Why the Analysis Table Is Part of the Scientific Question
An exposure-effect analysis table is not merely a convenient arrangement of columns. It makes explicit which exposure value is paired with each pharmacodynamic (PD) observation. A concentration recorded at a particular time, an area under the concentration-time curve (AUC) over a defined interval, and a time-above-threshold measure describe different aspects of exposure. A table that stores only a number, without its metric and time span, cannot reliably preserve that distinction.
The appropriate row usually represents one PD observation for one subject at one observation time and one dosing occasion. A subject may therefore appear on many rows. This structure retains repeated measurements without implying that all rows are independent or that a subject contributes only one record.
The exposure metric is chosen to answer the scientific question; the table should not silently substitute one metric for another. Earlier material on choosing exposure metrics and matching exposure windows establishes the rationale for that choice. Here, the task is to represent it faithfully in data so a later analysis can use the intended pairing.
Specify the Row, Keys, and Time Reference
Before combining source records, state what uniquely identifies a row. A useful key is often a combination of subject identifier, dosing-occasion identifier, and PD-record identifier. If there is exactly one PD observation per scheduled time within an occasion, a subject identifier, occasion identifier, and nominal time may suffice; if there can be duplicate or unscheduled observations, a separate PD-record identifier is safer.
Do not assume a subject identifier alone is a sufficient key. It identifies the person, not a particular observation or dose. Similarly, a time such as “2 hours” is ambiguous unless the reference event is clear. It may mean two hours since the first dose, the most recent dose, a study visit, or a sample. Store a defined time reference, such as elapsed time since the dose for that occasion, and retain actual timestamps if they are needed to audit the derivation.
A compact analysis table may include these fields:
- Identifiers: subject ID, dosing occasion or period ID, and PD-record ID.
- PD information: observed effect, effect units, actual or nominal observation time, and time reference.
- Exposure information: metric name, metric value, units, and metric window start and end when the metric is window-based.
- Context and provenance: dose or regimen identifier when relevant, source or derivation identifier, and a status or reason code for unavailable values.
A metric window should be stored with a clear convention. For example, an AUC from 0 to 4 hours after a dose can be represented by a start time of 0 hours and an end time of 4 hours, both relative to that dose. A window should not be inferred later from a label such as “AUC” alone. If an instantaneous concentration is used, record its sampling time; a window start and end are not meaningful in the same way, though the time of the concentration still must be explicit.
Worked Example: A Single-Time Concentration Paired With PD
Hypothetical data. Subject P014 receives one dose at time 0. At 2 hours, the scheduled concentration is 8.0 mg/L and the PD measure is 42 beats/min. The exposure metric selected for this question is instantaneous concentration at the PD observation time.
The paired record should identify the subject, occasion, and PD observation, and should preserve the common time reference. It can be represented as follows.
| Subject | Occasion | PD record | PD time (h after dose) | PD value (beats/min) | Exposure metric | Exposure value | Exposure units | Metric time |
|---|---|---|---|---|---|---|---|---|
| P014 | 1 | PD001 | 2 | 42 | Concentration | 8.0 | mg/L | 2 h after dose |
The pairing is justified here because the concentration was scheduled and observed at the same 2-hour time as the PD measurement, with both times measured from the same dose. The value is not “dose,” nor does the table claim that concentration caused the observed PD value. It records the intended exposure-effect pairing for analysis.
If the concentration had instead been measured at 1.5 hours, the table should preserve that actual sampling time. A separate, specified rule would be needed to determine whether and how that value represents concentration at 2 hours. Recording “2 h” merely because that is the PD time would conceal the mismatch.
Representing a Window-Based Exposure Metric
For a window-based metric, the row must carry enough information to establish the interval to which the value refers. In the next hypothetical example, PD observations are paired with AUC values for the immediately preceding four hours. The numerical calculation illustrates how the interval and value travel together in the dataset; it does not change the metric-selection question.
