Reconstruct Elapsed Time From Visit Timestamps

Why Reconstruct Elapsed Time?

Population pharmacokinetic records often contain both calendar timestamps and a time variable used to order observations relative to a reference event, such as a documented dose. A sample timestamp says when the sample was recorded on the calendar; an elapsed-time value says how long after or before the reference event it occurred. Reconstructing the elapsed time provides a direct check on the analysis-ready record and can reveal mismatches between timestamps, visit records, and recorded timing fields.

The calculation is simple only when the inputs are comparable and sufficiently precise. Both timestamps must refer to a consistent time basis, and the intended reference event must be clear. If one time is recorded only to the nearest minute and another to the nearest second, the resulting difference should not be reported as though it were known exactly to the second. Calendar dates must also be subtracted as dates, not by subtracting the displayed hour values alone.

Calculation From Harmonized Timestamps

Let \(T_R\) be the timestamp of the documented reference event and \(T_V\) the timestamp of the visit or sample. First calculate the difference on a common timeline, then convert it to the desired unit. For example, when the time difference is represented in seconds, elapsed time in hours is:

The subtraction here is between complete date-times, not merely clock readings. A calculation should retain enough intermediate precision to avoid avoidable arithmetic error, but the final reported precision must respect the precision of the source timestamps. If a visit occurs before the reference event, the subtraction is negative; that sign is meaningful and should not be changed just to make the time nonnegative.

Before calculating, confirm that the reference and visit timestamps have been harmonized to a comparable time basis. The earlier material on harmonizing dates, clock times, and time zones covers that preparation. A timestamp from one time zone must not be subtracted directly from a timestamp in another without accounting for the difference. Likewise, a local clock change can make clock-time subtraction misleading even when the calendar date appears unchanged. Use the harmonized timestamps rather than trying to repair such issues inside the elapsed-time calculation.

A useful check is to calculate the difference in a small base unit, such as seconds or minutes, and then convert once. For timestamps with different dates, a calendar-aware date-time calculation is essential: the number of days between the dates must be included. This also avoids errors around month ends and leap days. If the source records contain only dates, rather than times of day, a precise elapsed time in hours cannot be recovered from them.

Check Against Visit Records

A reconstructed value should be compared with the other timing information attached to the visit. That information may include a nominal visit label, a scheduled time, or a separately recorded actual elapsed time. These fields do not necessarily mean the same thing. A nominal value describes the intended or labelled sampling time; a value calculated from actual timestamps describes the observed timing relative to the chosen reference event. A difference between them is a reason to investigate, not automatic evidence that either field is wrong.

The comparison is most informative when the data record retains the pieces needed to reproduce it: the reference-event timestamp, the visit timestamp, the calculated elapsed time with units, and the available visit or nominal-time information. If the reconstructed and recorded values differ, check that the correct reference event was selected, that the timestamps belong to the same participant and relevant record, that dates and time zones were handled consistently, and that units were not confused. Only then decide whether a query or correction is warranted.

Rounding and Timestamp Precision

A timestamp recorded to a particular resolution does not generally identify an exact underlying time. For instance, if a timestamp is rounded to the nearest minute, the underlying time may be up to half a minute earlier or later than the displayed value. This is a statement about rounding resolution, not necessarily about the accuracy of the clock or the quality of the original observation. A timestamp can be recorded to the nearest second while still having other sources of error.

Under the explicit assumption that each displayed timestamp was rounded to the nearest unit, let \(q_R\) and \(q_V\) be the rounding resolutions for the reference and visit timestamps, expressed in the same unit. Each underlying time is within half its resolution of the displayed time. Because elapsed time subtracts one timestamp from the other, the maximum rounding deviation is the sum of the two half-resolutions:

This is a worst-case bound under the stated rounding assumption; it is not a confidence interval and does not assign probabilities to possible underlying times. If timestamps were truncated instead of rounded to nearest, the possible underlying times lie in different intervals, and the bound above should not be used without adjustment. The recording convention matters.

If both timestamps are recorded to the nearest minute, the maximum rounding deviation in their difference is one minute: \(0.5+0.5=1\) minute. If one timestamp is recorded only to the nearest day, its uncertainty can be as large as half a day under nearest-day rounding, so an elapsed time stated to a few minutes is not supported. When precision differs, the coarser timestamp often dominates the uncertainty, but both timestamps contribute.

A practical rule is to preserve the raw timestamps, calculate using their available values, document the output unit and precision, and avoid implying that displayed decimal places are newly observed information. A calculated value may be stored with computational precision for reproducibility, but a reported value should not be mistaken for exact knowledge of the event time.

Diagnostics, Alternatives, and Limitations

A reproducible calculation is not, by itself, proof that the inputs are correct. Diagnostics focus on whether the result is compatible with the source records and whether the calculation's assumptions hold. Investigate values that have unexpected signs, implausible magnitudes, a date difference that does not match the visit sequence, or a disagreement with a recorded timing field that exceeds what rounding can explain. Also check that the intended reference event—not a planned event or a different documented event—was used.

There are several reasonable representations of visit timing, but they answer different questions:

When trustworthy timestamps are available, direct reconstruction is a transparent way to check an elapsed-time field. A nominal time can still be useful for identifying the intended visit, but it should not be substituted for actual timing without a clear analysis reason. If the reference or visit timestamp is unavailable, a separately recorded elapsed-time field may be the only usable information; its source and meaning should then be documented rather than assumed.

The method cannot recover information that was never recorded. Date-only values do not establish time of day; coarse rounding cannot be undone; and a time-zone or clock error cannot be fixed by accurate subtraction. These limitations make preserving the original values and documenting any justified correction important. An unexplained discrepancy should be flagged for review, not “corrected” by choosing whichever field produces the most convenient elapsed time.

Common Pitfalls

• Subtracting clock times but ignoring dates. A sample after midnight may appear to precede its reference event if only the clock readings are compared. Subtract complete date-times.
• Treating nominal time as actual time. A “5-hour” visit label does not establish that the sample occurred exactly five hours after the reference event. Compare it with the reconstructed value and preserve the distinction.
• Reporting false precision. A difference such as 46.5 minutes does not mean that the actual elapsed time is known to a fraction of a second when one timestamp is rounded to a minute.
• Assuming rounding when the convention is unknown. The nearest-unit uncertainty calculation applies only when the values were rounded to nearest. Confirm the recording convention or state the assumption.
• Changing a negative result to positive. A negative elapsed time may correctly indicate that a visit occurred before the selected reference event. Check the event choice and chronology instead of discarding the sign.