From Candidate Biomarker to Surrogate Claim
A randomized trial can show that treatment changes a biomarker and improves a clinical outcome. Those findings matter, but they do not by themselves show that the biomarker can stand in for the clinical outcome. A treatment might affect the biomarker and the outcome through separate pathways, or its effect on the biomarker might fail to predict its clinical benefit in other trials or populations.
A careful evaluation therefore asks distinct questions. Does the biomarker vary with the clinical outcome among individuals? Across randomized trials, do treatment effects on the biomarker predict treatment effects on the outcome? Are these patterns credible in light of measurement, timing, missingness, and possible pathways that bypass the biomarker? The distinction between individual-level and trial-level evidence is central to this evaluation.
The introductory material on individual-level and trial-level surrogacy, potential-outcome estimands for biomarker mediation, the surrogate paradox and unmeasured treatment pathways, meta-analytic validation across randomized trials, and trial-level \(R^2\) and the surrogate threshold effect provides the conceptual groundwork. Here the emphasis is on bringing those considerations together in a worked evaluation.
Set the Evaluation Up Before Fitting Models
Before looking at estimates, specify the clinical endpoint, biomarker, population, treatment contrast, and time points. Define the direction of benefit for each measure so signs are interpretable. In the examples below, positive changes denote improvement for both the biomarker and the clinical outcome. For outcomes where a lower value is better, such as event risk, first express effects in a direction that makes positive values denote benefit.
Randomization supports estimating the effect of assignment to treatment on each endpoint, subject to consistent treatment definitions, no interference between participants, and suitable outcome ascertainment. It does not randomize participants to their observed post-baseline biomarker values. Consequently, an association between biomarker change and clinical outcome change is not, by itself, a causal effect of the biomarker.
For an individual-level analysis, a common starting point for a continuous outcome is a regression of clinical outcome on biomarker, treatment assignment, baseline measures, and any prespecified covariates. The coefficient for the biomarker summarizes an adjusted association under the chosen model. Its interpretation depends on the model form and covariates; a causal mediation interpretation additionally requires strong assumptions about confounding of the biomarker–outcome relationship. Those assumptions are not guaranteed by randomization.
For trial-level analysis, each randomized trial contributes an estimated treatment effect on the biomarker and an estimated treatment effect on the clinical outcome, using consistent definitions and follow-up. A regression across trials evaluates whether the former predicts the latter. Trials, not participants, are the units of this regression. With few trials, estimates of the relationship and its uncertainty can be unstable, and ordinary least squares (OLS) may inadequately account for the sampling uncertainty in each trial's estimated effects.
Worked Example: Separate Treatment Effects From Individual Association
Hypothetical data. In a randomized trial, 800 participants are assigned equally to an active treatment or control. At the specified follow-up, mean biomarker improvement is 4.0 units in the treatment group and 1.0 unit in the control group. Mean clinical improvement is 2.4 points and 1.5 points, respectively. A prespecified regression of clinical improvement on biomarker improvement, treatment assignment, baseline clinical score, and baseline biomarker gives a biomarker coefficient of 0.18 clinical points per biomarker unit, with robust standard error 0.04.
The unadjusted randomized treatment contrasts are:
These estimates show improvement in both outcomes on the defined positive-benefit scales. They are estimates of treatment effects on each endpoint, not a calculation showing that the biomarker explains the clinical benefit.
The adjusted individual-level association is tested using the reported coefficient and standard error:
Under a large-sample normal approximation, a 95% confidence interval is \(0.18\pm1.96(0.04)=[0.1016,0.2584]\) clinical points per biomarker unit. The estimate is compatible with a positive adjusted association in this trial. This does not show that intervening to change the biomarker would change the clinical outcome: the biomarker is post-baseline and may share causes with the outcome, or may be affected by treatment-related processes that also affect the outcome.
A suitable interpretation is therefore limited: the randomized trial supports treatment effects on both measures, and the fitted model finds an adjusted individual-level association. Neither result alone validates the biomarker as a surrogate endpoint.
Trial-Level Evidence and a Worked Regression
Trial-level evidence concerns prediction of treatment effects across trials, not correlation between participants within a trial. Let \(x_j\) be the estimated treatment benefit on the biomarker in trial \(j\), and \(y_j\) the estimated treatment benefit on the clinical outcome. A simple descriptive model is \(y_j=a+bx_j+\epsilon_j\), where \(a\) is the intercept, \(b\) is the trial-level slope, and \(\epsilon_j\) is the residual for trial \(j\). A positive slope means that trials with larger estimated biomarker benefits tended to have larger estimated clinical benefits in the observed set of trials.
