Encoding Child-Pugh Class in Population PK Models

From a Clinical Score to a PK Covariate

Child-Pugh class summarizes several aspects of hepatic disease in one ordered category. In a population PK model, it can be used as a covariate to describe how a typical PK parameter differs across classes. The encoding matters: a categorical model estimates separate contrasts, while an ordinal model imposes a trend. Neither choice turns the score into a direct measurement of hepatic drug-metabolizing capacity, and an estimated covariate relationship is not by itself a causal effect.

The usual score is formed from five components: serum bilirubin, serum albumin, INR, ascites, and hepatic encephalopathy. Each component contributes 1, 2, or 3 points. The total ranges from 5 to 15, with higher scores indicating greater impairment under this scoring system. The total is classified as Child-Pugh A for 5–6 points, B for 7–9, and C for 10–15.

These cutpoints describe a commonly used INR-based scoring scheme. Investigators should specify the version, units, and scoring rules applied in their data, including how exact boundary values and clinically assessed components are handled. A score should not be reconstructed by silently mixing incompatible conventions.

Categorical Encoding and Coefficient Interpretation

For a categorical model, choose a reference class and use indicator variables for the remaining classes. If class A is the reference, define \(I_{B,i}=1\) when participant \(i\) is class B and 0 otherwise, and define \(I_{C,i}\) analogously. For a positive PK parameter such as clearance, a common log-linear covariate model is:

Here \(TVCL_i\) is the typical clearance for participant \(i\), conditional on the covariates in this expression; \(\theta_{CL}\) is typical clearance in the reference class A; and \(\theta_B\) and \(\theta_C\) are log contrasts with class A. A full individual-level model may also include interindividual random effects, but those do not change the interpretation of these fixed covariate contrasts.

For class A, both indicators are zero, so \(TVCL_A=\theta_{CL}\). For class B, \(TVCL_B=\theta_{CL}\exp(\theta_B)\). Dividing gives \(TVCL_B/TVCL_A=\exp(\theta_B)\); similarly, \(TVCL_C/TVCL_A=\exp(\theta_C)\). Thus, exponentiating a coefficient gives a ratio, not an absolute change in clearance. The same form can be used for another positive parameter, with the parameter name and units interpreted accordingly.

Ordinal Coding and the Trend Assumption

Because A, B, and C are ordered, a model may instead assign them scores 0, 1, and 2. Let \(z_i\) denote this coding. An ordinal log-linear model for clearance is:

This model uses one coefficient, \(\beta\), rather than separate class contrasts. It assumes each step from A to B and from B to C has the same effect on log clearance. The predicted ratio for each adjacent class step is \(\exp(\beta)\); the C-to-A ratio is \(\exp(2\beta)\). This is a stronger assumption than simply recognizing that the classes are ordered. It does not assert that the clinical differences between the classes are equal in every other sense.

Assumptions, Diagnostics, and Alternatives

A covariate encoding is useful only if the score is consistently defined and the data support the comparisons being estimated. Before interpreting a class effect, check that the component measurements and clinical assessments correspond to a suitable, documented time point for the PK observations. If class can change during follow-up, a single baseline class assumes that the baseline category adequately represents the relevant period. If that is not credible, the fixed baseline coding may misrepresent exposure to the covariate.

The model also needs enough participants and information in each class to estimate its contrasts. A class with very few participants can produce imprecise estimates or unstable fitting; if no participant is observed in a class, its separate categorical contrast cannot be estimated from the data. Check class counts, the distribution of component scores within each class, parameter uncertainty, and whether estimates change substantially under reasonable alternative specifications. Examine model diagnostics for systematic residual patterns across classes. These checks cannot establish that the score captures every clinically relevant aspect of hepatic function, but they can reveal whether the proposed encoding is poorly supported.

The main encoding choices make different commitments:

Using the total point score as a numeric covariate is not identical to coding A, B, and C as 0, 1, and 2: it distinguishes scores within a class and assumes a constant trend for each point. Either numeric approach can be more efficient than fitting separate class contrasts if its trend assumption is reasonable. Conversely, an ordered scale does not automatically justify a linear effect. The categorical model is more flexible across the three classes but uses more parameters.

Score Composition and Within-Class Variation

Child-Pugh class compresses five components into a total and then groups totals into three categories. Consequently, participants in one class may reach the same total through different combinations of laboratory measurements and clinical findings. For example, a participant’s score may include more points from albumin and bilirubin, while another participant with the same total has more points from ascites and encephalopathy. The class alone does not preserve that component-level detail.

This composition can matter in PK interpretation. A class contrast describes average model differences between the observed groups, conditional on the other terms in the model; it does not identify which component accounts for the difference. Within-class differences can also remain substantial, so class membership should not be treated as a precise individual prediction of clearance. These limitations are reasons to interpret class effects cautiously, not reasons to assume that a fitted association is necessarily invalid.

A common mistake is to code A, B, and C as 1, 2, and 3, fit one linear coefficient, and then describe the result as if the model had estimated separate class effects. It has not: the single coefficient imposes the same multiplicative change from A to B as from B to C. The correction is to state the coding and its constraint explicitly, and to use class indicators when separate contrasts are needed and supported by the data.

The encoding also does not remove the need for sound clinical and data checks. Misclassified components, inconsistent score timing, or poorly documented handling of missing components can lead to a covariate that does not mean the same thing across participants. Do not silently assign missing component values or infer a class from incomplete data without a prespecified, justified rule. A more detailed analysis may consider the components themselves, but that choice brings additional modeling demands and is not equivalent to a class effect.