Race and Ethnicity Categories as Measured Covariates

Why the Measurement and Coding Matter

Population PK analyses sometimes include recorded race or ethnicity categories to describe variation in a pharmacokinetic parameter, assess model fit across observed groups, or summarize the study population. The first requirement is to be clear about what the data actually record. Categories can differ across studies, and race and ethnicity are not interchangeable labels. Neither is a direct measurement of genotype, ancestry, enzyme activity, or another specific biological mechanism.

A category coefficient is therefore a comparison between groups as classified in a particular data set, conditional on the other terms in the model. It does not establish why the groups differ, that the label itself causes a difference, or that the estimate will apply to people classified differently elsewhere. Sound analysis starts by describing how the categories were collected and then represents them explicitly rather than assigning arbitrary numerical values to them.

Representing Categories With Indicators

Suppose a study records one variable with three values: Group A, Group B, and Group C. These names are hypothetical placeholders; an analysis should use and explain the study’s actual category definitions. With an intercept in the model, choose one category as the reference and create an indicator for each of the other categories. Each indicator equals 1 when a participant is in that category and 0 otherwise.

Group A is the reference: both indicators are 0 for a participant recorded in Group A. Group B is represented by \((I_{iB}, I_{iC})=(1,0)\), and Group C by \((0,1)\). Do not include an indicator for every category alongside an intercept: because the indicators would sum to 1 for every participant, that coding is redundant and the separate coefficients cannot all be identified.

For a clearance model, one common form is:

Here \(CL_i\) is participant \(i\)’s clearance, \(TVCL\) is the typical clearance for the reference category when the other covariates in the model are at their reference or centered values, \(\beta_B\) and \(\beta_C\) are category coefficients, and \(\eta_{CL,i}\) is the participant-specific random effect on log clearance. Other modeled covariates can be added to the exponent. This form assumes that the category coefficients apply consistently across the modeled covariate range; an interaction or a different model is needed if the intended contrast varies across that range.

What a Category Coefficient Means

In the clearance model, the typical clearance for Group A is \(TVCL\), for Group B it is \(TVCL\exp(\beta_B)\), and for Group C it is \(TVCL\exp(\beta_C)\), holding the other modeled covariates fixed. The coefficient is on the log scale; exponentiating it gives a ratio of typical clearances. For example, \(\exp(\beta_B)=0.80\) corresponds to a modeled typical clearance 0.80 times that of the reference category, or 20% lower, under the stated conditions.

This interpretation follows directly by comparing the model predictions. Consider Group B and Group A at the same values of the other covariates and with the same random effect. Their clearances are:

Dividing the first expression by the second cancels the common terms and gives:

This is the model’s conditional typical-value ratio, not evidence that category membership itself caused the difference. Its interpretation also depends on the model being appropriate and on there being adequate data to estimate the contrast. If uncertainty is reported, it should accompany the estimate; a point estimate alone does not show how precisely the contrast is known.

Assumptions, Support, and Diagnostics

Indicator coding is a representation, not a guarantee that a coefficient can be estimated well or interpreted safely. Before fitting the model, check that the recorded categories are defined consistently, that each participant is assigned according to the stated rules, and that the reference category is identifiable from the data. The model’s usual assumptions also matter: its structural form should describe the concentration-time data adequately, and the random-effects and residual-error specifications should be reasonable for the analysis.

A category contrast is estimated from the information contributed by the people in the relevant groups. Very small groups, few informative concentration-time observations within a group, or little overlap in other covariates can make estimates unstable or make the comparison depend heavily on modeling assumptions. A fitted coefficient is not proof of a robust subgroup difference simply because software returned a number.

Useful checks include verifying the category labels and indicator values, reviewing counts and observation patterns by group, and examining whether the model’s predictions and residual behavior are systematically different across recorded categories. A strong estimate that changes markedly when a few participants are removed signals fragility. A contrast that is not estimable, has substantial uncertainty, or relies on extrapolation beyond the covariate overlap should not be given a confident interpretation.

Choosing a Parameterization Without Changing the Question

Reference coding is often convenient because the coefficients directly compare each nonreference group with a named reference. Other parameterizations can represent the same categorical model. For example, a sum-to-zero constraint can express category effects relative to an overall modeled level rather than a single reference group. If the model matrix spans the same category contrasts, the parameterization changes the coefficient meanings but not the fitted predictions. Comparisons must therefore state which parameterization and reference are used.

The main alternative is not merely a different coding scheme, but a different scientific representation. Treating categories as a single numeric score assumes a graded trend. Collapsing categories assumes that the groups combined can reasonably share the modeled effect. Omitting the covariate avoids estimating group contrasts but may leave relevant systematic variation undescribed. A study should select among these choices based on its question, measurement process, available data, and justification—not because one encoding produces a preferred result.

Common Mistakes and Limits of Interpretation

• Reading the labels as biological measurements. A race or ethnicity category does not directly measure a metabolic pathway, genotype, or ancestry. A coefficient alone cannot identify a mechanism.
• Using an arbitrary numeric score. Coding categories as 1, 2, and 3 imposes a numerical order and spacing. Use indicator variables unless a meaningful quantitative scale is actually measured.
• Omitting the reference and conditions. “Clearance was lower” is incomplete. State the recorded groups being compared, the reference, the parameter and units, and that the contrast is conditional on other modeled covariates.
• Claiming causation from a descriptive contrast. The fitted difference is an association within a model. It does not establish that a recorded label causes a PK difference.
• Interpreting sparse-group estimates as equally reliable. Each category needs adequate informative data; a large total sample does not ensure precise estimates for every group.

Category definitions and recording procedures may vary across settings, limiting transportability. Results should identify how the covariate was measured and avoid implying that a contrast generalizes automatically to differently classified populations. Where the goal is to understand a specific biological mechanism, the category label is not a substitute for measuring and evaluating that mechanism directly.