The ordinary least-squares slope with an intercept is obtained by choosing both \(a\) and \(b\) to minimize the residual sum of squares. Differentiating with respect to \(a\) gives the first normal equation; substituting its solution into the equation for \(b\) yields the centered-data slope.
Substitute \(a=\bar y-b\bar x\) into the second equation. Since \(\sum_j(x_j-\bar x)=0\), the resulting equation is \(\sum_j(x_j-\bar x)(y_j-\bar y)=b\sum_j(x_j-\bar x)^2\). Thus:
Worked Example: Fit and Interpret a Trial-Level Relationship
Hypothetical trial summaries. Five randomized trials estimate treatment benefits in consistent units. The \(x_j\) values are biomarker benefit in units; the \(y_j\) values are clinical benefit in points.
| Trial | Biomarker benefit, \(x_j\) | Clinical benefit, \(y_j\) |
|---|---|---|
| 1 | 2 | 0.8 |
| 2 | 3 | 1.7 |
| 3 | 4 | 1.8 |
| 4 | 5 | 2.8 |
| 5 | 6 | 2.9 |
The means are \(\bar x=4\) biomarker units and \(\bar y=2.0\) clinical points. The numerator of the slope is \(2.4+0.3+0+0.8+1.8=5.3\); the denominator is \(4+1+0+1+4=10\). Therefore:
The fitted line is \(\widehat y=-0.1200+0.5300x\). The fitted values at \(x=2,3,4,5,6\) are \(0.94,1.47,2.00,2.53,3.06\). Subtracting these from the observed clinical benefits gives residuals \(-0.14,0.23,-0.20,0.27,-0.16\), and the residual sum of squares is \(0.211\). The total sum of squares about \(\bar y=2.0\) is \(3.02\), so:
For a conventional OLS calculation that treats the five trial points as independent observations with constant-variance residuals, \(df=5-2=3\). The residual mean square is \(0.211/3=0.07033\). The slope standard error is \(\sqrt{0.07033/10}=0.08387\), giving \(t=0.5300/0.08387=6.32\). A two-sided \(t\)-test with 3 degrees of freedom gives \(p\approx0.0080\), and the corresponding 95% interval is \(0.5300\pm3.182(0.08387)=[0.263,0.797]\) clinical points per biomarker unit.
The fitted association is strong in these five hypothetical trial summaries. The interval and p-value describe uncertainty under the stated simple regression assumptions; they do not establish that the biomarker captures the treatment effect. Five trials provide little information for checking model assumptions, and these calculations ignore the fact that each trial's treatment-effect estimates have sampling error.
Diagnostics, Bias, and Robustness
A candidate surrogate should be evaluated against potential failure modes, not just the size of a regression coefficient. Inspect the direction and scale of effects, plot trial-level points and fitted residuals, and examine whether one influential trial determines the relationship. Nonlinearity, outliers, widely varying trial precision, or a relationship driven by differences in populations or treatment classes can make a single slope misleading. With few trials, diagnostics have limited power; a clean-looking plot is not proof that assumptions hold.
Measurement error can weaken the observed association between a true biomarker response and the measured biomarker. Different assays, visit schedules, or measurement reliability across trials can also distort comparisons. A small trial-level \(R^2\) may indicate poor prediction, but a high \(R^2\) based on a few noisy or selectively available trials can be overconfident. Where feasible, account for uncertainty in both estimated treatment effects and use sensitivity analyses for measurement error.
Post-baseline measurement creates additional risks. If biomarker values are missing more often for participants with clinical deterioration, complete-case associations may describe a selected subset rather than the randomized population. If a clinical event makes later biomarker measurement undefined, it is not automatically appropriate to impute a hypothetical biomarker value; the estimand and analysis must address that truncation. Timing also matters: a biomarker measured after, or in response to, the clinical event cannot straightforwardly be treated as an earlier predictor.
Unmeasured treatment pathways are a substantive limitation, not merely a statistical nuisance. A drug may improve the clinical endpoint through mechanisms not captured by the biomarker, or may change the biomarker without clinical benefit. Negative controls and sensitivity analyses can probe whether an apparent relationship is plausibly explained by bias, but robustness to selected checks is not proof that all alternative pathways have been excluded.
