Unobserved Health as a Confounder of Biomarker-Event Associations

Why a Biomarker–Event Association Can Mislead

A repeated biomarker may predict an event because it reflects worsening underlying health, not because changing the biomarker itself would change event risk. If latent disease severity affects both the biomarker trajectory and the event process, it is a common cause of the observed association. The biomarker can be useful for prediction while its association with the event does not identify a causal effect.

This distinction matters in longitudinal studies. Measurements taken repeatedly may track a person’s underlying condition more closely than a single baseline value does. But a more informative measure of severity is still not necessarily a cause of the event. The question is whether the biomarker contributes to event risk beyond the health state it reflects.

A simple data-generating model makes the idea explicit. Suppose \(U_i\) is a person’s underlying disease severity, which is not fully observed. Repeated biomarker values may follow

where \(m(t_{ij})\) describes a common time pattern, \(a\) describes how severity shifts the marker, and \(\epsilon_{ij}\) is measurement or within-person variation. Suppose event risk follows a separate model in which severity affects the event, but the biomarker itself does not:

In this illustration, a higher biomarker may be associated with a higher event rate because both share \(U_i\) as a cause. The model does not say that a biomarker intervention would change the event rate. It describes an association produced by shared latent health.

A Worked Binary Example of Confounding

Consider a hypothetical population followed for one year. Let \(U=1\) denote high latent disease severity and \(U=0\) low severity. Let \(X=1\) indicate an elevated biomarker at the start of follow-up, and let \(Y=1\) indicate an event during the year. Assume that severity causes both biomarker elevation and event risk, while the biomarker has no effect on the event in this example.

The assumptions and probabilities are:

• \(P(U=1)=0.40\).
• \(P(X=1\mid U=1)=0.80\) and \(P(X=1\mid U=0)=0.20\).
• \(P(Y=1\mid U=1,X)=0.30\) and \(P(Y=1\mid U=0,X)=0.05\), for either value of \(X\).
• Conditional on \(U\), the biomarker and event are independent in the data-generating model.

Why Repeated Measurements Can Strengthen the Association

Repeated measurements can provide more information about latent severity. That can make a biomarker history a stronger predictor of the event, even when no biomarker value causes the event. The following calculation uses the same hypothetical probabilities as above. Assume two biomarker readings are conditionally independent given \(U\), with each reading having probability 0.80 of being elevated if \(U=1\), and 0.20 if \(U=0\).

Adjustment: What It Can and Cannot Show

If severity were observed without error in this example, comparing biomarker groups within severity strata would remove the shared-cause association: within \(U=1\), both biomarker groups have risk 0.30; within \(U=0\), both have risk 0.05. Standardizing both biomarker groups to the same severity distribution also gives equal risks. For example, using the population severity proportions, each standardized risk is

This calculation relies on a simplified model with a measured, correctly classified confounder, overlap in biomarker groups at each severity level, and no other source of bias. In practice, disease severity is often only partly recorded. Adjusting for a noisy proxy may leave residual confounding because people with the same recorded proxy value can still differ in their underlying health.

A baseline severity measure may also fail to represent health as it evolves. If a repeated biomarker reflects changes in latent severity over follow-up, adjusting only for baseline information does not necessarily make the evolving biomarker independent of the evolving health state. The relevant question is not simply whether a model includes a baseline covariate, but whether the shared causes of the biomarker history and event process have been adequately represented.

Severity and the Changing Event-Free Risk Set

In time-to-event data, the mixture of latent severity among participants still at risk can change over time. High-severity participants may experience events earlier, leaving a growing proportion of low-severity participants in the event-free risk set. Consequently, a marginal hazard can change over time even when each severity group has a constant hazard. This is one reason that a crude association at one point in follow-up may not summarize the association at another.

Assumptions, Diagnostics, and Alternatives

The examples isolate shared-cause confounding by stipulating that severity causes both the biomarker and event, that the biomarker has no effect on the event, and that no other process changes the stated probabilities or hazards. Those assumptions make the source of the association transparent; they are not facts that can generally be verified from observed data alone. In an applied analysis, a causal interpretation additionally depends on whether relevant confounders have been measured and handled appropriately.

Useful checks include comparing biomarker histories across observed health-severity groups, assessing whether event associations weaken after adjustment for well-measured severity indicators, and checking whether conclusions change under plausible alternative assumptions about unobserved severity. Strong association with multiple measures of health can support the interpretation that the biomarker tracks underlying illness, but it does not prove that all confounding has been removed. A lack of measured imbalance is not proof that latent health is balanced.

The main alternatives answer different questions. A crude time-to-event analysis describes the observed predictive association. Adjustment for measured severity asks whether that association remains conditional on the included variables, subject to model and measurement assumptions. A joint model can represent dependence between a longitudinal process and an event process through shared latent structure. It may therefore be useful when unobserved health plausibly links the two processes, but fitting such a model does not automatically identify a causal biomarker effect: the result depends on the chosen structure and assumptions about the latent effects.

The limitation is fundamental: if severity is unobserved, the data may not distinguish a causal biomarker effect from an association generated by shared latent health without additional information or assumptions. Prediction can remain valuable, but prediction and intervention are different goals. This confounding pathway is also distinct from a biomarker changing in response to impending events; that is a separate explanation for an association.

Common Pitfall

• Wrong reasoning: “The biomarker is repeatedly associated with event risk, so changing the biomarker would change event risk.” Repeated association may simply show that the biomarker tracks a persistent or worsening latent health state.
• Correction: Ask what causes both the biomarker trajectory and the event. If latent severity is a shared cause, the observed association need not be causal. State whether the conclusion is predictive or causal, and identify the assumptions needed for the latter.