Confounding by Disease Severity in Exposure-Response

Why Disease Severity Can Confound Exposure–Response

An observed exposure–response relationship may partly reflect which patients achieve each exposure level, rather than the effect of exposure itself. Disease severity is a common reason: it can affect exposure through clearance or clinical dose changes, while also predicting efficacy or safety outcomes. The resulting association can be exaggerated, attenuated, or even reversed.

The key question is not simply whether severity is associated with exposure and outcome. It is whether severity is a pre-exposure common cause for the exposure contrast and outcome being studied. If it is, comparing patients at different exposures without appropriately accounting for severity can mix an exposure contrast with a difference in disease prognosis.

Several clinical pathways can create this structure. More severe disease may change organ function and drug clearance. Clinicians may also increase or reduce doses in response to severity, perceived vulnerability, or tolerability. Those mechanisms can push exposure in different directions: lower clearance can raise exposure, while dose reduction can lower it. The direction of confounding therefore cannot be inferred from the label “severe”; it depends on the actual pathways and patient data.

Severity can also predict outcomes directly. For example, patients with more advanced disease may have a lower probability of clinical response, or a higher underlying risk of an adverse event, even at the same exposure. Thus, a severity imbalance across exposure levels can create an exposure–outcome association even when the within-severity association is weak or absent.

Define the Contrast and Establish Temporal Order

Before adjustment, specify what exposure contrast is being interpreted and when severity was assessed. For a baseline severity measure, the relevant sequence is that severity is measured before the exposure period used to define the contrast, and the outcome is assessed afterward. The earlier material on causal assumptions in individual-level exposure–response provides the broader framework: an adjusted association has a causal interpretation only under appropriate assumptions, not merely because a covariate appears in a model.

A useful causal diagram has arrows from severity to exposure and from severity to outcome, as well as a possible arrow from exposure to outcome. In words, severity is a common cause of achieved exposure and outcome. The diagram is a way to state the assumed causal structure; it does not prove that the structure is true. Clinical knowledge and the timing and quality of the data must support it.

The adjustment set should include severity as measured before the exposure contrast, with enough detail to capture clinically important differences. A coarse severity category can leave residual confounding if patients within a category differ substantially in prognosis or clearance. Conversely, adjusting for a variable measured after exposure can be inappropriate if exposure has already affected that variable. Such a variable may be a mediator, or its adjustment may introduce bias through selection. This tutorial concerns severity that precedes the exposure contrast; histories in which severity and exposure evolve over time require additional methods.

Stratification and Standardization

A direct approach is to compare exposure groups separately within severity strata. The within-stratum comparison avoids mixing patients in different measured severity categories. To summarize those comparisons for a target population, standardize the stratum-specific outcomes to a common severity distribution.

The target weights might represent the severity distribution in the enrolled population or another clinically relevant population. Equal weights are sometimes used for a simple illustration, but they do not automatically represent the study population. A causal interpretation additionally requires, among other conditions, that the measured severity captures relevant confounding, that comparable patients at each severity level could occur at both exposure levels, and that the exposure contrast is sufficiently well defined.

Why the Crude Association Can Mislead

The crude risk in an exposure group averages the stratum-specific risks using that group’s own severity distribution. Consequently, two exposure groups can have different crude risks partly because they contain different proportions of patients in each severity stratum.

For two exposure groups, add and subtract \(\sum_s r_{0s}q_{1s}\) to separate the crude difference into a within-stratum outcome component and a severity-composition component:

The first term reflects within-stratum risk differences, averaged using the severity distribution among group 1. The second reflects differences in severity composition, evaluated using group 0’s stratum-specific risks. This identity is descriptive; it does not by itself establish causal effects. It explains why the crude contrast need not agree with a standardized contrast.

Safety Outcomes and the Importance of the Target Population

The same issue applies to safety. If severe disease is associated with greater background risk of an adverse event and also changes achieved exposure, an unadjusted exposure–safety association can partly reflect disease severity. Standardized risks make the severity distribution explicit, rather than allowing each exposure group’s observed composition to determine the comparison.

Assumptions, Diagnostics, and Alternatives

A severity-adjusted contrast is most informative when the following conditions are considered explicitly:

• Correct temporal ordering: severity used as a confounder is measured before the exposure contrast. A later severity measure may be affected by prior exposure.
• Conditional exchangeability: within measured severity levels and any other required pre-exposure covariates, exposure groups do not differ in unmeasured causes of the outcome. This is an assumption, not something proven by a nonsignificant test.
• Positivity: each clinically relevant severity stratum has patients at the exposure levels being compared. If a stratum contains only one exposure group, its missing contrast cannot be recovered from the data without extrapolation.
• Reliable measurement and specification: severity is recorded with sufficient accuracy and represented adequately. Misclassification or overly broad categories can leave residual confounding.
• Consistency and a meaningful contrast: the exposure levels or strategies being compared correspond to sufficiently well-defined versions of exposure for the outcome interpretation.

Inspect the severity distribution across exposure groups before relying on an adjusted result. Then examine stratum-specific exposure–outcome estimates and their sample sizes. Large differences between crude and adjusted results are a reason to investigate composition, model specification, and data quality; they are not, by themselves, proof that the adjusted estimate is correct. Sparse or empty exposure-by-severity cells signal weak support for some comparisons.

Stratification is transparent when there are few, sufficiently populated severity categories. Outcome regression can instead model the outcome conditional on severity and exposure, followed by predictions averaged over a chosen target population. It can use continuous severity measurements, but conclusions depend on an adequate functional form and any needed interaction terms. Weighting approaches can also balance measured severity, but extreme weights often reveal poor overlap and can make estimates unstable. None of these approaches removes confounding by severity that was not measured or measured inadequately.

A common mistake is to adjust automatically for every available severity measure, including one recorded after exposure began. If exposure affects that later measure, conditioning on it can remove part of an exposure effect or create bias. Another mistake is to treat dose as a substitute for severity adjustment. Dose changes can help explain achieved exposure, but they do not guarantee that the differences in underlying severity have been controlled. The covariates and their timing must follow the causal question, not a rule to include every correlated variable.