Why Time Ordering Matters
A biomarker measured after treatment begins is not simply another baseline covariate. Treatment may change the biomarker, while underlying prognosis, early response, or emerging symptoms may also change it. Those same factors can influence the clinical outcome and whether, or when, the biomarker is measured. Comparing outcomes among people with the same observed biomarker—or analyzing only people who survive and attend a measurement visit—can therefore compare groups that were not comparable at randomization.
The key diagnostic question is not just whether a biomarker predicts an outcome. It is what happened before the biomarker was measured, and what determined that it was measured? A biomarker association can reflect a biological pathway, differences in prognosis created by selection, unequal measurement times, or a mixture of these.
Draw the Timeline Before Choosing an Analysis
A useful first step is to put treatment, the biomarker, measurement availability, and outcome in chronological order. The arrows below represent possible causal influence, not a claim that every arrow must be present in every study.
If treatment and prognosis both affect whether a biomarker is observed, \(R\) is a common effect of \(T\) and \(U\). Restricting the analysis to \(R=1\) can associate \(T\) with \(U\), even when treatment was randomized and independent of prognosis at baseline. If \(U\) also predicts \(Y\), the selected-sample treatment groups can differ in outcome risk for reasons other than a treatment effect.
A post-baseline biomarker can have a similar structure: treatment may affect \(B\), while prognosis affects both \(B\) and \(Y\). Conditioning on \(B\) can then associate treatment with prognosis. Separately, if treatment changes \(B\) and \(B\) lies on a treatment-to-outcome pathway, adjusting for it also removes part of the pathway one may want to include when estimating the overall treatment effect. Thus, a treatment coefficient from a model that includes \(B\) does not automatically estimate a direct causal effect.
A Short Justification: How Conditioning Creates an Association
Consider a simple hypothetical setup in which \(T\) and \(U\) are independent at baseline, and a measurement indicator \(R\) is caused by both. Even though \(T\) and \(U\) start independent, the probability of observing the biomarker depends jointly on them. Among observed participants, the distribution of \(U\) within a treatment group is proportional to the baseline distribution of \(U\) multiplied by the chance of observation:
Baseline randomization gives \(P(U\mid T)=P(U)\). But if \(P(R=1\mid T,U)\) varies with \(U\) differently across treatment groups, the expression above can still differ by \(T\). If \(U\) predicts \(Y\), the selected groups can consequently have different outcome risks. This is selection, not evidence that treatment changed baseline prognosis.
The same logic applies when selection is implicit rather than recorded. For example, an analysis of the “biomarker at week 8” among those who reached week 8 with a sample is an analysis conditional on reaching that measurement occasion and having an observed value. The timeline and selection mechanism matter even if the analysis file contains only a biomarker column and no explicit selection variable.
Worked Example: Conditioning on a Post-Baseline Biomarker
Suppose a hypothetical randomized study has four equally frequent baseline combinations of treatment \(T\) and prognosis \(U\): \(T=0\) or \(1\), each with \(U=0\) or \(1\). Let \(Y=U\), so prognosis determines the binary outcome and treatment has no effect on it. A binary post-baseline biomarker is \(B=1\) if either \(T=1\) or \(U=1\); otherwise \(B=0\).
| Treatment \(T\) | Prognosis \(U\) | Biomarker \(B\) | Outcome \(Y\) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 |
Before conditioning, the outcome risk is \(1/2\) in each treatment group: among \(T=0\), one of two participants has \(Y=1\); among \(T=1\), one of two does as well. The treatment risk difference is therefore \(1/2-1/2=0\).
Now restrict to \(B=1\). In the \(T=0\) group, only the \(U=1\) participant remains, so the selected outcome risk is \(1/1=1\). In the \(T=1\) group, both prognosis values remain, so the selected risk is \(1/2\). The selected-sample risk difference is \(1/2-1=-1/2\), despite there being no treatment effect on \(Y\) in the stipulated data-generating setup. Conditioning on \(B\), which is influenced by both \(T\) and \(U\), changed the prognosis mix being compared.