Worked Example: Adding a Four-Hour AUC to Each PD Record
Hypothetical data. For subject P021, concentration measurements during one dosing occasion are 0 mg/L at 0 hours, 8 mg/L at 2 hours, 12 mg/L at 4 hours, 8 mg/L at 6 hours, and 4 mg/L at 8 hours. PD is observed at 4 and 8 hours. The selected exposure metric for each PD record is AUC over the preceding four hours. Use the linear trapezoidal calculation on the available concentration measurements.
For the PD observation at 4 hours, the window is 0–4 hours. The two trapezoid areas are
For the PD observation at 8 hours, the window is 4–8 hours. Its trapezoid areas are
The resulting analysis rows retain distinct windows even though they belong to the same subject and dosing occasion.
| Subject | Occasion | PD record | PD time (h) | PD value (units as defined by protocol) | Exposure metric | Window (h after dose) | Exposure value | Exposure units |
|---|---|---|---|---|---|---|---|---|
| P021 | 1 | PD011 | 4 | 0.72 | AUC | 0–4 | 28 | mg·h/L |
| P021 | 1 | PD012 | 8 | 0.65 | AUC | 4–8 | 32 | mg·h/L |
The table does not store just “28” and “32”: it stores which intervals produced them. The PD value units should also be filled with the actual protocol-defined units before analysis; the placeholder in this illustration is not a usable unit label. Window boundaries and the time reference are essential metadata, not optional notes.
Build and Validate the Link
Combining PD records and exposure summaries is a data-linkage operation. The intended relationship is commonly one exposure value for each PD record, but the source tables may have different row counts and levels of detail. A concentration-time table may contain many samples per subject and occasion, while a PD table contains a different number of observation times. A summary table may then contain one derived exposure value per PD record or per defined window.
A safe construction makes the intended relationship explicit before joining. In particular, determine whether the exposure source has one matching record for each PD key. If it has more than one, the join may multiply rows; if it has none, the exposure value is unmatched. The following check follows directly from the row-key definition: if the desired final table has one row per PD record, then after linking, each PD-record key should still occur exactly once. A duplicate key means the table no longer has the defined row structure.
State that one row represents one PD observation for one subject and occasion, and identify the fields that uniquely distinguish it.
Specify the metric, units, time reference, and any required window or sampling-time relationship before creating paired values.
Use identifiers that distinguish subjects, occasions, and PD records. Do not link on subject alone when that subject contributes repeated observations or occasions.
Confirm that each intended PD record appears once, investigate extra matches, and record why an exposure value is unavailable.
Check units, time references, window boundaries, and selected records against the source data and derivation rules.
Worked Example: Keeping Two Dosing Occasions Separate
Hypothetical data. Subject P032 has two occasions. At 2 hours after each occasion’s dose, one PD record is available. A summary file contains the corresponding 0–2-hour AUC values: 10 mg·h/L for occasion 1 and 14 mg·h/L for occasion 2. The PD values are 36 and 33 beats/min, respectively.
| Subject | Occasion | PD record | PD time (h after occasion dose) | PD value (beats/min) | AUC window | AUC (mg·h/L) |
|---|---|---|---|---|---|---|
| P032 | 1 | PD021 | 2 | 36 | 0–2 h after occasion 1 dose | 10 |
| P032 | 2 | PD022 | 2 | 33 | 0–2 h after occasion 2 dose | 14 |
The correct link uses subject and occasion identifiers, as well as the PD record when linking directly to PD rows. If the files are joined using subject ID alone, each of the two PD rows can match both AUC rows. The result has \(2\times2=4\) matched rows rather than the intended two. That multiplication duplicates records and incorrectly pairs occasion 1 PD with occasion 2 exposure, and vice versa.
For this example, checking that PD021 appears once with the occasion 1 AUC and PD022 appears once with the occasion 2 AUC verifies the intended linkage. The occasion identifier is not redundant just because the elapsed time happens to be 2 hours in both records; each elapsed time is referenced to a different dose.
