When a Better Biomarker Does Not Mean a Better Outcome
A treatment can move a biomarker in its favorable direction and still make patients’ clinical outcomes worse. This is the surrogate paradox: an apparent benefit on the proposed surrogate does not correspond to the treatment’s overall effect on the clinical outcome. The key is that a treatment may influence the outcome through more than one pathway. A beneficial pathway through the biomarker can be outweighed by a harmful pathway that bypasses it.
For clarity, let \(A=0\) denote control and \(A=1\) treatment. Let \(M\) be a biomarker coded so that larger values are favorable, and let \(Y\) be a clinical benefit outcome coded so that larger values are also favorable. The paradox occurs when treatment increases \(M\) on average but decreases \(Y\) on average. If the clinical endpoint is instead an adverse-event risk, its favorable direction is downward; signs must be interpreted accordingly.
A favorable association between \(M\) and \(Y\) does not rule out this pattern. Nor does a treatment-related improvement in \(M\) establish that all clinically important treatment effects operate through \(M\). The treatment’s total effect concerns the clinical outcome under treatment versus control; a mediation analysis asks how that effect may be distributed across pathways. Those are different questions.
Pathway Decomposition and Its Assumptions
Use \(Y(a,m)\) for the clinical outcome that would occur if treatment were set to \(a\) and the biomarker to \(m\). A total treatment effect on the additive scale is \(E[Y(1,M(1))-Y(0,M(0))]\). One useful decomposition compares outcomes under treatment while changing the biomarker from the value it would have under control to the value it would have under treatment:
The NIE captures the effect of changing the biomarker distribution from its control-treatment value to its treatment value while holding the outcome treatment setting at \(A=1\). The NDE captures the remaining treatment contrast when the biomarker is set to its control-treatment value. Adding the expressions cancels the two middle terms:
This algebraic identity defines a decomposition on the specified additive scale; it does not by itself establish that either component can be identified from observed data. Identification requires well-defined treatment and biomarker interventions, consistency, no interference between individuals, and positivity for the treatment and mediator values being compared. Random assignment supports identification of the total treatment effect, but does not randomize the biomarker. To identify natural effects from observational mediator data, additional assumptions are generally needed: no unmeasured mediator–outcome confounding after conditioning on appropriate baseline covariates, and no treatment-induced mediator–outcome confounder for the usual natural-effect identification strategy. The required cross-world assumptions concern outcomes under one treatment setting combined with the biomarker value under another.
A particularly important distinction is between a parallel treatment pathway and mediator–outcome confounding. A treatment may cause another variable \(W\) that affects \(Y\) without operating through \(M\); this is a pathway that can offset the benefit through \(M\). Separately, an unmeasured variable \(U\) may affect both \(M\) and \(Y\), making the observed biomarker–outcome relationship confounded. A causal diagram makes these different problems visible:
If \(W\) is itself a treatment-induced cause of both \(M\) and \(Y\), it can also violate the assumptions needed to identify natural effects. Adjusting for it mechanically is not a universal fix: the correct analysis depends on its causal role and the estimand. A diagram is a statement of causal assumptions, not proof that they are true.
Worked Examples
Worked Example: A Harmful Parallel Pathway Outweighs Biomarker Benefit
Suppose a hypothetical randomized study uses a continuous clinical benefit score \(Y\), with higher scores better. Treatment \(A\) increases a favorable biomarker \(M\), but also increases an unmeasured toxicity burden \(W\). Consider this structural model, where \(U_M\) and \(\varepsilon\) have mean zero and are not affected by treatment:
The treatment effect on the mean biomarker is \(E[M\mid A=1]-E[M\mid A=0]=2\) biomarker units. The path through the biomarker contributes \(1.5(2)=3\) clinical benefit-score points. The toxicity pathway contributes \(-4(1)=-4\) points. Therefore the total mean treatment effect is \(3-4=-1\) point.