The example is deliberately simple and deterministic; its purpose is to show the mechanism, not to represent a typical biomarker distribution. In real studies, the induced difference may be smaller, but the relevant question remains whether conditioning on the biomarker changed the distribution of causes of the outcome.
Selection Through Survival or Measurement Availability
A biomarker scheduled for a later visit is usually observed only for participants who are alive, still followed, and successfully measured at that time. Those conditions may depend on treatment and prognosis. A biomarker-only analysis can therefore select a post-randomization subset even when the protocol specifies the same nominal visit for everyone.
Worked Example: Outcome Risks Among Those Reaching Measurement
Consider a hypothetical randomized trial with 100 participants in each treatment arm. At baseline, each arm has 50 participants with high prognosis risk and 50 with low prognosis risk. The binary outcome \(Y\) is 1 for high-risk participants and 0 for low-risk participants, irrespective of treatment. Thus, the full randomized groups each have outcome risk \(50/100=0.50\).
Suppose the number of participants who survive to a scheduled biomarker measurement and provide a sample is as follows:
| Arm | High-risk participants measured | Low-risk participants measured | Total measured |
|---|---|---|---|
| Treatment | 45 | 25 | 70 |
| Control | 25 | 45 | 70 |
The outcome risk among the measured treatment participants is \(45/70=0.6429\), and among measured controls it is \(25/70=0.3571\). Using the exact counts, the selected-sample risk difference is
This selected-sample difference does not contradict the zero risk difference in the full randomized groups. The measurement sample contains more high-risk participants in the treatment arm and more low-risk participants in the control arm. Here, survival to measurement and sample availability select different prognosis mixes. If the risks are first rounded to four decimal places, their subtraction gives \(0.6429-0.3571=0.2858\); that small discrepancy is rounding. The exact-count calculation is the appropriate basis for reporting the difference as approximately \(0.2857\).
The example assumes that outcome status is defined for all randomized participants, including those who do not reach the biomarker visit. In a real study, the outcome definition and the timing of events must be made explicit: an event before measurement may itself determine whether a later biomarker can exist. The example diagnoses selection; it does not resolve the distinct estimand and analysis problems that arise when the clinical event prevents biomarker measurement.
Informative Visit Timing Can Distort Biomarker Comparisons
A measurement labeled “the observed biomarker” may represent different points in the biomarker trajectory. Visit time can depend on treatment schedules, symptoms, clinical response, or access to care. When the biomarker changes over time, comparing values measured at different times can confuse a time difference with a treatment difference. If prognosis or symptoms also drive visit timing, the measurement time can additionally select a different mix of participants.
Worked Example: A Visit-Time Difference Masquerading as a Biomarker Effect
Suppose a hypothetical study measures a biomarker at a visit whose timing depends on treatment and a baseline symptom indicator \(U\). Let \(T\) and \(U\) be independent, each with values 0 and 1 equally often. The visit occurs at \(V=2\) days if \(T=1\) or \(U=1\), and at \(V=1\) day otherwise. Every participant has the same biomarker trajectory, \(B(t)=t\) biomarker units. Treatment has no effect on that trajectory.
Among treated participants, \(T=1\) makes every visit occur at day 2, so the mean observed biomarker is \(2\) units. Among controls, half have \(U=0\) and are measured at day 1, while half have \(U=1\) and are measured at day 2. Their mean observed biomarker is \((1+2)/2=1.5\) units. The observed treatment-minus-control difference is \(2-1.5=0.5\) units.
That difference is entirely due to comparing measurements at different times: at any common time \(t\), the biomarker is \(B(t)=t\) in both treatment groups. The example shows why “week 1 value” should mean a measurement taken at a common time window, not merely the value at each participant’s first available visit. If visit timing is symptom-driven, both time alignment and selection by symptoms need consideration.
