Why assay performance and sampling time belong together
A biomarker measurement can be analytically precise yet uninformative if samples are collected only after a transient response has passed. Conversely, a well-chosen sampling schedule cannot rescue measurements that are unstable during handling, below the assay’s quantification limit, or compressed by detector saturation. Early-phase planning therefore needs two linked judgments: whether the assay can measure the expected samples reliably, and whether the sampling times can reveal the response features relevant to the stated biomarker estimand.
The aim is not to find a universally best assay or schedule. Performance requirements depend on the anticipated concentration range, sample matrix, handling conditions, and decision the measurements are intended to inform. Acceptance criteria should be set before examining study results and justified for the intended use. A criterion suitable for exploratory description may not be adequate for a decision that depends on distinguishing a small biomarker change.
Precision, accuracy, and replicate measurements
Precision is often summarized by the standard deviation \(s\) of repeated measurements and, when the mean is positive and meaningfully away from zero, by the coefficient of variation (CV):
Here, \(\bar{x}\) is the mean of the repeated measurements, and \(s\) is their sample standard deviation. A lower CV indicates less relative dispersion in those measurements. Precision is not the same as accuracy: measurements can cluster tightly while all being shifted away from the true or reference value. Accuracy or bias must be assessed separately using appropriate reference material or comparison procedures. A CV is also a poor summary when the mean is near zero; in that setting, report the absolute variability in the assay’s measurement units.
Precision conditions matter. Repeatability concerns measurements made under similar short-term conditions, such as within one run. Variation across runs, days, operators, or reagent lots can be larger. An assay evaluation should match the conditions likely to affect the study samples and should examine the concentration range expected in those samples. A single precision estimate at one concentration does not establish precision throughout the assay range.
Worked Example: Calculating within-run precision
A hypothetical quality-control sample with a nominal concentration near \(50\) pg/mL is measured three times in one run: \(48\), \(52\), and \(50\) pg/mL. Calculate the mean, sample standard deviation, and CV.
The mean is \(\bar{x}=(48+52+50)/3=50\) pg/mL. The squared deviations from the mean are \(4\), \(4\), and \(0\) \((\mathrm{pg/mL})^2\), so:
Thus, \(\mathrm{CV}=100\times(2.00/50)=4.00\%\). If a \(10\%\) CV limit had been specified in advance for this concentration and run condition, these three measurements would meet that precision criterion. They do not establish accuracy, performance at other concentrations, or between-run precision; three replicates provide only a limited estimate of variability.
Technical replicates can help characterize measurement variability, but they do not create additional independent participants. If \(m\) independent replicate measurements each contain random error with standard deviation \(\sigma\), their average has random-error standard deviation \(\sigma/\sqrt{m}\). This follows because the variance of the average is:
The result assumes independent errors with the same variance. Replication does not remove a shared systematic shift, such as an incorrectly calibrated assay, and it does not reduce variability between participants. Averaging replicates can also conceal a failed replicate or a handling problem if raw results are not reviewed.
Stability, quantification limits, and saturation
Stability must be evaluated under conditions relevant to the planned samples: for example, the time from collection to processing, refrigerated or frozen storage, and the number of freeze-thaw cycles. Compare measurements after the specified condition with an appropriate reference measurement, using a tolerance chosen in advance. A common descriptive calculation is percent recovery:
Recovery summarizes relative change; it does not itself determine acceptability. The allowable range must be justified for the assay’s intended use. Stability under one tested condition does not imply stability under a different duration, temperature, matrix, or handling procedure. Samples outside validated conditions should not be treated as though their results were known to be unaffected.
The LLOQ is the lowest concentration at which the assay has demonstrated adequate quantitative performance under its validation conditions; the ULOQ is the highest. A result below the LLOQ is not a precise numerical concentration merely because the instrument returns a signal. Similarly, a result above the ULOQ should not be reported as a reliable extrapolation from the validated range. The appropriate reporting convention depends on the assay and analysis plan, but the distinction between a measured value and a result outside the quantitative range must be preserved.
At the high end, saturation can arise from a detector’s finite response or from another assay component becoming limiting. When detector response flattens, meaningfully different analyte concentrations may produce nearly indistinguishable signals. This is a measurement limitation, not evidence that the biological response itself has reached a plateau. If dilution is considered to bring a sample into range, dilution performance and any required dilution correction must be validated; an unvalidated correction does not restore quantitative reliability.
Worked Example: Applying stability criteria
In a hypothetical stability assessment, a reference aliquot measures \(120\) pg/mL. A prespecified acceptable recovery range is \(90\%\) to \(110\%\). Aliquots held under two proposed handling conditions measure \(114\) and \(105\) pg/mL. Calculate recovery and interpret each condition.
For the first condition, recovery is \(100\times(114/120)=95.0\%\), which is within the specified range. For the second, recovery is \(100\times(105/120)=87.5\%\), which is below the \(90\%\) lower limit. Under these criteria, the first condition passes and the second does not. The results support the tested condition only as evaluated; they do not justify assuming that every storage duration or processing delay is acceptable. The criterion is a study-specific hypothetical choice, not a universal stability rule.
Worked Example: Interpreting results near assay limits
A hypothetical assay has a validated range from \(10\) to \(200\) pg/mL. Four samples return instrument-derived estimates of \(6\), \(12\), \(178\), and \(224\) pg/mL. Classify each result and assess a proposed two-fold dilution of the highest sample.
