Defining Analysis Populations in the Report

Why Analysis Populations Need Explicit Definitions

A population pharmacokinetic (PK) report describes both a model and the people whose data informed it. A reader cannot interpret the model's relevance or reproduce its analysis if terms such as “evaluable” or “included” are left undefined. The same label can refer to different criteria in different studies, and one participant can contribute to one analysis but not another.

The analysis objectives determine which participants and data are relevant, but the population definitions should be stated independently and precisely. A description such as “adult patients with the disease were analyzed” does not say which clinical setting is represented, how eligibility was determined, or whether every enrolled participant contributed to the final model. A clear account connects the clinical population to the actual analysis set without implying that these groups are identical.

These labels do not define a universal sequence by themselves. For example, a study may enroll participants who meet protocol eligibility criteria but later find that some have no usable concentration data. Conversely, a participant may be evaluable for the primary PK model but not for a secondary analysis that requires a covariate not collected for that participant. Therefore, define each set with reference to an analysis and its data requirements, rather than relying on a label alone.

From Source Population to Analysis Set

Describe the source population in terms that communicate the clinical context: relevant disease or treatment setting, age range or category, care setting, and any other characteristics that define the intended scope. The source population is not simply the enrolled sample. It states the context in which the results are meant to be considered; it does not guarantee that every group in that context was represented or that findings apply equally to every individual.

State eligibility criteria in operational terms. If an age threshold, renal-function threshold, treatment history, or sampling requirement determines eligibility, identify the rule and the time at which it was assessed when that matters. Separate criteria for study enrollment from criteria for a particular analysis. A participant could be enrolled according to the protocol but excluded from an analysis because that analysis requires a recorded dose history or a measurement within a defined interval.

“Evaluable” is especially prone to ambiguity. It should be followed by the criteria that make a participant evaluable for a named purpose. For a PK analysis, a report might define evaluability as having at least one concentration measurement with a usable sampling time and dose history. Another analysis may require several concentration measurements, a particular dosing occasion, or a specific covariate. These are different rules and can produce different evaluable sets.

Likewise, “modeled” should mean that the participant’s data were included in the stated model fit, not merely that the participant was eligible or had a concentration measurement. If a participant was not included, give the reason in terms of the analysis decision, such as unresolved dose-time records or failure to meet a prespecified model-data requirement. The reason should be factual and should not suggest that the participant’s treatment response was unfavorable unless that was genuinely the exclusion rule.

Set Relationships and Denominators

When the criteria are nested, set notation makes the relationship and its arithmetic explicit. Let \(E\) be the set of enrolled participants, \(A\) the set evaluable for a specified analysis, and \(M\) the set included in that analysis's model. If the report defines every modeled participant as evaluable and every evaluable participant as enrolled, then \(M\subseteq A\subseteq E\). The counts must satisfy \(N_M\leq N_A\leq N_E\), where \(N\) denotes the number of participants in a set.

These equalities follow from the subset relationships: the enrolled participants divide into those in \(A\) and those outside \(A\); the evaluable participants divide into those in \(M\) and those outside \(M\). If the report uses different definitions—for example, if “evaluable” is assigned only after a model-fit assessment—the sets may not be nested in this way. In that case, do not use these subtractions as if they were valid; describe the rules and overlaps directly.

Percentages are meaningful only alongside their denominator and population definition. “Ninety-two percent were evaluable” is incomplete unless it states whether the denominator is enrolled participants, eligible participants, or another set. Participant counts should also be kept distinct from observation counts: one participant can contribute multiple concentration observations, while another contributes only one.

Analysis-Specific Sets and Clear Reporting

A population PK report may contain several analyses with different data requirements. A primary model may use all participants with usable concentration and dosing records, while a covariate analysis may require additional covariate measurements. A sensitivity analysis may apply a different, prespecified rule. It is therefore often more accurate to define separate sets for separate objectives than to imply that one universal “analysis population” serves every purpose.

When sets differ, name the analysis each set supports and explain the rule that creates the difference. Do not describe a participant as simply “excluded from the study” if that person remained enrolled and was omitted only from one model. Similarly, do not call a participant “modeled” in a way that obscures that their data were absent from a particular model fit. Population definitions should align with the analysis objectives and terminology used elsewhere in the report.

A useful reporting sequence is to state the source population and study eligibility, define the analysis sets, then identify the set used for each model. The account should be internally consistent: if a table labels 108 participants as modeled, the methods and results should not later describe a different count without explaining the analysis-specific difference.

Common Pitfalls, Diagnostics, and Alternatives

• Using “evaluable” without a rule. Readers cannot tell whether the term means any recorded concentration, sufficient data for an individual fit, or successful inclusion in a population model. Define the rule for the named analysis.
• Calling enrolled participants “modeled.” Enrollment does not establish that data were available or used. Report the actual model set separately.
• Giving a percentage without its denominator. “Ninety percent included” could mean 90% of enrolled, eligible, or evaluable participants. Name the denominator and the set.
• Combining participants and observations. A count of concentration records is not a count of modeled participants. Label both quantities and their units explicitly.
• Making an unsupported generalization. The source population describes intended clinical relevance; it does not prove that the enrolled sample represents every person in that population.

A practical diagnostic is to check whether a reader could reconstruct each stated count from the definitions and whether the report distinguishes study eligibility from model-data requirements. Check that percentages use the stated denominators, that model membership matches the analysis being described, and that exclusions are explained without conflating a participant with an individual observation. If a single “analysis population” is used for several objectives, verify that all those analyses truly used the same participants; otherwise, provide objective-specific definitions.

One alternative is to define a single common analysis set for every analysis. This can simplify presentation when the same participants and criteria genuinely apply throughout, but it can needlessly remove data from analyses with less demanding requirements or obscure which participants informed a particular model. The other alternative is to define a separate set for every analysis. That is transparent when requirements differ, but excessive or shifting labels can make the report difficult to follow. The appropriate approach is the simplest set of definitions that accurately represents the analyses, with stable names and explicit criteria.

Population definitions also have limits. A carefully defined modeled set improves transparency but does not by itself establish representativeness, remove bias from missing data, or ensure that model conclusions apply beyond the observed clinical setting. Those questions require interpretation of the study design and evidence, not merely a count of participants.