Missing Values, Diagnostics, and Alternatives
An exposure value can be unavailable because a required concentration sample was not collected, a window is incomplete under the prespecified rule, a dose time is unknown, or a derivation failed. These are different situations and should not be represented as the same numeric value. In particular, zero means the measured or derived metric is zero; it does not mean “not available.” Preserve a missing value and, where feasible, a reason or status field that distinguishes the cause.
Useful checks include:
- Count rows and distinct PD-record keys before and after linking; the final table should retain the intended number of PD observations.
- Check for duplicate keys and exposure records that match more than one PD record unexpectedly.
- Review unmatched PD records and unmatched exposure summaries rather than silently dropping them.
- Check that metric names agree with units: for example, concentration and AUC must not share a unit label.
- Verify that window start precedes window end and that the window agrees with the stated time reference and dosing occasion.
- Compare selected values and their source records for a sample of subjects, including repeated occasions and records near window boundaries.
These checks can reveal structural problems, but a table that passes them is not proof that the chosen metric is scientifically appropriate. The metric and timing rule still need to match the question and the measurement process.
| Structure | Useful when | Main caution |
|---|---|---|
| Long analysis table: one row per PD observation | Subjects have repeated observations or occasions; each row needs its own paired exposure | Rows are repeated records within subjects, not automatically independent observations |
| Wide table: separate columns for each time or occasion | A small, fixed schedule makes direct visual comparison convenient | Irregular times, missing records, and additional occasions can make columns ambiguous or unwieldy |
| Separate linked tables | Source records are naturally stored at different levels, such as one table for PD and another for exposure summaries | The key and matching rule must be documented and checked whenever tables are combined |
The long format is often a practical analysis input because each effect observation has its own row and its own paired exposure fields. A wide format may be useful for display or a fixed-schedule calculation, but reshaping must preserve the identifiers and timing. Keeping separate linked tables may be preferable when it preserves source-level detail; it does not remove the need to define and validate the relationship between records.
Common Pitfall and Limits
Wrong reasoning: “The subject has one exposure summary, so I can merge it onto every PD record for that subject.” This is only valid if that single summary is truly the selected metric for every observation under the analysis definition. If the exposure varies by time or dosing occasion, this merge assigns the same value to records that require different values and may conceal a timing mismatch.
Correction: define the metric at the level required by the PD observation, preserve its time or window, and link using keys that identify the subject, occasion, and observation as needed. If an intended value cannot be obtained, retain that record with an explicit missing status rather than substituting a convenient value.
A well-formed table does not resolve every scientific limitation. Exposure estimates may be imprecise, a selected window may not capture the relevant time course, and some subjects may lack usable paired records. Nor does a row-wise pairing alone account for repeated measurements within subjects. The dataset is a transparent foundation for analysis, not a guarantee of valid interpretation or a causal conclusion.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A subject has PD measurements at 1, 3, and 6 hours after a dose. What does one row represent in a long exposure-effect table, and which identifiers could distinguish the rows?
- For a PD measurement at 6 hours, the selected metric is AUC from 2 to 6 hours after dose. Name the timing fields and units that should accompany the AUC value.
- A merge produces twice as many rows as there are PD records. Give one likely cause and one check that would locate the problem.
- A required exposure window cannot be calculated because a concentration sample is missing. Should the exposure value be entered as zero? Explain what should be recorded instead.
Solutions. (1) Each row represents one PD observation for that subject at one time and occasion. Subject ID, occasion ID, and a unique PD-record ID distinguish the three rows; time can be part of the key only when it is unambiguous and unique within that context. (2) Record the metric name AUC, its value in concentration-times-time units appropriate to the concentration and time units, window start 2 hours and end 6 hours, and that both times are relative to the dose for the specified occasion. (3) The exposure source may have multiple matching rows per PD key, or the join may omit the occasion identifier. Check duplicate keys and the number of matches for each PD record; each intended PD key should occur once in the final table. (4) No. Zero asserts a zero exposure value. Preserve the exposure as missing and record a reason such as an unavailable required sample or incomplete window.