Designing Trials For Rare Biomarker Subgroups

Recruitment Is a Pipeline, Not Just a Prevalence

A trial designed around a rare biomarker subgroup can have sound eligibility criteria and a defensible sample-size target yet still fail operationally: too few eligible marker-positive participants may be identified, approached, or enrolled within the recruitment window. The design question is therefore not only “How prevalent is the marker?” but also “How many people will move through each step of this recruitment route?”

Three common routes are broad screening, referral networks, and recruitment from a registry or service that already identifies marker-positive people. Each route has a different starting population and a different conversion process. A useful comparison estimates the number of marker-positive participants who will actually be randomized, not merely the number who test positive or are referred.

For a simple pipeline, let \(N\) be the number of people entering the route, \(p\) the probability that a person is marker-positive, and \(c\) the probability that a marker-positive person is eligible, consents, and is randomized. If these probabilities are stable and participants’ outcomes are independent, the per-person probability of randomized marker-positive enrollment is \(q=pc\). The expected yield is \(Nq\). If the route starts with already identified marker-positive people, \(p\) is effectively one for planning purposes, and \(c\) represents the remaining conversion steps.

These calculations assume the marker is assessed using the qualified process specified for the trial, that the inputs reasonably represent the recruitment population, and that the planned recruitment window and site capacity are feasible. Assay errors and missing biomarker measurements require their own handling; treating every test result as correct or available without checking those conditions can distort the forecast. The earlier material on power under uncertain biomarker prevalence is relevant when prevalence itself is uncertain, but operational yield also depends on the route’s eligibility and enrollment steps.

Modeling Accrual and Its Uncertainty

When \(N\) people independently have the same probability \(q\) of becoming randomized marker-positive participants, the accrual count \(Y\) follows a binomial model, \(Y\sim\operatorname{Binomial}(N,q)\). Its mean is \(Nq\), and its variance is \(Nq(1-q)\). The expected count is not a guarantee: a route with expected yield equal to the target will often finish below it. A binomial model is unsuitable if the opportunities are strongly dependent, the conversion probabilities vary substantially across sites, or capacity limits make the individual outcomes non-independent.

For large \(N\), a normal approximation may be used when both \(Nq\) and \(N(1-q)\) are sufficiently large. For an integer target \(K\), a continuity-corrected approximation to the probability of meeting or exceeding the target is

The correction uses \(K-0.5\) because the discrete event \(Y\ge K\) corresponds approximately to values above the midpoint between \(K-1\) and \(K\). When the expected number or its complement is small, use an exact binomial calculation or a suitable predictive model rather than relying on a poor normal approximation. If the planning inputs were estimated, uncertainty in those inputs should also be considered; the binomial calculation conditional on fixed \(q\) does not include uncertainty about \(q\).

Worked Example: Probability of Meeting a Screening Accrual Target

Compare Routes Using the Whole Conversion Process

A screening route starts with a broad pool and tests people to identify the subgroup. Its strength is that it does not depend on a small set of existing referral sources; its burden is that many people may need screening for each randomized subgroup participant. A referral network can increase the proportion of marker-positive people among those considered, but its performance depends on referral volume, clinical practice, and relationships with referring providers. A registry or service that already identifies marker-positive people can reduce screening burden, but may have limited size, outdated records, or a lower-than-expected rate of current eligibility and consent.

For planning, calculate the full route-specific probability of reaching randomization. Do not compare routes using marker prevalence alone: a high prevalence among referrals does not help if few referrals arrive or most fail eligibility. Conversely, a low-prevalence screening pool can still be viable if it is large and accessible, although the screen-failure burden may be substantial.

Accrual and Randomization Are Separate Sources of Uncertainty

The number of marker-positive participants accrued determines how many people can be randomized; randomization then determines how those participants are distributed between treatment arms. A recruitment strategy does not by itself guarantee equal arm sizes. Under independent 1:1 randomization, if \(m\) marker-positive participants are randomized, the number assigned to one specified arm follows \(\operatorname{Binomial}(m,0.5)\). Its expected value is \(m/2\), with standard deviation \(\sqrt{m(0.5)(0.5)}=\sqrt{m}/2\).

Diagnostics, Comparisons, and Limitations

A recruitment forecast should be checked against observed progress, not treated as a fixed promise. Useful diagnostics include the number entering each pipeline stage by site and time period, the observed marker-positive proportion, the fraction meeting eligibility criteria, the consent rate, and the time between referral and randomization. If the observed counts differ materially from assumptions, update the forecast and investigate the source: a low yield may reflect fewer referrals, lower prevalence, assay availability, eligibility failures, or refusal. Combining all losses into one “conversion rate” can hide which part of the route needs intervention.

Comparisons should use the same time horizon, target definition, and cost accounting. Broad screening may have higher testing costs and more screen failures but greater reach. Referrals may reduce unnecessary testing while relying on external provider behavior. Existing marker-positive records may reduce identification effort but can be small or stale. A hybrid plan may diversify these risks, though its component yields should not simply be added if the routes draw on overlapping people.

The calculations are only as reliable as their assumptions. Site capacity, seasonal variation, competing studies, uneven site performance, dependence among referrals, changing eligibility criteria, and differences between the forecast population and the actual recruitment pool can all undermine a simple binomial model. The estimate \(Nq\) is a mean, not a promised count. A design that can succeed only if recruitment equals its expected value has little operational margin. Re-estimation should respect the trial’s prespecified governance and statistical procedures.

Common Mistake

Wrong reasoning: “The expected yield is 60 and the target is 60, so the plan should enroll 60.” The expected value describes the center of a distribution, not a minimum. Random variation means a substantial chance of falling below the target, as the referral calculation showed.

Correction: Model the probability of meeting the target under plausible inputs, and plan enough recruitment volume to achieve an acceptable probability, allowing for uncertainty in the inputs and operational constraints. Also keep the two events distinct: meeting the accrual target and obtaining a particular arm balance are not the same probability.