Why Keep Two Sampling Times?
A protocol may request a blood sample at a target time, but the sample is collected at a particular observed time. These values answer different questions. The nominal time records when the sample was scheduled; the actual time records when it was collected. Keeping both preserves the intended design and the observed data. Replacing one with the other loses information that is important for quality control and pharmacokinetic analysis.
For example, a sample scheduled for two hours after a dose might be collected at two hours and twelve minutes. The nominal value describes the schedule, while the observed value describes the sample. When the analysis requires time since dose, the relevant analysis time is calculated from the actual collection time and the relevant actual dose time. A nominal target is not a substitute for that elapsed time.
In a well-structured analysis dataset, the two values have separate fields, such as NOMINAL_TIME and ACTUAL_TIME, with units and reference conventions documented. If a model uses time since dose, the analysis-time field must represent elapsed time from the appropriate actual dose event, not merely a scheduled visit label. The dose-sample event ordering established in the earlier material on dose-sample ties remains relevant when events share a recorded time.
Representing and Calculating a Deviation
Suppose nominal and actual sample times are both expressed in hours from the same study origin. Define the signed deviation as:
A positive value means collection occurred later than the scheduled target; a negative value means it occurred earlier. The absolute deviation, \(\lvert\Delta_{\text{schedule}}\rvert\), describes the size of the departure without its direction. If the values use different units, convert them first. If they use different origins, do not subtract them until each is expressed relative to a common origin.
Worked Example: Calculate Signed Deviations
In a hypothetical study, three samples are scheduled at 1, 4, and 8 hours after a specified study reference time. Their actual collection times on that same scale are 1.08, 3.75, and 8.20 hours. Calculate the signed and absolute deviations.
For the first sample, \(\Delta_{\text{schedule}}=1.08-1.00=0.08\) hours. Since \(0.08\times60=4.8\) minutes, it was collected 4.8 minutes late; its absolute deviation is 4.8 minutes.
For the second sample, \(\Delta_{\text{schedule}}=3.75-4.00=-0.25\) hours. Since \(-0.25\times60=-15\) minutes, it was collected 15 minutes early; its absolute deviation is 15 minutes.
For the third sample, \(\Delta_{\text{schedule}}=8.20-8.00=0.20\) hours, or \(0.20\times60=12\) minutes late. Its absolute deviation is 12 minutes.
The signed values retain direction, which can reveal a pattern of early or late collection. The absolute values are useful for summaries such as the largest departure or the proportion within a predefined tolerance. Neither summary replaces the stored actual time.
The common-origin condition matters. A nominal time of two hours after a scheduled dose and an actual time of 1.9 hours after an actual dose are not automatically comparable: their reference doses may have occurred at different times. In that situation, retain the nominal target as defined by the protocol and calculate actual elapsed time from the actual dose record for analysis. The schedule deviation should be calculated on a clearly specified common reference scale, rather than by subtracting values that happen to be in hours but refer to different events.
Worked Example: A Delayed Dose Changes the Elapsed Sample Time
In a hypothetical study, a dose is scheduled for 08:00, and a sample is nominally scheduled for 10:00, two hours after that planned dose. The dose is actually administered at 08:15, and the sample is collected at 10:12. Find (a) the deviation from the scheduled sample clock time and (b) the actual elapsed time since dose.
(a) On the clock-time scale, the scheduled sample is 10:00 and collection is 10:12. Therefore, the sample was collected \(10{:}12-10{:}00=12\) minutes late relative to its scheduled target.
(b) The actual dose occurred at 08:15. The elapsed time from that dose to collection is \(10{:}12-08{:}15=1\) hour 57 minutes. In hours, \(1+57/60=1.950\) hours.
The nominal post-scheduled-dose target is 2.00 hours, but the sample's actual time since the administered dose is 1.950 hours. For an analysis record whose time variable is elapsed time since that dose, use 1.950 hours. Retain the 2.00-hour nominal target and the 12-minute schedule deviation in their separate fields. They describe distinct aspects of the record.
Which Time Belongs in the Analysis Record?
For a pharmacokinetic analysis using sample time relative to dosing, the analysis record should use the actual collection time expressed relative to the relevant actual dose event. If the model instead uses another time origin, use the actual sample time on that model's documented scale. The rule is not simply “always use hours since the most recent dose”: the relevant dose and time origin depend on the dosing history and analysis model. They must be identified from the study records and the model definition.
Nominal time remains valuable. It identifies the planned sampling occasion, supports checks against the protocol, and allows departures from the design to be summarized. It may also be useful for design-based displays or sensitivity checks, but it should not silently replace the observed time in a concentration-time analysis.
A short justification shows why substituting nominal time can matter. Let \(f(t)\) denote a model-predicted concentration at time \(t\), and let \(\delta=t_{\text{actual}}-t_{\text{nominal}}\), with both times on the same analysis scale. For a small timing difference, a first-order Taylor expansion gives:
Thus, using the nominal time instead of the actual time can create an approximate prediction discrepancy of \(f'(t_{\text{nominal}})\delta\). Its size depends both on the timing departure and on how rapidly the predicted concentration is changing. Near a steep rise or decline, even a modest time discrepancy can matter more than it does in a relatively flat part of the profile. The direction of the resulting discrepancy depends on the local slope and whether the sample was early or late; there is no universal direction of bias.
