread preserved. Choosing among these approaches depends on what the model requires and what the source supports; no one representation is universally preferable.
- Mistake: “Below LOQ means equal to the LOQ.” The incorrect reasoning is that the limit is the nearest available number, so it can stand in for the result. The correction is that the reported result is below that limit; using the limit as a point value adds information the assay did not provide.
- Mistake: “The reported range defines a uniform distribution.” Endpoints alone do not describe how values are distributed between them. Preserve the range’s reported meaning and do not invent a distribution.
- Mistake: “Mean plus or minus SD is a confidence interval.” SD describes sample variability; it is not automatically an interval for the population mean. Preserve the label used by the source.
- Mistake: “A population mean is the value for every individual.” A group mean may be a candidate typical value, but it does not erase between-person variability or establish that each individual has that value.
A key limitation is that faithful transcription cannot repair incomplete reporting. If the paper omits a range’s meaning, a limit’s units, or the summary statistic, those details remain unresolved. The appropriate response is to preserve the stated information and mark what is missing, not to guess silently.
Check Your Understanding
For each item, identify what can be extracted and what should not be inferred.
- A hypothetical result is reported as “concentration > 8 mg/L.” Is 8 mg/L an exact concentration?
- A paper reports “median 4.1, IQR 2.8–6.0” for 20 samples. What are the summary and spread measures?
- A result is reported as “not detected,” but no detection limit is given. Can you enter zero as the measured value?
- A hypothetical parameter is reported as mean 7.0 units and SD 1.5 units for 25 observations. Is 1.5 the standard error of the mean?
- A report gives a range of 3–9 but does not say what kind of range it is. What should be recorded?
Solutions. (1) No. The result is greater than 8 mg/L; 8 mg/L is a lower bound, not an exact measurement. (2) The median is 4.1, and the reported IQR is 2.8–6.0, for 20 samples; do not call the median a mean or the IQR a confidence interval. (3) No. “Not detected” is a qualified result, and without the limit it does not establish a numeric bound or an exact zero. (4) No. The reported SD is 1.5 units. If the observations are independent and this is their sample SD, the standard error is \(1.5/\sqrt{25}=0.30\) units. (5) Record “range 3–9, type unspecified,” with any reported units, and do not assume it is an observed range, confidence interval, or assay range.