The same result follows by substituting \(M\) and \(W\) into the outcome equation:
Thus the biomarker improves by 2 units while the clinical benefit score falls by 1 point. This is a surrogate paradox generated by a harmful treatment pathway that does not operate through the biomarker. The numerical decomposition relies on the stated linear model and its additive scale; it should not be treated as an empirical estimate without the study assumptions and data supporting it.
Worked Example: A Favorable Biomarker Response but Higher Adverse-Event Risk
In a second hypothetical randomized trial, let \(M=1\) indicate a favorable biomarker response and let \(Y=1\) indicate a clinical adverse event. Suppose the biomarker response probability is 0.20 under control and 0.80 under treatment. Assume the event risk under a specified treatment and biomarker value follows:
The model gives valid risks for all four combinations: 0.30 for control with no response, 0.10 for control with response, 0.55 for treatment with no response, and 0.35 for treatment with response. At either treatment level, a favorable biomarker response lowers event risk by 0.20, or 20 percentage points. Treatment also adds 0.25, or 25 percentage points, to risk at a fixed biomarker value.
Average over each arm’s biomarker response probability. Under control, the event risk is \(0.20(0.10)+0.80(0.30)=0.26\). Under treatment, it is \(0.80(0.35)+0.20(0.55)=0.39\). The total risk difference is \(0.39-0.26=0.13\): treatment increases adverse-event risk by 13 percentage points, despite increasing the favorable response probability by 60 percentage points.
On this risk-difference scale, the biomarker-mediated contribution is \((0.80-0.20)(-0.20)=-0.12\), or a 12-percentage-point reduction in risk. The parallel treatment contribution is \(+0.25\), or a 25-percentage-point increase. Their sum is \(-0.12+0.25=+0.13\), matching the total risk difference. If each arm had 1,000 participants and these probabilities held exactly, the expected event counts would be 260 under control and 390 under treatment. These are hypothetical expected counts, not observed study results.
Worked Example: An Unmeasured Common Cause Distorts Mediation
A third hypothetical setting illustrates why an observed biomarker–outcome association cannot automatically be interpreted as a mediated effect. Let randomized treatment \(A\) be independent of a mean-zero, unmeasured baseline factor \(U\). Suppose:
where \(\varepsilon\) has mean zero and is independent of \(A\) and \(U\). Under an intervention on treatment that leaves \(U\) unchanged, the mean biomarker contrast is \(1\). Substitution into the outcome equation gives \(Y=-A+7U+\varepsilon\), so the total mean treatment effect is \(-1\) outcome unit. The causal contribution through \(M\), holding the other terms fixed, is \(2(1)=+2\) units; the direct \(A\) term contributes \(-3\) units. Their sum is \(-1\).
But \(U\) causes both \(M\) and \(Y\). Because \(M=A+U\), we have \(U=M-A\), and the outcome equation can also be written \(Y=7M-8A+\varepsilon\). A regression of \(Y\) on \(A\) and \(M\) would therefore assign a coefficient of 7 to \(M\), rather than the structural causal coefficient 2. The discrepancy arises because the regression’s mediator comparison also changes \(U\), which affects the outcome. Randomization protects the treatment comparison, not this mediator comparison. The diagram contains \(U\rightarrow M\) and \(U\rightarrow Y\), so an unmeasured common cause is a warning against reading the adjusted biomarker coefficient as a causal indirect effect.
Diagnostics, Alternatives, and Limitations
A sound analysis begins with the clinical endpoint, not with the biomarker’s apparent success. Estimate or describe the treatment’s total effect on the clinical outcome, with its uncertainty and units, and state the favorable directions of both endpoints. Then draw a causal diagram that includes plausible treatment-induced pathways, common causes of biomarker and outcome, and the timing of each variable. Ask whether a proposed pathway is observed, whether it can be adjusted for without creating another bias, and which assumptions would be needed to estimate its contribution.
- Check the direction and scale. A reduction in an adverse-event risk is favorable, whereas a reduction in a benefit score may be harmful. An additive decomposition on one scale need not carry over unchanged to a ratio scale.