Worked Example: Why a Small Timing Difference Can Matter
Consider a hypothetical concentration after a single bolus dose during a period in which a one-compartment elimination model applies: \(C(t)=C_0e^{-kt}\), where \(C_0\) is the concentration at time zero and \(k\) is the elimination rate constant. Suppose \(k=0.20\) per hour, and a sample is collected 2.12 hours after the dose although its nominal time is 2.00 hours. Compare the model predictions at those times as a ratio.
The ratio is \(C(2.12)/C(2.00)=e^{-0.20(2.12-2.00)}=e^{-0.024}\approx0.9763\). Under this hypothetical model, the predicted concentration at the actual time is about 97.63% of the prediction at the nominal time, or about 2.37% lower.
This calculation illustrates a timing effect under the stated elimination model; it does not establish that every 7.2-minute timing difference causes a 2.37% difference. The effect depends on the model and the local concentration-time behavior. The analysis should use the recorded actual timing rather than applying a generic correction based on this example.
Quality Checks and Common Failure Modes
Keeping two time fields makes checks possible, but only if their meanings are explicit. For each analysis record, verify that the nominal value corresponds to the intended scheduled occasion, the actual value comes from the sample collection record, and units and reference origins are documented. If the analysis time is derived relative to a dose, confirm that the selected dose event matches the dosing history and that the calculation uses actual event times.
- Overwriting actual time with nominal time: this makes the dataset look protocol-compliant while concealing collection departures.
- Mixing reference origins: subtracting time since scheduled dose from time since actual dose produces a meaningless deviation, even if both values are in hours.
- Using scheduled dose time as the analysis origin: this can make the calculated time since dose wrong when administration was delayed or otherwise changed.
- Rounding too early: converting a recorded clock time to a coarse time value before calculating elapsed time can discard useful precision. Retain source precision and apply a documented rounding rule only for the analysis representation.
- Treating a large deviation as proof of an error: it is a reason to investigate, not evidence by itself that the collection time is incorrect. Preserve the source value and document any resolution.
A diagnostic review can summarize signed deviations, absolute deviations, and the count or proportion outside a prespecified operational tolerance. Plotting signed deviation against nominal time or visit can help reveal systematic early or late collection. These checks assess timing records; they do not establish that a particular deviation is harmless for a given pharmacokinetic analysis. An implausible time or an unexplained discrepancy should be flagged for investigation rather than silently corrected.
Alternative Representations and Limitations
| Representation | Useful for | Main limitation |
|---|---|---|
| Actual time only | Analyses that require observed timing | Does not by itself show the planned target or schedule departure |
| Nominal time only | Identifying scheduled occasions and describing the design | Conceals actual timing deviations and can misstate analysis time |
| Both fields, kept distinct | Analysis plus schedule checks and deviation summaries | Requires documented units, origins, and rules linking records to dose events |
Using nominal time alone may appear convenient when a study has tightly scheduled visits, but it assumes that observed timing is sufficiently close to the target for the intended analysis. That assumption should be assessed, not built into the data by replacing observations. Conversely, storing actual time alone removes information about the planned design. Keeping both fields is generally the more transparent representation, although it cannot resolve an incorrect source timestamp or an uncertain dose history. Those issues require review of the source records and documented resolution.
Worked Example: Choose the Appropriate Record Fields
A hypothetical participant has a sample scheduled at 6 hours after a planned dose. The dose is administered at 09:30, and the sample is collected at 15:42. Assume the planned dose time was 09:30 and both timestamps are confirmed. State the nominal time, actual elapsed time since dose, and schedule deviation.
The nominal time is 6.00 hours after the planned dose. Actual elapsed time is \(15{:}42-09{:}30=6\) hours 12 minutes, or \(6+12/60=6.20\) hours. Because the scheduled and actual dose times coincide, the actual sample is 12 minutes later than the nominal target: \(\Delta_{\text{schedule}}=6.20-6.00=0.20\) hours.
The record should preserve the nominal value 6.00 hours and the actual elapsed time 6.20 hours, as separate fields, along with the underlying source timestamps or traceable references. If the model's time variable is elapsed time since dose, 6.20 hours belongs in that analysis-time field. The 0.20-hour deviation is appropriate because the nominal and actual values share the same dose-time origin in this example.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A sample is scheduled at 3.0 hours and collected at 3.25 hours on the same time scale. What are the signed and absolute deviations, in minutes?
- A dose is scheduled for 07:00 but administered at 07:20. A sample is collected at 09:10 and nominally scheduled for two hours after the planned dose. What are its schedule deviation and actual elapsed time since dose?
- Why should a dataset retain nominal time if actual time is used as the analysis time?
- A record has nominal time since scheduled dose and actual time since actual dose. Can these values be directly subtracted to calculate schedule deviation? Explain.
Solutions. (1) The signed deviation is \(3.25-3.00=0.25\) hours, or \(0.25\times60=15\) minutes late; the absolute deviation is 15 minutes. (2) The scheduled sample time is 09:00, so collection at 09:10 is 10 minutes late relative to schedule. Actual elapsed time is \(09{:}10-07{:}20=1\) hour 50 minutes, or \(1+50/60=1.833\) hours. (3) Nominal time identifies the planned occasion and supports schedule-deviation checks; actual time represents observed timing. Keeping both makes those uses possible without conflation. (4) No. The origins differ, so subtraction does not yield a valid schedule deviation. Express both values on a common, documented reference scale first.