Worked Example: Quantify the Effect of Missing Biomarker Values
Hypothetical data. In each randomized arm, 100 participants were assigned. Biomarker measurements are available for 80 treatment participants, whose mean improvement is 4.0 units, and 90 control participants, whose mean improvement is 1.0 unit. The other 20 treatment and 10 control participants lack a measurement, with missingness associated with early clinical deterioration.
Among measured participants, the difference in mean biomarker improvement is \(4.0-1.0=3.0\) units. As a simple sensitivity calculation only, suppose the biomarker is conceptually defined for everyone and assign a mean improvement of 0 to each arm's missing participants. The resulting arm means are:
Under that explicit assignment, the between-arm difference is \(3.2-0.9=2.3\) units, rather than 3.0 units among those measured. This does not prove that either calculation is unbiased: the assumed missing values may be wrong, and a measurement undefined after an event cannot be made valid merely by assigning zero. The example shows why the number and reasons for missing measurements, and the estimand they permit, must be part of the surrogate evaluation.
Compare the Evidence and State Its Limits
| Evidence | What it can support | What it cannot establish alone |
|---|---|---|
| Randomized treatment contrasts on biomarker and clinical outcome | Treatment affects each endpoint in the studied trial and population | That the biomarker explains or captures the clinical treatment effect |
| Individual-level biomarker–outcome association | Participants with different biomarker responses also tend to differ in clinical outcome, conditional on the model | That biomarker change causes clinical benefit or predicts benefit across trials |
| Trial-level association across randomized trials | Biomarker treatment effects predict clinical treatment effects in the set of trials studied | Reliable prediction in new settings or absence of treatment pathways outside the biomarker |
A single-trial individual-level analysis is not a substitute for trial-level validation. Conversely, a trial-level relationship can be statistically impressive yet fail to transport to a different population, intervention, or clinical context. Meta-analytic validation and prediction of clinical benefit require relevant trials and careful attention to trial comparability and uncertainty. No universal \(R^2\), slope, or p-value turns a biomarker into a valid surrogate.
A calibrated conclusion names the evidence and its scope. For example: “In these trials, treatment improved both endpoints, and larger estimated biomarker benefits were associated with larger clinical benefits. The limited number of trials, uncertainty in trial estimates, missing measurements, and possible pathways not represented by the biomarker prevent concluding that it can replace the clinical endpoint.” Stronger claims require correspondingly broad, reliable evidence that the relationship predicts clinical treatment effects in the intended use.
Common Mistakes
- Equating treatment effects on both endpoints with surrogacy. Improvement in both measures is necessary evidence to examine, but it does not show that one captures the other.
- Interpreting an individual-level slope causally. Randomization of treatment does not randomize post-baseline biomarker response; confounding and treatment-induced pathways remain possible.
- Using participant counts as the trial-level sample size. A regression of treatment effects across trials has the number of trials as its sample size.
- Treating a high trial-level \(R^2\) as proof. The fit may be unstable with few trials, depend on one trial, or fail to predict in a new setting.
- Dropping participants with missing biomarkers without qualification. If measurement depends on clinical status, complete cases may be selected in a way that biases the association.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A trial shows a positive treatment effect on a biomarker and a positive treatment effect on a clinical endpoint. What does this establish, and what remains unestablished?
- In a regression across six randomized trials, what is the sample size for the trial-level slope analysis? Why is it not the total number of participants?
- A trial-level model has a slope of 0.40 clinical points per biomarker unit, with a 95% interval from 0.10 to 0.70. State an appropriate interpretation and one important limitation.
- Biomarker measurements are disproportionately missing among participants with early deterioration. Why may a complete-case biomarker–outcome association be biased?
- Why does a strong adjusted association between post-baseline biomarker response and clinical outcome not by itself establish a causal effect of changing the biomarker?
Solutions. 1. It establishes estimated treatment effects on both endpoints in that trial, subject to the design and ascertainment assumptions; it does not establish that biomarker change captures the clinical effect or predicts it across trials. 2. The sample size is six trials because each data point is a trial-level treatment-effect pair; participants within a trial do not create additional independent trial-level observations. 3. Under the fitted model and its assumptions, a one-unit larger biomarker treatment benefit is associated with an estimated 0.40-point larger clinical benefit; the interval describes uncertainty in the slope, not proof of surrogacy. A key limitation could be few trials, noisy treatment-effect estimates, or uncertain prediction outside the trials studied. 4. Measured participants may be a selected subset whose clinical status differs from those without measurements, so the observed association need not represent the randomized population. 5. Biomarker response is post-baseline and not randomized; shared causes, treatment-related confounding, and pathways bypassing the biomarker can produce an association without a causal biomarker effect.