- Look for competing pathways. Toxicity, off-target pharmacology, altered disease processes, or changes in clinical management may affect the outcome without being represented by the proposed biomarker.
- Separate treatment randomization from mediator identification. Random allocation can identify the total treatment effect under the trial’s conditions; it does not eliminate confounding between a post-treatment biomarker and the outcome.
- Check temporal and causal plausibility. The biomarker must be measured in a way that supports its proposed role, and the diagram must not omit credible common causes or treatment-induced variables.
The main alternatives answer different questions. A randomized comparison of clinical outcomes estimates the total clinical treatment effect and remains essential even when a biomarker is promising. A mediation analysis attempts to partition that effect, but depends on stronger assumptions about mediator–outcome relations and treatment pathways. Treating the biomarker as a surrogate endpoint for clinical benefit makes a broader claim: changes in the biomarker should reliably stand in for changes in the clinical outcome in the intended setting. Evidence that the biomarker is prognostic, or that it responds to treatment, is not alone enough to establish that claim.
| Approach | Primary question | Important limitation |
|---|---|---|
| Randomized total-effect analysis | What is the treatment effect on the clinical outcome? | Does not by itself explain which pathways produced the effect. |
| Mediation analysis | How might the treatment effect be divided across biomarker and other pathways? | Requires assumptions beyond treatment randomization, especially about mediator–outcome confounding. |
| Surrogate-endpoint use | Can the biomarker stand in for the clinical outcome when evaluating treatment effects? | A biomarker response or individual-level association alone does not establish reliable substitution. |
These approaches do not replace one another. A mediation analysis can be informative about mechanisms, but its decomposition may be model-dependent or unidentified if important pathways are unmeasured. Conversely, a clear harmful total clinical effect cannot be dismissed because a biomarker improved. When a treatment-induced variable confounds the mediator–outcome relation, standard natural-effect estimates may fail; the estimand and analysis must be reconsidered rather than assuming routine adjustment repairs the problem.
Common Pitfall
Correction: This reasoning confuses a biomarker association with a causal treatment effect. A treatment may have a harmful pathway that bypasses the biomarker, and unmeasured common causes may distort the biomarker–outcome association. Evaluate the randomized total clinical effect separately, draw the plausible causal pathways, and state the assumptions behind any mediation claim.
Check Your Understanding
For each question, first identify the causal contrast or assumption at issue. Solutions follow the questions.
- A treatment raises a favorable biomarker by 1.5 units. The biomarker pathway contributes \(+3\) points to a clinical benefit score, while another treatment pathway contributes \(-5\) points. What is the total effect under an additive decomposition, and is this a surrogate paradox?
- In a randomized trial, why does randomization of treatment not guarantee an unbiased causal estimate of the effect of changing the biomarker on the clinical outcome?
- Draw or describe the arrows for an unmeasured baseline factor that affects both the biomarker and clinical outcome, alongside the pathway from treatment through the biomarker.
- If treatment lowers adverse-event risk by 4 percentage points overall but improves the biomarker, what conclusion can be made about the total clinical effect, and what cannot be concluded from that fact alone?
Solutions. (1) The total is \(+3-5=-2\) benefit-score points. Since the biomarker improves but the clinical benefit score declines, the signs disagree and the pattern is a surrogate paradox. (2) Randomization balances causes of treatment assignment, but the biomarker is post-treatment and may share causes with the outcome; mediator–outcome confounding can remain. (3) The arrows are \(A\rightarrow M\rightarrow Y\), \(U\rightarrow M\), and \(U\rightarrow Y\). The unmeasured \(U\) is a common cause of mediator and outcome. (4) On the stated risk scale, the total clinical effect is favorable: adverse-event risk is 4 percentage points lower under treatment. The biomarker improvement alone does not show that the risk reduction was mediated by the biomarker or establish that the biomarker can stand in for the clinical endpoint in other settings.