The \(6\) pg/mL estimate is below the LLOQ, so it is not a validated quantitative result. The \(12\) and \(178\) pg/mL results are within the stated range. The \(224\) pg/mL estimate exceeds the ULOQ and should not be treated as a validated concentration. A two-fold dilution would nominally give \(224/2=112\) pg/mL in the assay well; multiplying by two would give a dilution-corrected estimate of \(224\) pg/mL. That estimate is usable only if the assay’s dilution procedure and correction have been validated for this sample type and concentration. The arithmetic alone cannot establish that the diluted measurement is reliable.
Choosing sampling windows for the expected response
A sampling schedule should reflect the response features the biomarker estimand is intended to describe. Depending on prior biological and translational evidence, those features may include the earliest plausible onset, a period near the expected maximum response, persistence, and recovery. Samples collected too sparsely can miss a brief change or make its timing unclear. A dense schedule may improve temporal description, but it increases burden and can add little information if the response is expected to change slowly.
The schedule must also be feasible for the assay. Collection and processing should occur within validated stability conditions, and the expected sample concentrations should lie within the quantitative range as far as can reasonably be anticipated. If concentrations may be close to the LLOQ or ULOQ, this uncertainty should inform assay preparation and the plan for handling out-of-range results. Sampling time is not a substitute for analytical validation, and a sample collected at the nominally ideal time remains uninformative if it cannot be measured reliably.
Worked Example: Selecting windows for a transient biomarker response
For a hypothetical biomarker, prior evidence suggests that a response could begin about \(1\) hour after dosing, be largest between \(3\) and \(5\) hours, and move toward baseline by \(12\) hours. The intended description is whether a transient response occurs and how its timing changes across that interval. Propose a schedule and explain its purpose.
One reasonable schedule is a predose sample followed by samples at \(1\), \(2\), \(4\), \(6\), and \(12\) hours. The \(1\)- and \(2\)-hour samples bracket the anticipated onset; \(4\) hours samples the expected high-response window; \(6\) hours helps characterize decline; and \(12\) hours assesses whether the response has moved back toward baseline. These are planned windows, not proof that the true onset or maximum lies at those exact times. If the assay cannot maintain sample stability for the time needed to process the \(12\)-hour sample, the handling plan must be changed or validated before using this schedule. If the expected response is substantially faster or slower than assumed, the times should be revised using that evidence rather than retained by habit.
Specify whether the objective is to capture onset, a high-response period, persistence, recovery, or another time-dependent feature.
Use relevant biological and translational evidence to choose times that can distinguish the anticipated phases, without assuming those times are exact.
Compare anticipated concentrations with the validated range and ensure collection, processing, and storage fit the tested stability conditions.
Look for excessive replicate disagreement, condition-dependent drift, results clustered at assay limits, and evidence of a flattened response at high concentrations.
Diagnostics, alternatives, and limitations
A useful review examines raw replicate measurements and performance across relevant concentrations and runs, not only a single overall summary. Warning signs include unexpectedly high CVs, consistent shifts between runs, recovery outside prespecified stability criteria, an accumulation of results below the LLOQ or above the ULOQ, and signals that stop increasing as expected at the high end. Such patterns can indicate assay limitations, handling problems, or a mismatch between the anticipated and observed concentration range. They should be investigated rather than resolved by selectively averaging, discarding, or numerically extrapolating results.
Possible responses depend on the cause. If within-run measurement variability is the concern, replicate testing may help characterize it; if run-to-run shifts are the concern, assessment across runs and relevant operating conditions is needed. If samples are unstable, validated handling conditions or a different collection-to-processing plan may be required. If results fall outside the quantification range, a validated assay range or dilution procedure may be necessary. If a transient response may have been missed, future sampling windows may need adjustment. These options address different problems and are not interchangeable.
The approach has important limits. Assay performance established with quality-control material may not fully describe every participant sample or matrix condition. A small precision or stability assessment cannot prove performance under all circumstances. Sampling windows are chosen using uncertain expectations, so no finite schedule guarantees that an unanticipated brief response will be observed. Finally, an assay’s measurement limitations should not be confused with biological properties: a flat instrument signal can mask concentration differences, while a sparse schedule can obscure timing. Neither alone establishes the underlying response shape.
Check Your Understanding
Answer each question, then compare with the solutions below.
- Four hypothetical replicate results are \(96\), \(100\), \(104\), and \(100\) pg/mL. Calculate their mean, sample standard deviation, and CV.
- A sample measures \(80\) pg/mL before storage and \(72\) pg/mL after storage. If the prespecified acceptable recovery range is \(90\%\) to \(110\%\), does it meet the criterion?
- An assay has an LLOQ of \(5\) pg/mL and a ULOQ of \(150\) pg/mL. How should estimates of \(3\) and \(160\) pg/mL be interpreted?
- Prior evidence suggests a short-lived response may occur from \(2\) to \(6\) hours and return toward baseline by \(10\) hours. Name a reasonable set of sampling windows and explain why one sample at \(10\) hours would be inadequate for describing the transient response.
Solutions. 1. The mean is \((96+100+104+100)/4=100\) pg/mL. The squared deviations sum to \(16+0+16+0=32\), so \(s=\sqrt{32/(4-1)}=\sqrt{10.667}=3.266\) pg/mL. The CV is \(100\times(3.266/100)=3.266\%\). 2. Recovery is \(100\times(72/80)=90.0\%\), exactly the lower acceptance boundary, so it meets the stated criterion. 3. \(3\) pg/mL is below the LLOQ and is not a validated quantitative result; \(160\) pg/mL is above the ULOQ and should not be treated as a validated concentration. 4. For example, collect at \(2\), \(4\), \(6\), and \(10\) hours, with a predose reference if required by the study objective. The earlier samples can describe the anticipated response window, while \(10\) hours can assess later recovery. A single \(10\)-hour sample could miss the transient change entirely and cannot describe its timing.