Objective First, Method Second: Why the Estimand Definition Comes First in Pharmacometric Covariate Modeling

ABSTRACT

Pharmacometric covariate analyses support both mechanistic understanding and clinical decision‐making, that is, two different objectives which require different analysis targets. Adopting the ICH E9(R1) estimand framework clarifies this distinction, reconciling mechanistic modeling (conditional covariate effects) with regulatory and clinical needs (unconditional covariate effects), clarifying that estimand definition, i.e. the objective, and not the estimator, is the first choice to make in covariate modeling. This structured approach optimizes quantitative evidence for communicating clinical impact and patient care.

1. Background

Covariates in pharmacometric models have two important objectives. First, they support mechanistic understanding by helping to identify underlying physiological drivers. Second, they support clinical decision making, for example, dose selection and drug labeling. In a recent paper, Jonsson et al. [1] highlighted that these objectives necessitate two distinct types of covariate effects: conditional and unconditional.

While conditional and unconditional covariate effects are often thought to be the same, this is not true. The conditional effect, derived from a multivariable model, isolates a covariate's impact while holding others constant. In contrast, the unconditional effect, often obtained from a univariable model, describes the total impact of the covariate irrespective of other covariates [1].

In pharmacometrics, the distinction between conditional and unconditional effects has historically been blurred by a focus on physiological mechanisms and a lack of standardized terminology [2, 3]. As noted by Rogers et al. [3], the lack of distinction between conditional and unconditional (marginal) effects can lead to significant misinterpretations of a covariate's true clinical impact.

Building on the statistical distinction established by Jonsson et al. [1], this paper provides a structured framework for the definition, standardization, and communication of these effects by adopting the ICH E9(R1) estimand guidelines [4].

2. An Illustrative Example

Consider a drug where clearance (CL) is influenced by both weight (WT) and creatinine clearance (CrCL).

$$\mathrm{CL}=\theta {\mathrm{e}}^{{\beta }_1\left(\mathrm{WT}-\overline{\mathrm{WT}}\right)+{\beta }_2\left(\text{CrCl}-\overline{\text{CrCl}}\right)}$$ (1)

In a conditional multivariable view, the estimated effect of WT (${\beta }_1$) represents how CL changes with WT for individuals with the same CrCL. This is important for mechanistic understanding, such as understanding how WT influences the component of CL not explained by renal function. In an unconditional view, the overall association between WT and CL (${\beta }_1^{*}$) is assessed without taking CrCL into account.

$$\mathrm{CL}=\theta {\mathrm{e}}^{{\beta }_1^{*}\left(\mathrm{WT}-\overline{\mathrm{WT}}\right)}$$ (2)

Since WT and CrCL are typically correlated, the unconditional weight effect captures the combined impact of WT and the part of the unaccounted CrCL effect that is associated with WT. This total association is what a clinician would observe and what a drug label is intended to report for a specific weight group [5].

3. Defining Covariate Estimands

An estimand is the target of the analysis, the specific scientific question the analysis aims to answer; the estimator is the mathematical method or model used to reach that target, and the estimate is the numerical result produced by the estimator. An estimate is only meaningful if it matches the estimand, and the estimator should be chosen to match the estimand.

Conditional and unconditional covariate effects can be defined as two distinct estimands in line with the ICH E9(R1) estimand framework (see Supporting Information: Appendix A for formal estimand specifications). The choice depends on whether the objective is mechanistic interpretation or clinical application.

3.1. Mechanistic Interpretation: Conditional Covariate Effects

This estimand targets the isolated impact of a covariate, that is, the sensitivity of a parameter to the covariate, keeping all other covariates fixed. It is the natural choice for establishing or verifying mechanistic hypotheses. The most common estimator for this effect are the coefficients (β) from a multivariable covariate model. Note that the estimates of the β will depend on the correlation between the covariate of interest and the other covariates included in the model (hence conditional).

3.2. Clinical Decision Making: Unconditional Covariate Effects

This estimand targets the total impact of the covariate, that is, the overall impact of the covariate regardless of any other covariates, mimicking the real world setting, where other covariates vary according to their natural correlations. This is the relevant target for clinical guidance and labeling. The most direct estimators for this estimand are coefficients from all simple univariable models (β*) or derived from multivariable Full Random Effects Models (FREM) [6]. The estimates of the β* accounts for any correlations to the other covariates (i.e., unconditional) [1]. An alternative estimator, which requires additional effort, would be simulations from a multivariable model.

4. Methodological Alignment With Analysis Objectives

The two distinct covariate modeling objectives suggest that a rational analytical approach would be to first define the analysis objective (estimand) before the selection of a methodology (estimator). In current practice, however, the methodology is often selected without consideration for the estimand, based on tradition or software defaults, to construct a single model that is used to address several questions. This practice risks a mismatch where a model optimized for one objective, for example, mechanistic parsimony, is inadvertently used to answer a question that requires a different perspective, for example, total clinical impact, without consideration for whether the resulting estimates align with the intended question.