Practical Diagnostics and Analysis Choices
Before interpreting a model that uses post-baseline biomarker data, examine how the data were generated and who entered the analysis. The following checks do not by themselves remove bias, but they help locate where it may arise.
- Draw a dated timeline. Mark randomization, treatment initiation and changes, biomarker collection, symptoms or clinical events, and outcome assessment. A biomarker measured after an early outcome cannot be treated as its cause.
- Tabulate measurement and visit patterns by randomized arm. Compare the proportions measured and the distributions of actual visit times, not only nominal visit labels.
- Describe measured and unmeasured participants using baseline information. Differences in prognostic factors can reveal selection. Similarity on recorded factors does not establish that unmeasured causes are balanced.
- Separate the primary randomized comparison from a biomarker-conditioned analysis. For an overall treatment effect, the primary comparison generally preserves randomized assignment and does not condition on a post-baseline biomarker.
- Check sensitivity to time alignment and selection assumptions. Compare analyses at clearly defined times or windows where appropriate, and state what assumptions would be needed for any adjustment for measurement availability.
The main alternative approaches answer different questions and rely on different assumptions. A randomized, intention-to-treat comparison targets the overall effect of assignment when outcomes are ascertained for the randomized population; it does not explain how much of an effect operates through the biomarker. A model adjusted for a post-baseline biomarker gives a conditional association, but that coefficient is not automatically a direct effect because of mediation and selection. Analyses restricted to observed biomarker values describe that selected sample unless additional assumptions justify generalizing beyond it. Weighting or modeling measurement processes can sometimes address observed selection, but requires correctly measured predictors of observation, adequate overlap (positivity), and a correctly specified model; it cannot guarantee correction for unmeasured causes.
Limitations of the Diagnostic
A timeline and selection diagram identify plausible routes to bias; they do not prove which route operated or quantify its impact. Recorded visit schedules may not capture unscheduled contacts, and measured baseline prognostic variables may not capture all causes of survival, attendance, biomarker values, or outcome. Further, a common-time comparison may still be selected if some participants cannot survive or remain under observation until that time. The right interpretation therefore depends on the estimand, the outcome definition, and the events that occur before measurement.
These diagnostics are especially important in surrogate evaluation. A biomarker can be strongly associated with outcome among measured participants while the association partly reflects prognosis or selection. Such a relationship alone does not establish that changing the biomarker would change the clinical outcome, or that a treatment effect on the biomarker predicts the treatment effect on the clinical endpoint.
Check Your Understanding
For each question, give a brief answer before reading the solutions.
- In the post-baseline biomarker example, what caused the selected treatment and control groups to differ in outcome risk?
- Why does randomization at baseline not ensure comparable treatment groups among those with \(R=1\)?
- In the survival-to-measurement example, calculate the exact-count selected-sample risk difference and state why it differs from the full-population difference.
- In the visit-time example, what is the treatment-minus-control difference in observed mean biomarker, and why is it not a treatment effect on the common-time trajectory?
- Name two data checks that can help diagnose selection or timing problems, and one limitation of those checks.
Solutions. (1) Conditioning on \(B=1\) changed the prognosis mix: the selected control participant had \(U=1\), while selected treated participants included both \(U=0\) and \(U=1\). Since \(Y=U\), their risks differed without a treatment effect. (2) If treatment and prognosis both affect observation, conditioning on \(R=1\) can make treatment associated with prognosis in the observed sample, even though they were independent at baseline. (3) The difference is \(45/70-25/70=20/70\approx0.2857\). It differs from the full-population difference of zero because the measured treatment and control groups contain different proportions of high-risk participants. (4) The observed difference is \(2-1.5=0.5\) biomarker units. Visits occurred at different times, while both groups shared the same trajectory \(B(t)=t\); at a common time there is no treatment difference. (5) Examples include tabulating measurement rates by arm, inspecting actual visit times, and comparing baseline predictors in measured versus unmeasured participants. These checks can reveal patterns but cannot rule out selection caused by unmeasured variables or establish that a corrective model is valid.