Missing Biomarkers and Truncation by Clinical Events

Why the Reason a Biomarker Is Unavailable Matters

A biomarker measurement can be absent for different reasons. A scheduled blood sample may have been missed, a specimen may have been lost, or a participant may have withdrawn before the visit. In these cases the value may still be conceptually defined at the scheduled time, even though it was not recorded. By contrast, a biomarker value at week 12 may not be defined for a participant who died at week 8. The issue is not merely that the measurement is absent: the clinical event prevents the scheduled measurement from existing as an outcome under the participant’s observed course.

These cases call for different estimands and analyses. Treating every unavailable value as if it were an unrecorded version of the same underlying measurement can silently change the scientific question. The analysis should first state what outcome is being compared, for whom, and how the event is handled. The earlier material on Post-Baseline Biomarkers, Time Ordering, and Selection Bias is relevant because analyses restricted to people with observed post-baseline values can select different kinds of participants in the treatment groups.

An estimand is the precise treatment-effect quantity the study aims to estimate. At minimum, its specification identifies the target population, the treatment conditions being compared, the outcome variable, how relevant events are handled, and the population-level summary. For a biomarker measured at a fixed visit, possible summaries include an arm-specific mean and the difference between those means. If a clinical event can make the biomarker undefined, the event-handling choice is part of the outcome definition, not a technical detail to be decided after seeing the data.

Estimands for Defined but Unobserved Measurements

Suppose the target is the mean week-12 biomarker under each randomized treatment among the original trial population, and the biomarker remains defined for every participant at week 12. Some values are unrecorded, but the outcome still exists conceptually. An analysis may estimate the full-population mean by using observed information, provided its assumptions about the measurement process are credible.

A common assumption is missing at random conditional on recorded information: within treatment arm, the probability that a value is observed may depend on measured history, but not on the unobserved biomarker itself after conditioning on that history. If \(H\) denotes the recorded history used in the analysis, this assumption can be written as \(R(t)\) independent of \(Y(t)\) conditional on \(A\) and \(H\), among participants for whom \(Y(t)\) is defined. It is not established merely because the data set includes many covariates. It requires that the relevant predictors of both measurement and biomarker value are adequately recorded and modeled. Positivity is also needed: each history pattern targeted by the analysis must have a nonzero chance of a recorded measurement.

Under these assumptions, multiple imputation can draw plausible values from a model for the missing biomarker conditional on treatment and recorded history; the treatment contrast is then estimated across completed data sets, with uncertainty reflecting both within- and between-imputation variation. Inverse-probability weighting instead gives more weight to observed participants whose measured histories predict a lower chance of observation. Either approach depends on the model and assumptions. Neither turns an implausible missingness assumption into a fact.

When a Clinical Event Makes the Biomarker Undefined

If death or another event makes the scheduled biomarker undefined, imputing a value as though it were merely unrecorded answers a different and usually incoherent question. For example, a post-death biomarker concentration is not an unknown measurement that could be recovered by asking for a blood sample. A model can generate a number, but that number is an extrapolation to a hypothetical outcome, not a value observed or defined under the participant’s actual clinical course.

Several estimand strategies are possible, each with a different interpretation:

• Composite strategy: define an outcome that includes both the clinical event and the biomarker, such as being alive with a biomarker response at the scheduled visit. This retains everyone in the randomized population, but the result concerns the combined outcome, not the biomarker alone.
• While-alive summary: compare the biomarker distribution among participants alive and eligible for measurement in each arm. This describes each arm’s observed survivors. Because treatment may affect who survives, the groups need not represent the same underlying people, so the contrast is not automatically a causal effect in a common population.
• Principal-stratum estimand: target participants who would be event-free under either treatment. This “always-event-free” group is defined by the pair of potential event outcomes under both treatments. Randomization alone does not reveal each participant’s membership in that group, so estimating its treatment effect requires additional assumptions.
• Hypothetical strategy: ask what the biomarker would have been under a specified hypothetical condition in which the event did not occur. This requires a meaningful hypothetical intervention or scenario and a model for outcomes that are not observed after the event. It must not be described as an estimate of the actual post-event biomarker.

A composite can be useful when the clinical event itself is unfavorable and the combined endpoint matches the decision of interest. Its definition must be prespecified: for instance, “alive and at least a 30% biomarker reduction” makes death a failure, whereas “alive with a measured biomarker” would mix survival and measurement availability. A while-alive comparison can be descriptively useful, but it should report survival and measurement patterns alongside the biomarker summary. A principal-stratum result may have a focused causal interpretation, but the stratum is latent and often not identified without strong assumptions.

Sensitivity Analyses and Diagnostics

For defined but missing values, a primary analysis under missing at random should generally be accompanied by sensitivity analysis for departures from that assumption. A transparent approach is a delta adjustment: imputed missing values are shifted by a specified amount from their missing-at-random predictions. The shift should be expressed in biomarker units and chosen to represent clinically plausible departures, not selected to produce a preferred conclusion.

Diagnostics for ordinary missingness include tabulating observation rates by treatment, visit, and recorded prognostic history; checking whether dropout or missed visits relate to prior biomarker values; and examining overlap in estimated observation probabilities. Very small observation probabilities make weighting unstable and signal that the full-population estimate relies heavily on a few participants. Imputation models should respect the biomarker’s scale and include treatment, relevant baseline and post-baseline history, and predictors of missingness. These checks can reveal model weaknesses, but observed data cannot verify missing-at-random for values that were never observed.

For truncation by a clinical event, report event incidence and timing by treatment, and make clear which estimand is being presented. Do not label an analysis “missing-data imputation” if it assigns biomarker values after death without defining a hypothetical estimand. In a while-alive analysis, differences in survival can change the composition of the groups being compared. In a composite analysis, inspect each component separately as well as the overall result, since a contrast can be driven primarily by event frequency rather than biomarker response.

Choosing an Approach and Avoiding Common Errors

A frequent mistake is to say, “The week-12 value is missing, so we will impute it under missing at random,” without first asking whether the value is defined. The correction is to classify each unavailable measurement by its reason. If the participant was alive and eligible for measurement, a missing-data analysis may be appropriate under explicit assumptions. If death made the value undefined, choose and state an event strategy; do not disguise an unobserved hypothetical value as an ordinary missing observation.

A second mistake is to interpret the mean among observed survivors as the treatment effect on the biomarker for the original randomized population. The correction is to name the survivor-conditioned target and acknowledge that the treatment arms may contain different survivor populations. A third mistake is to treat a composite result as if it were a pure biomarker effect. The correction is to state the composite rule precisely and report its components, so the clinical interpretation follows the quantity actually estimated.