Data‐driven methods, such as stepwise covariate modeling, are optimized for the identification of a parsimonious set of covariates. By evaluating the statistical significance of adding one covariate while accounting for others, these methods implicitly produce multivariable models, that is, estimators for the conditional estimand. This approach is most appropriate for mechanistic interpretation. In contrast, when the objective is inference of total clinical impact, univariable models with the covariate added on all model parameters [7], are more appropriate choices, as they retain the overall association between covariates and parameters. It is worth noting that with the FREM approach it is possible to address both the conditional and unconditional estimands based on a single model estimation [6].

The corollary of the above is that a single data set or analysis may need to support multiple types of models to support multiple scientific questions. In statistical modeling this is sometimes referred to as the “Rashomon effect” and occurs when multiple models describe a dataset with comparable accuracy but offer different interpretations [8]. The “best” model is therefore determined by the intended objective rather than statistical superiority alone. Given their complementary nature, a good practice would be to report both the conditional and unconditional coefficients [1].

5. Regulatory and Clinical Implications

5.1. Aligning Regulatory Expectations and Clinical Evidence

The regulatory lifecycle of a drug involves a change in focus, and therefore, in the estimand.

Initially, during the assessment of clinical documentation, the focus is typically on the evaluation of biological plausibility, identification of independent predictors of variability, and verification of the mechanistic integrity of claims. In other words, the focus is on the conditional estimand.

However, once the assessment phase is complete and the focus moves to communicating implications via the drug label, the perspective aligns with the unconditional view. Drug labeling and clinical guidance are typically built on univariable expectations, such as the exposure in a geriatric population or the expected difference in males compared to females. The unconditional perspective can partly be motivated by the need for straightforward communication that is at little risk of misunderstanding, and partly because the unconditional perspective also matches the logic of randomized clinical trials, which isolate the total effect of an intervention by balancing all other covariates through randomization. Since the regulatory guidelines are open to support sub‐population statements in drug labels by both dedicated trials and model based results [5], an unconditional estimand would provide the observational equivalent of dedicated trials and therefore minimize the risk of the “Table 2 fallacy.” The “Table 2 fallacy” describes the common error of interpreting all coefficients in a multivariable model as total effects, whereas they are actually conditional effects that may not reflect the total clinical impact of interest [9].

5.2. Communication via Forest Plots

Forest plots are one of the standard methods for communicating covariate impacts in regulatory documentation. Although they can visualize both conditional and unconditional covariate effects, they may misrepresent clinical relevance if they present conditional effects that are based on correlated covariates shown individually [1]. For example, if WT and CrCL are correlated, a forest plot showing only the conditional WT effect may lead the viewer to underestimate the total expected impact for a heavy patient, as some of the total WT effect is mediated through CrCL [1]. Also, since forest plots are typically used during the later phases of the regulatory lifecycle, it is often more appropriate for them to visualize unconditional effects.

Regardless of the type of covariate effect that is visualized, the target estimand, conditional or unconditional, should be clearly stated whenever forest plots are presented. This clarity will prevent misinterpretation and help the audience understand whether the results represent an isolated mechanistic signal or the total expected clinical impact.

5.3. Precision Dosing and Individualized Care

The unconditional estimand provides population level labeling information but may not always sufficiently control between patient variability in a clinical setting. This is when Model‐Informed Precision Dosing (MIPD) becomes important. For a priori dosing in MIPD, the conditional multivariable perspective is important to utilize all available individual information. Accounting for the conditional effects of multiple covariates simultaneously, MIPD can provide more accurate dosing recommendations than univariable label recommendations.

6. A Shared Language for Covariate Effects

The nomenclature used to describe covariate effects varies significantly across quantitative fields, often creating semantic barriers. Table 1 provides a cross‐disciplinary mapping to improve fluency.  

TABLE 1.

Comparison of terms for covariate effects.

Term used in this document	Common synonyms (typical context) a	Description
Conditional effect	Partial effect (Statistics) Direct effect (Causal inference) Adjusted effect (Epidemiology) Ceteris paribus (Econometrics)	The isolated impact of a covariate on a parameter, while holding all other covariates constant.
Unconditional effect	Marginal effect (Statistics) Total effect (Causal inference) Crude association (Epidemiology) Reduced‐form (Econometrics)	The total impact of the covariate irrespective of other covariates.

^a The mapping of synonyms to specific fields or contexts is not exhaustive or exclusive, but represents an interpretation of common usage across disciplines.

7. Conclusion

As pharmacometrics integrates into Model‐Informed Drug Development (MIDD) [10], analytical frameworks must adapt to address diverse scientific and clinical objectives. As the discipline becomes more deeply integrated into regulatory and clinical workflows, the analytical frameworks must also adapt to address diverse scientific and clinical objectives.

The adoption of the estimand framework from ICH E9(R1) for covariate effects represents a progression in this context. It provides a structured approach to reconcile a mechanistic analytical tradition with the pragmatic requirements of clinical decision‐making. Implementing greater estimand awareness will facilitate a more effective communication across the drug development lifecycle and ensure that quantitative evidence is optimized to improve patient care.

Funding

The authors have nothing to report.

Conflicts of Interest

The authors declare no conflicts of interest. As the Editor‐in‐Chief of CPT: Pharmacometrics & Systems Pharmacology, France Mentre was not involved in the review or decision process for this paper.

Supporting information

Appendix A.