Confounding by Indication in Co-medication Analyses

Why the Reason for Treatment Matters

A concomitant medication may be associated with a PK parameter because it changes drug disposition. But the condition that prompted the medication can also be associated with disposition. For example, a treatment may be prescribed more often to patients with a disease state that changes hepatic blood flow, renal function, inflammation, or protein binding. A difference in clearance between medicated and unmedicated patients can therefore reflect the medication, the condition, or both.

This is confounding by indication: the reason for prescribing a medication is associated with medication exposure and also influences the PK outcome being analyzed. The concern is not resolved by accurately coding medication use. Correct exposure coding is necessary, but it does not by itself separate a medication effect from differences in the patients who receive it.

The interpretation depends on the question. A model can estimate an association between medication status and clearance in the observed data. Calling that association a medication effect is a stronger claim: it requires that indication-related differences and other relevant causes have been adequately handled, in addition to appropriate exposure timing, model specification, and data support. Covariate adjustment can reduce measured confounding, but it cannot guarantee that unmeasured differences have been removed.

A Simple Derivation of Omitted-Indication Bias

Consider a simplified model for log clearance, \(\log(CL)\), with a binary medication indicator \(M\) and a binary indication indicator \(D\), where each equals 1 when present and 0 otherwise:

Here, \(\beta_M\) is the medication-associated contrast conditional on indication, \(\gamma_D\) is the indication-associated contrast conditional on medication, and \(\varepsilon\) contains remaining variation. Suppose the model is correctly specified, the error has mean zero conditional on \(M\) and \(D\), and the indication effect is adequately represented by this binary term. If a regression instead omits \(D\), the coefficient for \(M\) absorbs some of the indication contrast whenever \(M\) and \(D\) are associated.

The omitted-variable relationship can be derived by taking the covariance of both sides of the full model with \(M\). Under the stated zero-conditional-mean assumption, \(\operatorname{Cov}(M,\varepsilon)=0\). Dividing by \(\operatorname{Var}(M)\), the slope from the model omitting \(D\) is:

The second term is the omitted-indication contribution. If the indication is more common among medicated patients, the covariance is positive. If that indication is associated with lower clearance, then \(\gamma_D\) is negative, and the unadjusted medication coefficient is shifted downward. If the indication is associated with higher clearance, the direction can reverse. This derivation is exact for the stated linear model; nonlinear mixed-effects PK models may not have this simple coefficient formula, but the same problem remains: medication groups with different indication profiles can have different PK parameters for reasons other than medication exposure.

Representing the Indication in a PK Analysis

A useful first step is to describe the clinical pathway linking the condition, medication, and PK outcome. The indication can influence prescribing, while the condition or its severity can influence clearance, volume of distribution, absorption, or other PK parameters. Other patient characteristics may also influence prescribing and PK. These relationships make the medication coefficient difficult to interpret if indication-related covariates differ between exposure groups.

A covariate model can represent measured indication-related factors alongside medication exposure. For example, a simplified typical-clearance model might be written:

where \(CL_i\) is the typical clearance for individual \(i\), \(CL_{\mathrm{typ}}\) is the reference clearance, \(M_i\) indicates medication exposure, and \(D_i\) indicates the indication. With this log-linear parameterization, \(\exp(\beta_M)\) is the clearance ratio for medicated versus unmedicated individuals with the same value of \(D_i\), conditional on the rest of the model. The model assumes that the medication and indication effects combine multiplicatively on clearance, that the specified indication measure is adequate for the intended adjustment, and that the observed data can distinguish their contributions. If the medication effect plausibly differs by indication or severity, a single common medication coefficient may not represent the pattern; that possibility should be considered rather than hidden by the main-effects model.

In practice, the relevant indication may be more complex than a yes-or-no diagnosis. Severity, duration, recent exacerbation, or a physiologic consequence of the condition may be more informative. A diagnosis code that is present for nearly everyone in one medication group and nearly no one in the other may also provide little basis for separating the two effects. Covariate patterns and overlap therefore matter alongside the fitted coefficient.

Patterns and Sensitivity Checks

The following checks help determine whether confounding by indication is plausible and whether the available data can support an adjusted comparison:

• Compare indication prevalence and severity. Summarize the indication and relevant severity measures by medication status. Large differences signal that a crude contrast is difficult to interpret as a medication effect.
• Check overlap. Ask whether both medication groups include patients across the observed indication and severity range. If almost all patients with severe disease are treated, the model has little direct information about what their clearance would be without treatment. Adjustment then relies heavily on model form rather than comparison of similar observed patients.
• Fit a clinically justified adjusted model. Include measured indication-related factors that are plausible predictors of the PK parameter and prescribing, with appropriate forms and timing. Compare the medication estimate and its uncertainty with the less-adjusted result. A change is informative about sensitivity to measured covariates, not proof of which estimate is correct.
• Use a restriction or within-indication analysis when feasible. Comparing medication groups among patients with a similar indication can reduce differences in the broad reason for treatment. It may also reduce sample size, worsen precision, or leave severity differences unresolved.
• Vary assumptions about unmeasured severity. Ask how strongly an omitted indication-related factor would need to relate to medication use and clearance to explain the remaining contrast. State the direction and magnitude assumed rather than labeling an estimate simply “robust.”

These checks require care in how exposure and indication are defined. The indication should refer to the condition prompting the medication, not merely a condition recorded at some unrelated time. The medication exposure window should correspond to the concentrations or PK observations being analyzed. For a condition that changes over time, a single baseline label may fail to represent the clinical state relevant to later treatment and PK. This does not mean every analysis must include every possible clinical measure: covariates should be selected and defined using clinical knowledge and the study timeline.

Alternatives, Diagnostics, and Limits

A crude exposure contrast is easy to calculate but leaves all indication-related differences uncontrolled. Covariate adjustment can address measured differences while retaining more observations, but depends on suitable measurements, adequate overlap, and a reasonable model. Restriction or stratification compares a narrower or more homogeneous group, but can discard information and cannot adjust for unmeasured differences within that group. A randomized comparison, when ethically and practically appropriate, can balance indication-related factors in expectation, but observational PK analyses commonly rely on clinical data for which treatment was not randomized.

Warning signs include a large shift between crude and adjusted medication estimates, strong imbalance in indication severity, sparse or absent overlap, unstable estimates when a few patients are removed, and a fitted medication contrast that changes substantially under reasonable alternative indication definitions. These patterns do not prove bias, but they weaken confidence in a simple medication-effect interpretation. Conversely, similar estimates across measured-covariate adjustments do not rule out residual confounding by unrecorded disease severity or other unmeasured factors.

A common mistake is to reason, “The medication coefficient remains after adjustment, so the medication caused the PK difference.” The correction is that the coefficient is conditional on the covariates and assumptions represented in that model. It can still reflect unmeasured or poorly measured indication-related differences, lack of overlap, or model misspecification. Report the estimated contrast with its units and uncertainty, describe the indication adjustment, and distinguish a model-based association from a causal interpretation.