Ordering Simultaneous Dose and Sample Events

Why Event Order Matters When Times Match

A dose record and a sample record can have the same recorded time without representing events that occurred simultaneously. The times may have been rounded, truncated, or stored only to a coarse resolution. Conversely, records may share a genuinely exact timestamp, while the data still do not establish which event occurred first. These are different situations, and a reliable dataset should not treat them as if they were interchangeable.

Order matters because a pharmacometric model uses event records to represent the history that generated each observation. For an instantaneous bolus, the modeled concentration changes at the dose time. A sample interpreted immediately before the dose can therefore have a different model prediction from one interpreted immediately after it. The key task is not to impose a universal ordering rule: none applies in every dataset. It is to use documented event details where available and to define a transparent, reproducible convention for any unresolved tie.

Start With the Source Records

Before assigning a sequence to tied events, check what the time fields mean and how they were produced. A time recorded to the nearest minute is not equivalent to an exact time recorded to the second. Nor is a planned collection time necessarily the same as the actual collection time, or a scheduled dose time the same as actual administration. Use the source details that describe when the sample was collected and when the dose was administered, including the relevant administration time for an infusion.

When source records provide finer timing than the analysis dataset, retain or recover that precision if it is reliable and permitted by the data specification. Compare the underlying times before deciding whether a tie exists. Do not infer an order simply from the order of rows in a source export: that order may reflect entry, transfer, or sorting rather than event chronology. Also check whether the relevant dates and time zones are consistent, since a time-of-day comparison alone can misorder events across date boundaries.

If reliable documentation establishes the order, carry that order into the analysis dataset, even when the stored timestamps match. If the sources do not resolve the order, apply a declared fallback convention consistently. A convention might specify that a sample record precedes a dose record when their times tie, or specify the reverse. Neither is universally correct. The choice should be compatible with the study documentation and model-data requirements, and the unresolved tie should remain identifiable for review.

Define a Reproducible Ordering Rule

A sound ordering procedure separates the recorded time from the sequence used to resolve ties. One practical specification is: sort first by the analysis time; within a tied time, use verified source chronology; if chronology is unavailable, apply the documented fallback priority; and use a stable final tie-breaker for otherwise indistinguishable records. The final tie-breaker might be a retained source-record identifier. It should make processing reproducible without pretending to reveal an unknown physical order.

For example, a data specification can define a priority for sample and dose records when their analysis times match. The priority should be stated in words, implemented explicitly, and checked after every sort or merge that might change row order. If two events of the same type also tie, use a stable identifier or source sequence rather than allowing software-specific sort behavior to decide their order.

Why the Order Can Change a Model Prediction

The consequence is clearest for an idealized instantaneous bolus in a one-compartment model. Assume a known volume of distribution \(V\), an instantaneous dose \(D\), and no simultaneous process that changes concentration discontinuously. Concentration immediately after the bolus exceeds concentration immediately before it by the dose divided by volume:

This follows from the model’s bolus rule: the dose adds an amount \(D\) to the amount in the compartment at time \(t\). Dividing that amount by the compartment volume gives the concentration increment \(D/V\). Thus, if an observation at the same represented time is ordered after the dose, its prediction uses the post-dose state; if ordered before, its prediction uses the pre-dose state. This distinction does not by itself say which sequence is correct for a particular sample. That must come from the documented event chronology or the declared convention.

Diagnostics, Alternatives, and Limitations

A useful review checks both the raw time information and the final event sequence. Flag dose–sample ties, ties involving multiple dose or sample records, unexpectedly reversed chronology, and records whose source precision exceeds the precision retained for analysis. Check that a sort by time and within-time rank gives the same sequence each time. After data joins or exports, verify that the rank and source identifiers remain attached to the correct records.

Also compare the ordering rule with study documentation: does it match actual collection and administration details where available? If a protocol describes a predose collection but actual timing is missing, treat that as evidence about the planned procedure, not automatic proof of what happened for every participant. Where source times disagree, or clocks are known to be unreliable, flag the conflict rather than silently choosing one source. A missing or inconsistent time cannot be repaired merely by imposing a deterministic sort.

There are two common ways to represent tied events. One is to keep the same time and provide an explicit within-time ordering field, if the modeling workflow supports and respects it. Another is to preserve source times at finer precision when they are reliable. Altering a time by adding a small artificial offset can force an order in software that otherwise cannot represent ties, but it changes the event time. Such an adjustment is not a neutral substitute for an ordering field: it should be used only when required, documented, and shown to be small enough not to distort relevant time intervals.

The limitation is fundamental: a fallback rule makes the dataset deterministic, but it does not recover chronology that was never recorded. If the modeled outcome is sensitive to alternative plausible orders, the unresolved tie may warrant a sensitivity check using each defensible sequence. This is a data-interpretation check, not a way to infer which chronology actually occurred.